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1
Shah, Raj, Rui Chen, Mathias Woydt, Christoph Baumann, Joshua Jurs, and Philip Iaccarino. "High Temperature Tribology under Linear Oscillation Motion." Lubricants 9, no. 1 (December 30, 2020): 5. http://dx.doi.org/10.3390/lubricants9010005.
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High temperature tribology is considered to begin from a minimum temperature of 300–350 °C, where organic base oils and polymers begin to decompose, until a temperature of 1000 °C. In this field of tribology, tests are typically run under dry or solid-state friction, unless a solid lubricant is used, since most lubricants will oxidize or break down when exposed to these extreme temperatures. Therefore, this form of tribotesting is useful to determine the friction, wear, and other tribological characteristics of coatings, ceramics, alloys, cermets, and similar materials. Additionally, high temperature tribology is important to further understand the frictional interactions and adhesive behavior of contacts that operate at these high temperatures. When considering measurements of the tribological parameters in a high temperature application, the standard Schwingung, Reibung, Verschleiž (SRV) (Oscillating, friction, wear, in English) reciprocating, linear-oscillatory tribometer can be modified for testing temperatures of up to 1000 °C by using a high temperature heating block. With this configuration, the instrument can accurately monitor many parameters of the tribosystem, such as coefficient of friction, electrical resistance, zero stroke point, sliding speed, and others. As a result, the SRV instrument is shown to be a powerful tool for high temperature tribotesting. This paper will provide an overview of this high temperature tribology test rig and will discuss its versatility and efficacy, and will show how it can effectively be implemented in both research and practical applications for the development of various coatings and other high temperature tribological contacts.
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Wright, W. G., P. DiZio, and J. R. Lackner. "Vertical linear self-motion perception during visual and inertial motion: More than weighted summation of sensory inputs." Journal of Vestibular Research 15, no. 4 (August 1, 2005): 185–95. http://dx.doi.org/10.3233/ves-2005-15402.
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We evaluated visual and vestibular contributions to vertical self motion perception by exposing subjects to various combinations of 0.2 Hz vertical linear oscillation and visual scene motion. The visual stimuli presented via a head-mounted display consisted of video recordings of the test chamber from the perspective of the subject seated in the oscillator. In the dark, subjects accurately reported the amplitude of vertical linear oscillation with only a slight tendency to underestimate it. In the absence of inertial motion, even low amplitude oscillatory visual motion induced the perception of vertical self-oscillation. When visual and vestibular stimulation were combined, self-motion perception persisted in the presence of large visual-vestibular discordances. A dynamic visual input with magnitude discrepancies tended to dominate the resulting apparent self-motion, but vestibular effects were also evident. With visual and vestibular stimulation either spatially or temporally out-of-phase with one another, the input that dominated depended on their amplitudes. High amplitude visual scene motion was almost completely dominant for the levels tested. These findings are inconsistent with self-motion perception being determined by simple weighted summation of visual and vestibular inputs and constitute evidence against sensory conflict models. They indicate that when the presented visual scene is an accurate representation of the physical test environment, it dominates over vestibular inputs in determining apparent spatial position relative to external space.
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Smirnov, Alexey, and Boris Smolnikov. "COLLINEAR CONTROL OF OSCILLATION MODES OF SPATIAL DOUBLE PENDULUM WITH VARIABLE GAIN." Cybernetics and Physics, Volume 10, 2021, Number 2 (October 1, 2021): 88–96. http://dx.doi.org/10.35470/2226-4116-2021-10-2-88-96.
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This article is devoted to the study of controlled movements of spatial double pendulum with non-parallel cylindrical joints axes. The collinear control is used to swinging of the system by feedback. The most important property of collinear control is the ability of increasing system oscillations only on one oscillation mode. A modification of the collinear control law with variable gain depending on the energy level is investigated. It allows to control the system motions more flexible than in the case of constant gain. As a result, it is possible to observe a smooth transition from a linear oscillation mode to a nonlinear one with a gradual output to a steady oscillation motion with a given energy level. The obtained results are clearly illustrated by graph dependencies that demonstrate the swinging of the system on one oscillation mode from small to finite amplitudes.
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Baranov, A. S. "Non-Linear Oscillations and Beats in the Beta Canis Majoris Stars." International Astronomical Union Colloquium 134 (1993): 73–76. http://dx.doi.org/10.1017/s0252921100013944.
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Notwithstanding a great number of hypotheses, suggested for explaining superpositions of the light- and of the velocity variations of the ß Canis Majoris stars, no one of these does it satisfactorily. Possibly it is due to an inadequate elaboration of the non-linearly oscillation theory. Analysis and critical evaluation of the existing hypotheses are given by Mel’nikov and Popov (1970). Our explanation consists in existence of close frequencies corresponding to various oscillation modes which are non-linearly interacting.Equations of motion of an ideal incompressible fluid under condition of preserving the equilibrium figure symmetry with respect to the equatorial plane (lateral oscillations) have the form (Baranov 1988):
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Olshanskiy, V., and M. Slipchenko. "OSCILLATION OF PULSE-LOADED OSCILLATOR WITH DEGREE POSITIONAL FRICTION." Mechanics And Mathematical Methods 3, no. 1 (June 2021): 37–46. http://dx.doi.org/10.31650/2618-0650-2021-3-1-37-46.
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Nonstationary oscillations of the oscillator with nonlinear positional friction caused by an instantaneous force pulse are described. The power dependence of the positional friction force on the displacement of the system, which generalizes the known models, is accepted. The corresponding dynamics problems were solved precisely by the method of adding and approximated by the method of energy balance. In the study, using periodic Ateb-functions, an exact analytical solution of the nonlinear differential equation of motion was constructed. Compact formulas for calculating oscillation ranges and half-cycle durations are derived. It is shown that the decrease in the amplitude of oscillations, as well as under the action of the force of linear viscous resistance, follows the law of geometric progression. The denominator of the progression is less than one and depends on the positional friction constants, in particular on the nonlinearity index. Thus, we have not only a decrease in the amplitude of oscillations, but also an increase in the durations of half-cycles, which is characteristic of nonlinear systems with a rigid force characteristic. Approximate displacement calculations use Pade-type approximations for periodic Ateb-functions. The error of these approximations is less than one percent. From the obtained analytical relations, as separate cases, the known dependences covered in the theory of oscillations for linear positional friction follow. It is shown that even in the case of nonlinear positional friction the process of oscillations caused by an instantaneous momentum has many oscillations and is not limited in time. In the case of power positional friction, the oscillation ranges of the pulse-loaded oscillator can be calculated by elementary formulas. The calculation of displacements in time is associated with the use of periodic Ateb-functions, the values of which are not difficult to determine by known asymptotic formulas. Calculations confirm that the obtained approximate formula does not give large errors. In order to verify the adequacy of the obtained analytical solutions, numerical computer integration of the original nonlinear differential equation of motion was performed. The results of the calculation, which lead to analytical and numerical solutions of the Cauchy problem, are well matched.
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Olshanskiy, V., and M. Slipchenko. "OSCILLATION OF PULSE-LOADED OSCILLATOR WITH DEGREE POSITIONAL FRICTION." Mechanics And Mathematical Methods 3, no. 1 (June 2021): 37–46. http://dx.doi.org/10.31650/2618-0650-2021-3-1-37-46.
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Nonstationary oscillations of the oscillator with nonlinear positional friction caused by an instantaneous force pulse are described. The power dependence of the positional friction force on the displacement of the system, which generalizes the known models, is accepted. The corresponding dynamics problems were solved precisely by the method of adding and approximated by the method of energy balance. In the study, using periodic Ateb-functions, an exact analytical solution of the nonlinear differential equation of motion was constructed. Compact formulas for calculating oscillation ranges and half-cycle durations are derived. It is shown that the decrease in the amplitude of oscillations, as well as under the action of the force of linear viscous resistance, follows the law of geometric progression. The denominator of the progression is less than one and depends on the positional friction constants, in particular on the nonlinearity index. Thus, we have not only a decrease in the amplitude of oscillations, but also an increase in the durations of half-cycles, which is characteristic of nonlinear systems with a rigid force characteristic. Approximate displacement calculations use Pade-type approximations for periodic Ateb-functions. The error of these approximations is less than one percent. From the obtained analytical relations, as separate cases, the known dependences covered in the theory of oscillations for linear positional friction follow. It is shown that even in the case of nonlinear positional friction the process of oscillations caused by an instantaneous momentum has many oscillations and is not limited in time. In the case of power positional friction, the oscillation ranges of the pulse-loaded oscillator can be calculated by elementary formulas. The calculation of displacements in time is associated with the use of periodic Ateb-functions, the values of which are not difficult to determine by known asymptotic formulas. Calculations confirm that the obtained approximate formula does not give large errors. In order to verify the adequacy of the obtained analytical solutions, numerical computer integration of the original nonlinear differential equation of motion was performed. The results of the calculation, which lead to analytical and numerical solutions of the Cauchy problem, are well matched.
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Scannell, Brian D., Yueng-Djern Lenn, and Tom P. Rippeth. "Impact of acoustic Doppler current profiler (ADCP) motion on structure function estimates of turbulent kinetic energy dissipation rate." Ocean Science 18, no. 1 (February 3, 2022): 169–92. http://dx.doi.org/10.5194/os-18-169-2022.
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Abstract. Turbulent mixing is a key process in the transport of heat, salt, and nutrients in the marine environment, with fluxes commonly derived directly from estimates of the turbulent kinetic energy dissipation rate, ε. Time series of ε estimates are therefore useful in helping to identify and quantify key biogeochemical processes. The velocity structure function method can be used to determine time series of ε estimates using along-beam velocity measurements from suitably configured acoustic Doppler current profilers (ADCPs). Shear in the background current can bias such estimates; therefore, standard practice is to deduct the mean or linear trend from the along-beam velocity over the period of an observation burst. This procedure is effective if the orientation of the ADCP to the current remains constant over the burst period. However, if the orientation of the ADCP varies, a proportion of the velocity difference between bins is retained in the structure function and the resulting ε estimates will be biased. Long-term observations from a mooring with three inline ADCPs show the heading oscillating with an angular range that depends on the flow speed: from large, slow oscillations at low flow speeds to smaller, higher-frequency oscillations at higher flow speeds. The mean tilt was also determined by the flow speed, whilst the tilt oscillation range was primarily determined by surface wave height. Synthesised along-beam velocity data for an ADCP subject to sinusoidal oscillation in a sheared flow indicate that the retained proportion of the potential bias is primarily determined by the angular range of the oscillation, with the impact varying between beams depending on the mean heading relative to the flow. Since the heading is typically unconstrained in a tethered mooring, heading oscillation is likely to be the most significant influence on the retained bias for a given level of shear. Use of an instrument housing designed to reduce oscillation would mitigate the impact, whilst if the shear is linear over the observation depth range, the bias can be corrected using a modified structure function method designed to correct for bias due to surface waves.
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ERMANYUK, EUGENY V., and NIKOLAI V. GAVRILOV. "On internal waves generated by large-amplitude circular and rectilinear oscillations of a circular cylinder in a uniformly stratified fluid." Journal of Fluid Mechanics 613 (October 1, 2008): 329–56. http://dx.doi.org/10.1017/s0022112008003261.
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This paper presents an experimental study of internal waves generated by circular and rectilinear oscillations of a circular cylinder in a uniformly stratified fluid. The synthetic schlieren technique is used for quantitative analysis of the internal-wave parameters. It is shown that at small oscillation amplitudes, the wave pattern observed for circular oscillations is in good agreement with linear theory: internal waves are radiated in the wave beams passing through the first and third quadrants of a Cartesian coordinate system for the clockwise direction of the cylinder motion, and the intensity of these waves is twice the intensity measured for ‘St Andrew's cross’ waves generated by purely horizontal or vertical oscillations of the same frequency and amplitude. As the amplitude of circular oscillations increases, significant nonlinear effects are observed: (i) a strong density-gradient ‘zero-frequency’ disturbance is generated, and (ii) a region of intense fluid stirring is formed around the cylinder serving as an additional dissipative mechanism that changes the shape of wave envelopes and decreases the intensity of wave motions. In the same range of oscillation amplitudes, the wave generation by rectilinear (horizontal and vertical) oscillations is shown to be by and large a linear process, with moderate manifestations of nonlinearity such as weak ‘zero-frequency’ disturbance and weak variation of the shape of wave envelopes with the oscillation amplitude. Analysis of spatiotemporal images reveals different scenarios of transient effects in the cases of circular and rectilinear oscillations. In general, circular oscillations tend to generate disturbances evolving at longer time scales.
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Feng, J., H. H. Hu, and D. D. Joseph. "Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid Part 1. Sedimentation." Journal of Fluid Mechanics 261 (February 25, 1994): 95–134. http://dx.doi.org/10.1017/s0022112094000285.
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This paper reports the result of direct simulations of fluid–particle motions in two dimensions. We solve the initial value problem for the sedimentation of circular and elliptical particles in a vertical channel. The fluid motion is computed from the Navier–Stokes equations for moderate Reynolds numbers in the hundreds. The particles are moved according to the equations of motion of a rigid body under the action of gravity and hydrodynamic forces arising from the motion of the fluid. The solutions are as exact as our finite-element calculations will allow. As the Reynolds number is increased to 600, a circular particle can be said to experience five different regimes of motion: steady motion with and without overshoot and weak, strong and irregular oscillations. An elliptic particle always turn its long axis perpendicular to the fall, and drifts to the centreline of the channel during sedimentation. Steady drift, damped oscillation and periodic oscillation of the particle are observed for different ranges of the Reynolds number. For two particles which interact while settling, a steady staggered structure, a periodic wake-action regime and an active drafting–kissing–tumbling scenario are realized at increasing Reynolds numbers. The non-linear effects of particle–fluid, particle–wall and interparticle interactions are analysed, and the mechanisms controlling the simulated flows are shown to be lubrication, turning couples on long bodies, steady and unsteady wakes and wake interactions. The results are compared to experimental and theoretical results previously published.
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Kuo, Chih-Yu, and Ann P. Dowling. "Oscillations of a moderately underexpanded choked jet impinging upon a flat plate." Journal of Fluid Mechanics 315 (May 25, 1996): 267–91. http://dx.doi.org/10.1017/s002211209600242x.
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The oscillation of a moderately underexpanded choked jet impinging upon a flat plate is investigated both analytically and numerically. The feedback mechanism between oscillations of the standoff-shock and the plate is clarified. Pressure waves produced by the motion of the shock are reflected by the plate. In addition, oscillations in the shock position lead to downstream entropy fluctuations, which generate pressure waves as they are convected through the stagnation flow near the plate. A linear stability analysis is used to investigate the stability threshold and frequencies of oscillation, as a function of jet pressure ratio and nozzle-to-plate distance. The analytical predictions are compared to results from a numerical simulation and to the experimental data of Powell (1988) and Mørch (1963, 1964).
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Volina, T., S. Pylypaka, and V. Babka. "THE MOTION OF A PARTICLE ON A WAVY SURFACE DURING ITS TRANSLATIONAL CIRCULAR OSCILLATIONS IN HORIZONTAL PLANES." Odes’kyi Politechnichnyi Universytet Pratsi 1, no. 63 (2021): 44–52. http://dx.doi.org/10.15276/opu.1.63.2021.05.
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The rough plane is a universal structural element of many machines and devices for sifting and separation of parts of technological material. The motion of particles on the horizontal plane, which performs oscillating rectilinear or circular motion, is the most studied. A wavy surface with a sinusoidal cross-sectional line as a working surface will significantly change the trajectories of their motion. The mathematical description of such a motion will change accordingly. The sliding of a particle in a plane will be a partial case of sliding on a wavy surface when the amplitude of the sinusoid is equal to zero. When the wavy surface oscillates and all its points describe circles, the motion of the technological material changes significantly. The regularities of the motion of material particles on such a surface during its circular translational oscillations in the horizontal planes are investigated in the article. Differential equations of relative particle displacement are compiled and solved by numerical methods. The trajectories of the particle sliding on the surface and the graphs of its reaction are constructed. A partial case of a surface is a plane, and the sliding trajectory of a particle is a circle. An analytical expression to determine its radius is found. During circular oscillations of a wavy linear surface with a cross section in the form of a sinusoid relative trajectory of a particle after stabilization of the motion can be closed or periodic spatial curves. To avoid the breakaway of the particle from the surface, the oscillation mode should be set, which takes into account the shape of the surface and the kinematic parameters of oscillations. With the diameter of the circle, which is described by all points of the surface during its oscillation, is equal to the period of the sinusoid, the trajectory of the relative motion of the particle can be a periodic curve. In this case, the particle moves in a direction close to the transverse, overcoming depressions and ridges. In other cases, the trajectory is a closed spatial curve, the horizontal projection of which is close to a circle. The found analytical dependencies allow determining the influence of structural and technological parameters of the surface on the trajectory of the particle.
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Kuaykaew, Siranee, Supoj Kerdmee, Paitoon Banyenugam, Piyarut Moonsri, and Artit Hutem. "The Analytical Description of Projectile Motion of Cricket Ball in a Linear Resisting Medium the Storm Force." Applied Mechanics and Materials 855 (October 2016): 188–91. http://dx.doi.org/10.4028/www.scientific.net/amm.855.188.
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A detailed work based on the second-order ordinary differential equation is presented to solve oscillation in the trajectory projectile motion of cricket ball for damped alternating external force ( ) problems. This paper purpose to compute the distance time depends horizontal and the distance time depends vertical. The parabolic path of trajectories for a projectile motion of cricket ball increase oscillation with the value of parameter and is the storm force.
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Allen, Dennis P., and Christopher G. Provatidis. "Inclined Large-angle Pendulum May Produce Endless Linear Motion of a Cart When Friction is Negligible." WSEAS TRANSACTIONS ON APPLIED AND THEORETICAL MECHANICS 17 (December 31, 2022): 184–97. http://dx.doi.org/10.37394/232011.2022.17.23.
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We present the mechanics for the oscillation of an inclined large-angle pendulum-drive attached to a cart which is allowed to perform translation in one direction only. Neglecting the overall friction, the application of Newton’s second law shows that the oscillation of the pendulum is continuously converted into oscillating linear motion thus achieving a travel of infinite length. It is also shown that the frequency depends on the usual data of any pendulum plus the mass of the cart on which it is attached. After the determination of a novel effective pendulum length, a closed-form accurate analytical expression is presented for the amplitude of the pendulum, whereas semi-analytical formulas are provided for the period as well as the time-variation of the large azimuthal-like angle. Moreover, a simple expression was found for the position of the cart in terms of the azimuthal angle of the pendulum and the elapsed time. The extraction of the analytical formulas was facilitated by a computer model programmed in MATLAB®.
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Paige, G. D., and D. L. Tomko. "Eye movement responses to linear head motion in the squirrel monkey. II. Visual-vestibular interactions and kinematic considerations." Journal of Neurophysiology 65, no. 5 (May 1, 1991): 1183–96. http://dx.doi.org/10.1152/jn.1991.65.5.1183.
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1. Horizontal, vertical, and torsional eye movements were recorded (search coil technique) from five squirrel monkeys during horizontal linear oscillations at 0.5, 1.5, and 5.0 Hz, 0.36 g peak acceleration. Monkeys were positioned to produce linear motion in their nasooccipital (NO), interaural (IA), and dorsoventral (DV) axes. Responses of the linear vestibuloocular reflex (LVOR) were recorded in darkness and in the light with the subjects viewing a head-fixed field 22 or 9.2 cm from the eye. The latter condition provided a measure of "visual suppression" of the LVOR (VSLVOR). Responses were also recorded while monkeys viewed earth-fixed targets, which allowed visual enhancement of the LVOR (VLVOR). Vergence angle was recorded in two monkeys to assess directly the point of binocular fixation in space during linear motion. 2. Two LVOR response types, vertical responses during 0.5-Hz NO-axis translation (NO-vertical) and torsional responses at all frequencies during IA-axis oscillation (IA-torsional) could not be compensatory reflexes for head translation because they either move the eye off target (NO-vertical) or tort the eye relative to the visual world (IA-torsional), thereby degrading visual image stability. 3. Other response types are considered compensatory because they help maintain ocular fixation in space during linear head translation. These include horizontal responses to IA-axis motion (IA-horizontal), vertical responses to DV-axis translation (DV-vertical), and both horizontal and vertical responses to NO-axis oscillation (1.5 and 5 Hz). Observations focus on responses to 5-Hz oscillations, in which visual inputs are essentially ineffective in modifying the LVOR. 4. The kinematics of perfect ocular compensation during head translation indicate that the ideal ocular response is governed by the motion of the eye relative to target position. Relevant variables include target distance, which is crucial for all axes of motion, and target eccentricity, which is important only for head motion roughly parallel to the target (NO-axis translation). Findings are compatible with predictions based on ideal kinematics. However, it is the point of binocular fixation in space, not actual target position, that governs LVOR behavior. 5. The IA-horizontal and DV-vertical LVOR is in response to head motion roughly orthogonal to the line of sight. Responses under all stimulus conditions (LVOR, VSLVOR, and VLVOR) behaved similarly at 5 Hz, and were modulated linearly with vergence [in meter angles (MA), the reciprocal of binocular fixation distance].(ABSTRACT TRUNCATED AT 400 WORDS)
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Olshanskiy, Vasyl, Maksym Slipchenko, Oleksandr Spolnik, and Olena Solona. "VIBRATIONS OF AN INSTANTLY LOADED DISSIPATIVE OSCILLATOR." Vibrations in engineering and technology, no. 1(100) (March 23, 2021): 21–31. http://dx.doi.org/10.37128/2306-8744-2021-1-3.
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The work investigates non-stationary oscillations of dissipative oscillators. The joint influence of resistance forces of different nature in the composition of the dissipative force on the oscillations of an elastic linear oscillator caused by its instantaneous loading by a constant external force is investigated. The work was limited to the case of small displacements, when the elastic characteristic of the system can be considered linear. The problem is nonlinear due to the account of the action of the dry friction force, but it allows the construction of exact analytical solutions in elementary functions. In this work, by the method of adding solutions, formulas are derived for calculating the amplitude of oscillations and the duration of half cycles. First, a variant is considered when the resistance force consists of linear viscous and dry friction forces. Then a generalization is made to the case of three resistance forces. The third force is the force of positional friction, which arises in elastic elements such as a leaf spring. It is shown that as a result of the action of the total resistance force, the oscillatory process of a loaded oscillator has a finite number of cycles and is limited in time, which is usually observed in practice. The system dynamic factor is less than two. Examples of calculations that illustrate the possibilities of the stated theory are considered. To check the adequacy of the derived calculation formulas, numerical computer integration of the nonlinear differential equations of the oscillator motion was additionally carried out. The full agreement of the numerical results obtained using various methods is shown. In addition to direct problems of dynamics, the inverse problems of determining the characteristics of the load and resistance from the results of measuring the amplitude of oscillations are also considered. The derived calculation formulas are also suitable for identifying the characteristics of the load and resistance based on the results of experimental measurements of the oscillation ranges. Examples of identifying these characteristics are given. The study showed that the nonlinear problem of motion of an instantly loaded oscillator with the total resistance of several forces of different nature has an analytical solution in elementary functions. The presence of such resistance significantly affects the motion of the oscillator after loading. The constructed analytical solutions give results such as the numerical integration of the original nonlinear differential equation on a computer, which confirms the adequacy of the formulas obtained.
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Zrnić, D., P. Berglez, and G. Brenn. "Weakly nonlinear shape oscillations of a Newtonian drop." Physics of Fluids 34, no. 4 (April 2022): 043103. http://dx.doi.org/10.1063/5.0085070.
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Nonlinear axisymmetric shape oscillations of a Newtonian drop in a vacuum are investigated theoretically, for fundamental interest and for their relevance in transport processes across the drop surface. The weakly nonlinear analysis is carried out for, but not limited to, the modes of initial drop deformation up to m = 4. The drop Ohnesorge number covers the range between 0.01 and 1. The weakly nonlinear approach, which is carried to third order, accounts for the coupling of different oscillation modes. With increasing surface deformation, the oscillations develop an asymmetry of the times during one period the drop spends in different states of deformation, a frequency decrease below the linear value, and quasi-periodicity of the motion. In contrast to the inviscid case [D. Zrnić and G. Brenn, “Weakly nonlinear shape oscillations of inviscid drops,” J. Fluid Mech. 923, A9 (2021)], the present analysis reveals the frequency decrease and the quasi-periodicity already in the second-order approximation. The results are positively validated against relevant literature. The theory quantifies the effects of viscosity, measured by the drop Ohnesorge number, dampening the nonlinear behavior and enhancing the coupling of different oscillation modes [E. Becker et al., “Nonlinear dynamics of viscous droplets,” J. Fluid Mech. 258, 191 (1994)]. The present theory reveals the quasi-periodicity of nonlinear viscous drop shape oscillations at strong deformation. The resultant drop motion, starting from a higher-order mode of initial deformation, for which the drop exhibits aperiodic linear behavior, may turn into damped oscillatory with ongoing time due to the coupling to lower-order modes.
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Oiwa, Takaaki. "Friction control using ultrasonic oscillation for rolling-element linear-motion guide." Review of Scientific Instruments 77, no. 1 (January 2006): 016107. http://dx.doi.org/10.1063/1.2162457.
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Popov, V. S., A. A. Popova, and A. V. Christoforova. "Non-Linear Oscillations of the Channel Wall Filled with a Viscous Liquid Induced by the Vibrating Foundation." Journal of Physics: Conference Series 2182, no. 1 (March 1, 2022): 012058. http://dx.doi.org/10.1088/1742-6596/2182/1/012058.
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Abstract The paper considers the issues of mathematical modelling nonlinear vibrations for the wall of a narrow parallel walled channel filled with a viscous incompressible liquid. The upper channel wall is a rigid rectangular plate supported by nonlinear spring with a cubic restoring force, while the bottom one is a fixed rigid rectangular plate. The case of nonlinear oscillations of the upper channel wall due to channel’s foundation vibration has been investigated in the frame of hydroelasticity problem. The main attention is paid to the consideration of steady-state nonlinear oscillations for the upper channel wall and the creeping motion of the liquid in the channel. The liquid layer reaction acting on the upper channel wall is found and the channel’s wall nonlinear oscillation equation is obtained taking into account the energy dissipation due to the liquid viscosity. It was shown that this equation coincided with the Duffing one. The solution of the nonlinear oscillation equation was carried out by the harmonic balance method. Based on the found solution, the hydroelastic response of the channel wall on a nonlinear elastic suspension to the channel foundation vibration was determined.
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Singh, S. N., and S. Mani. "Control of Oscillating Foil for Propulsion of Biorobotic Autonomous Underwater Vehicle (AUV)." Applied Bionics and Biomechanics 2, no. 2 (2005): 117–23. http://dx.doi.org/10.1155/2005/419135.
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The paper treats the question of control of a laterally and rotationally oscillating hydrofoil for the propulsion of biologically inspired robotic (biorobotic) autonomous underwater vehicles (BAUVs). Sinusoidal oscillations of foils produce maneuvering and propulsive forces. The design is based on the internal model principle. Two springs are used to transmit forces from the actuators to the foil. Oscillating fins produce periodic forces, which can be used for fish-like propulsion and control of autonomous underwater vehicles (AUVs). The equations of motion of the foil include hydrodynamic lift and moment based on linear, unsteady, aerodynamic theory. A control law is derived for the lateral and rotational sinusoidal oscillation of the foil. In the closed-loop system, the lateral displacement and the rotational angle of the foil asymptotically follow sinusoidal trajectories of distinct frequencies and amplitudes independently. Simulation results are presented to show the trajectory tracking performance of the foil for different freestream velocities and sinusoidal command trajectories.
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Zhou, Lin, Wangyang Yu, and Kai Li. "Dynamical Behaviors of a Translating Liquid Crystal Elastomer Fiber in a Linear Temperature Field." Polymers 14, no. 15 (August 4, 2022): 3185. http://dx.doi.org/10.3390/polym14153185.
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Liquid crystal elastomer (LCE) fiber with a fixed end in an inhomogeneous temperature field is capable of self-oscillating because of coupling between heat transfer and deformation, and the dynamics of a translating LCE fiber in an inhomogeneous temperature field are worth investigating to widen its applications. In this paper, we propose a theoretic constitutive model and the asymptotic relationship of a LCE fiber translating in a linear temperature field and investigate the dynamical behaviors of a corresponding fiber-mass system. In the three cases of the frame at rest, uniform, and accelerating translation, the fiber-mass system can still self-oscillate, which is determined by the combination of the heat-transfer characteristic time, the temperature gradient, and the thermal expansion coefficient. The self-oscillation is maintained by the energy input from the ambient linear temperature field to compensate for damping dissipation. Meanwhile, the amplitude and frequency of the self-oscillation are not affected by the translating frame for the three cases. Compared with the cases of the frame at rest, the translating frame can change the equilibrium position of the self-oscillation. The results are expected to provide some useful recommendations for the design and motion control in the fields of micro-robots, energy harvesters, and clinical surgical scenarios.
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Zylev, Vladimir, Alexey Steyn, and Nikita Grigoryev. "NON-CONSERVATIVENESS OF FORMULAS AS AN OBSTACLE TO THE MOTION SIMULATION." International Journal for Computational Civil and Structural Engineering 15, no. 2 (June 24, 2019): 159–64. http://dx.doi.org/10.22337/2587-9618-2019-15-2-159-164.
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The paper considers the specifics of connection setting between deformations and stresses as applied to the problem of large non-linear oscillations, when deformations are considered arbitrarily large. It is noted that the introduction of some arbitrary physical relations in the computational model can lead to the establishment of a nonconservative system. It is shown, for example, that distribution of the ordinary Hooke’s law formulas to the area of large deformations leads to the establishment of material with the non-conservative properties. The examples are given for the numerical solution of problems with the nonlinear oscillations, where an increase in the oscillation amplitudes or occurrence of unauthorized internal friction is shown. The simplest version of the material properties free from the indicated deficiencies is given. One of the paper conclusions is that when specifying the elastic properties of the material, it is necessary to ensure that the resulting system is conservative.
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Fu, Hailing, Stephanos Theodossiades, Ben Gunn, Imad Abdallah, and Eleni Chatzi. "Ultra-low frequency energy harvesting using bi-stability and rotary-translational motion in a magnet-tethered oscillator." Nonlinear Dynamics 101, no. 4 (September 2020): 2131–43. http://dx.doi.org/10.1007/s11071-020-05889-9.
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Abstract Harvesting ultra-low frequency random vibration, such as human motion or turbine tower oscillations, has always been a challenge, but could enable many potential self-powered sensing applications. In this paper, a methodology to effectively harness this type of energy is proposed using rotary-translational motion and bi-stability. A sphere rolling magnet is designed to oscillate in a tube with two tethering magnets underneath the rolling path, providing two stable positions for the oscillating magnet. The generated magnetic restoring forces are of periodic form with regard to the sphere magnet location, providing unique nonlinear dynamics and allowing the harvester to operate effectively at ultra-low frequencies (< 1 Hz). Two sets of coils are mounted above the rolling path, and the change of magnetic flux within the coils accomplishes the energy conversion. A theoretical model, including the magnetic forces, the electromagnetic conversion and the occurring bi-stability, is established to understand the electromechanical dynamics and guide the harvester design. End linear springs are designed to maintain the periodic double-well oscillation when the excitation magnitude is high. Parametric studies considering different design factors and operation conditions are conducted to analyze the nonlinear electromechanical dynamics. The harvester illustrates its capabilities in effectively harnessing ultra-low frequency motions over a wide range of low excitation magnitudes.
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Kondratyeva, Lidiya Nikitovna, Yuri Lazarevich Routman, Alexander Matveyevich Maslennikov, and Oleg Vladimirovich Golykh. "Analytical Method of Determining Folded Depressed Shells’ Free Oscillation Frequency." Advanced Materials Research 1020 (October 2014): 291–96. http://dx.doi.org/10.4028/www.scientific.net/amr.1020.291.
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The paper shows a conclusion and a solution of principal resolving equations of the motion of linear and geometrically non-linear theories of thin depressed shells with median surface breaks. A formula has been obtained for determining the shell’s free bending harmonic oscillation frequency in case of a hinge support on rigid diaphragms. Charts are supplied showing the dependence of free oscillation frequency on the change of different factors. A conclusion has been drawn concerning the analytical method efficiency.
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Carmigniani, Remi A., Michel Benoit, Damien Violeau, and Morteza Gharib. "Resonance wave pumping with surface waves." Journal of Fluid Mechanics 811 (December 6, 2016): 1–36. http://dx.doi.org/10.1017/jfm.2016.720.
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In this paper, we present a novel extension of impedance (Liebau) wave pumping to a free-surface condition where resonance pumping could be used for hydraulic energy harvesting. Similar pumping behaviours are reported. Surface envelopes of the free surface are shown and outline two different dynamics: U-tube oscillator and wave/resonance pumping. The latter is particularly interesting, since, from an oscillatory motion, a unidirectional flow with small to moderate oscillations is generated. A linear theory is developed to evaluate pseudo-analytically the resonance frequencies of the pump using eigenfunction expansions, and a simplified model is proposed to understand the main pumping mechanism in this type of pump. It is found that the Stokes mass transport is driving the pump. The conversion of energy from paddle oscillation to mean flow is evaluated. Efficiency up to 22 % is reported.
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Liu, Zhong, Shan Wen Tan, and G. Brenn. "Numerical Study for Shape Oscillation of Free Viscoelastic Drop Using the Arbitrary Lagrangian-Eulerian Method." Applied Mechanics and Materials 789-790 (September 2015): 316–23. http://dx.doi.org/10.4028/www.scientific.net/amm.789-790.316.
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The free oscillation of liquid droplet is one of the classical questions in science research, liquid drops play important role in a lot of engineering applications. Theory study of droplet oscillation mainly based on the linear method, this method is only adapted to the small-amplitude oscillatory motion of drops. Except the linear method used in this study, numerical method have been successfully applied in simulation of the free oscillation of liquid droplet. In this paper, the finite element method is used to investigate numerically the influence of viscoelasticity on the small-amplitude oscillation of drop of polymer solutions. A spatial discretization is accomplished by the finite element method, the time descretization is carried by the Crank-Nicolson method, and the arbitrary Lagangian-Eulerian (ALE) method is used to track the change of the interface. Numerical results are compared with the ones of linear theory. The behaviors of oscillation are found to depend on the viscosity and the stress relaxation time of viscoelastic fluid, the results of numerical simulation and linear theory are identical.
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Yu, Jin, Haiyin Piao, Yaqing Hou, Li Mo, Xin Yang, and Deyun Zhou. "DOMA: Deep Smooth Trajectory Generation Learning for Real-Time UAV Motion Planning." Proceedings of the International Conference on Automated Planning and Scheduling 32 (June 13, 2022): 662–66. http://dx.doi.org/10.1609/icaps.v32i1.19855.
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In this paper, we present a Deep Reinforcement Learning (DRL) based real-time smooth UAV motion planning method for solving catastrophic flight trajectory oscillation issues. By formalizing the original problem as a linear mixture of dual-objective optimization, a novel Deep smOoth Motion plAnning (DOMA) algorithm is proposed, which adopts an alternative layer-by-layer gradient descending optimization approach with the major gradient and the DOMA gradient applied separately. Afterward, the mix weight coefficient between the two objectives is also optimized adaptively. Experimental result reveals that the proposed DOMA algorithm outperforms baseline DRL-based UAV motion planning algorithms in terms of both learning efficiency and flight motion smoothness. Furthermore, the UAV safety issue induced by trajectory oscillation is also addressed.
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Syamsul, Hashim, Takaaki Oiwa, Toshiharu Tanaka, and Junichi Asama. "Positioning error improvement based on ultrasonic oscillation for a linear motion rolling bearing during sinusoidal motion." Precision Engineering 38, no. 3 (July 2014): 617–27. http://dx.doi.org/10.1016/j.precisioneng.2014.02.012.
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Saeed, Nasser A., Osama M. Omara, M. Sayed, Jan Awrejcewicz, and Mohamed S. Mohamed. "Non-Linear Interactions of Jeffcott-Rotor System Controlled by a Radial PD-Control Algorithm and Eight-Pole Magnetic Bearings Actuator." Applied Sciences 12, no. 13 (July 1, 2022): 6688. http://dx.doi.org/10.3390/app12136688.
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Within this work, the radial Proportional Derivative (PD-) controller along with the eight-poles electro-magnetic actuator are introduced as a novel control strategy to suppress the lateral oscillations of a non-linear Jeffcott-rotor system. The proposed control strategy has been designed such that each pole of the magnetic actuator generates an attractive magnetic force proportional to the radial displacement and radial velocity of the rotating shaft in the direction of that pole. According to the proposed control mechanism, the mathematical model that governs the non-linear interactions between the Jeffcott system and the magnetic actuator has been established. Then, an analytical solution for the obtained non-linear dynamic model has been derived using perturbation analysis. Based on the extracted analytical solution, the motion bifurcation of the Jeffcott system has been investigated before and after control via plotting the different response curves. The obtained results illustrate that the uncontrolled Jeffcott-rotor behaves like a hard-spring duffing oscillator and responds with bi-stable periodic oscillation when the rotor angular speed is higher than the system’s natural frequency. It is alsomfound that the system, before control, can exhibit stable symmetric motion with high vibration amplitudes in both the horizontal and vertical directions, regardless of the eccentricity magnitude. In addition, the acquired results demonstrate that the introduced control technique can eliminate catastrophic bifurcation behaviors and undesired vibration of the system when the control parameters are designed properly. However, it is reported that the improper design of the controller gains may destabilize the Jeffcott system and force it to perform either chaotic or quasi-periodic motions depending on the magnitudes of both the shaft eccentricity and the control parameters. Finally, to validate the accuracy of the obtained results, numerical simulations for all response curves have been introduced which have been in excellent agreement with the analytical investigations.
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Olshanskiy, Vasyl, Maksym Slipchenko, Oleksandr Spolnik, and Oleksіі Tokarchuk. "POST-IMPACT VIBRATIONS OF A SQUARE NONLINEAR DISPATIVE OSCILLATOR." Vibrations in engineering and technology, no. 4(99) (December 18, 2020): 29–39. http://dx.doi.org/10.37128/2306-8744-2020-4-4.
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An oscillator damped by viscous linear resistance, due to the instantaneous increase in its mass after impact, can become a dissipative oscillatory system under the action of dry or positional friction. In the article describes the oscillations of a dissipative oscillator with an asymmetric quadratically nonlinear elastic characteristic and dry Coulomb friction, arising as a result of an inelastic vertical impact of a rigid body on it. In the article, the Cox model is used, which does not take into account local deformations of solid bodies subjected to impact. The paper establishes the dependences on the impact velocity and the values of other parameters at which the effect of asymmetry of the elastic characteristic of the system may appear or may not appear. The conditions are derived when the dynamic effect of asymmetry of the power characteristic is manifested in the system. It consists in the fact that the maximum displacement of the oscillator (oscillation range) in the direction of the shock pulse is less than the opposite extreme displacement (range) after the shock oscillations. The existence of such a critical value of the shock impulse is established, the excess of which leads to the loss of motion stability. The second integral of the oscillation equation describes the movement of the oscillator in time, expressed in terms of Jacobi elliptic functions. An approximate formula for their calculation is proposed. Formulas are also derived to determine the time to reach extreme deviations of the system from the equilibrium position. This time is expressed in terms of elliptic integrals of the first kind, which refer to the tabulated functions. Examples of calculations are considered, where, in addition to using the derived formulas, numerical computer integration of the original nonlinear differential equation of motion is carried out. A comparison of the results obtained for the displacement values of a quadratically nonlinear oscillator with dry friction expressed in terms of Jacobi elliptic functions and obtained by numerical integration is carried out. Good consistency of the calculation results in two ways confirmed the adequacy of the obtained analytical solutions of the nonlinear Cauchy problem.
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Freeman, M. P., N. C. Freeman, and C. J. Farrugia. "A linear perturbation analysis of magnetopause motion in the Newton-Busemann limit." Annales Geophysicae 13, no. 9 (September 30, 1995): 907–18. http://dx.doi.org/10.1007/s00585-995-0907-0.
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Abstract. The response of the magnetopause surface to time-varying solar wind dynamic pressure is examined. We argue that to a first approximation the magnetopause surface may be considered as analogous to an elastic membrane. Upon displacement from equilibrium resulting from a change in applied external pressure, it moves to a new equilibrium under the equation of motion of a forced, damped, simple harmonic oscillator. We derive this equation of motion by linearising for small perturbations the momentum equation for flow past a nonrigid ellipsoidal body in the Newton-Busemann limit. Though our approach is only an approximation to the real dynamics of the magnetopause boundary, it serves to demonstrate the importance of inertia in the system response. It allows us to estimate the natural eigenperiod of magnetopause oscillation as typically around 7 min, the precise value depending on solar wind conditions. However, the magnetopause eigenoscillation is furthermore found to be strongly damped, regardless of solar wind conditions. One consequence of these properties is that short-period fluctuations in the solar wind dynamic pressure elicit a suppressed magnetospheric response. We outline other theoretical expectations by which our model may be tested against observation, and discuss the implications of our findings for current interpretations of spacecraft observations made in the dynamic magnetopause environment.
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Farrugia, C. J., V. A. Osherovich, and L. F. Burlaga. "The self-similar, non-linear evolution of rotating magnetic flux ropes." Annales Geophysicae 13, no. 8 (August 31, 1995): 815–27. http://dx.doi.org/10.1007/s00585-995-0815-3.
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Abstract. We study, in the ideal MHD approximation, the non-linear evolution of cylindrical magnetic flux tubes differentially rotating about their symmetry axis. Our force balance consists of inertial terms, which include the centrifugal force, the gradient of the axial magnetic pressure, the magnetic pinch force and the gradient of the gas pressure. We employ the "separable" class of self-similar magnetic fields, defined recently. Taking the gas to be a polytrope, we reduce the problem to a single, ordinary differential equation for the evolution function. In general, two regimes of evolution are possible; expansion and oscillation. We investigate the specific effect rotation has on these two modes of evolution. We focus on critical values of the flux rope parameters and show that rotation can suppress the oscillatory mode. We estimate the critical value of the angular velocity Ωcrit, above which the magnetic flux rope always expands, regardless of the value of the initial energy. Studying small-amplitude oscillations of the rope, we find that torsional oscillations are superimposed on the rotation and that they have a frequency equal to that of the radial oscillations. By setting the axial component of the magnetic field to zero, we study small-amplitude oscillations of a rigidly rotating pinch. We find that the frequency of oscillation ω is inversely proportional to the angular velocity of rotation Ω; the product ωΩbeing proportional to the inverse square of the Alfvén time. The period of large-amplitude oscillations of a rotating flux rope of low beta increases exponentially with the energy of the equivalent 1D oscillator. With respect to large-amplitude oscillations of a non-rotating flux rope, the only change brought about by rotation is to introduce a multiplicative factor greater than unity, which further increases the period. This multiplicative factor depends on the ratio of the azimuthal speed to the Alfvén speed. Finally, considering interplanetary magnetic clouds as cylindrical flux ropes, we inquire whether they rotate. We find that at 1 AU only a minority do. We discuss data on two magnetic clouds where we interpret the presence in each of vortical plasma motion about the symmetry axis as a sign of rotation. Our estimates for the angular velocities suggest that the parameters of the two magnetic clouds are below critical values. The two clouds differ in many respects (such as age, bulk flow speed, size, handedness of the magnetic field, etc.), and we find that their rotational parameters reflect some of these differences, particularly the difference in age. In both clouds, a rough estimate of the radial electric field in the rigidly rotating core, calculated in a non-rotating frame, yields values of the order mV m–1.
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Vasyl, Olshanskiy, and Olshanskiy Stanislav. "ON THE POSSIBILITY OF STAGNATION OF FREE OSCILLATIONS OF A NONLINEARLY ELASTIC OSCILLATOR WITH A LINEAR VISCOUS RESISTANCE." Vibrations in engineering and technology, no. 4(95) (December 20, 2019): 38–46. http://dx.doi.org/10.37128/2306-8744-2019-4-5.
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The free oscillations of an oscillator with a power-nonlinear elasticity characteristic under the action of linear viscous resistance are considered. Using the energy balance method, which is widespread in mechanics, the calculation of the amplitudes of free damped oscillations is reduced to calculating the roots of an algebraic equation, which has an exact analytical solution only with linear elasticity of the oscillator. In the case of an arbitrary positive indicator of nonlinear elasticity, a numerical solution of the equation is required. For this, the Newton's iterative method was used in the work, which has fast convergence of iterations at an arbitrary initial approximation. According to the results of the analysis of the coefficients of the equation established, that in the case of a rigid characteristic of elasticity, when the nonlinearity is greater than unity, the oscillations are reduced to a finite number of decaying ranges, that is, they are limited in time, and in the case of a soft characteristic of elasticity, when the nonlinearity is less than unity, they continue to infinity, as linear dissipative oscillator. The research is given by the method of energy balance and numerical integration of the differential equation of oscillations on a computer. The work of the force of viscous resistance is calculated approximately using periodic Ateb functions that accurately describe free undamped oscillations in the absence of resistance. As a result, approximate iterative dependences are obtained for calculating the amplitudes of the ranges that decay during movement. The numerical results obtained using approximate formulas and numerical computer integration of the nonlinear Cauchy problem are compared. Their satisfactory agreement was noted. A satisfactory agreement was noted between the results for both hard and soft elastic characteristics, which confirmed the adequacy of approximate analytical solutions to the dynamics problem. The main advantage of the described approximate calculation method is that there is no need to build an analytical solution to the nonlinear differential equation of motion of the oscillator, which is a rather complicated mathematical problem. Furthermore, it made it possible to establish conditions under which the oscillator with a viscous and dry friction resistance have similar oscillation properties.
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Smirnov, Alexey S., and Boris A. Smolnikov. "Optimization of oscillation damping modes of spatial double pendulum. I. Formulation of the problem." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 9, no. 2 (2022): 357–65. http://dx.doi.org/10.21638/spbu01.2022.215.
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The paper discusses the issues of optimal damping of oscillations of a spatial double pendulum, whose joint axes are not collinear to each other. As options for damping, both simply passive damping associated with the influence of viscous friction, and combined passive and active damping are considered, and active influences are formed according to the principle of collinear control. The analytical solution of the system motion equations is given for both cases in the framework of the linear model, and it clearly demonstrates the damping of motions on the natural oscillation modes of the original conservative model. The optimization criteria characterizing the efficiency of the damping processes of system movements are considered. It is noted that in order to obtain the most strongly marked damping modes, the degree of stability should be maximized or the integral energy-time indicator should be minimized. In addition, the main advantages and disadvantages of these optimization criteria are discussed. This article is the basis for further research, which will be presented as a separate article “Optimization of oscillation damping modes of spatial double pendulum. II. Solving the problem and analyzing the results”.
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Yoshida, Ryo. "Self-Oscillating Gel as Smart Materials." Advances in Science and Technology 57 (September 2008): 1–4. http://dx.doi.org/10.4028/www.scientific.net/ast.57.1.
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We have developed polymer and gels with an autonomous self-oscillating function by utilizing the Belousov-Zhabotinsky (BZ) reaction. Under the coexistence of the substrates, the polymer undergoes spontaneous cyclic soluble-insoluble changes or swelling-deswelling changes (in the case of gel) without any on-off switching of external stimuli. By using microfabrication technique, ciliary motion actuator or self-walking gel have been demonstrated. Further, in order to realize nano-actuator, the linear polymer chain and the submicrometer-sized gel beads were prepared. By grafting the polymers or arraying the gel beads on the surface of substrates, we have attempted to design self-oscillating surface as nano-conveyer. For application to biomaterials, it is necessary to cause the self-oscillation under biological condition without using non-biorelated BZ substrates. So we attempted to introduce pH-control site and oxidant-supplying site into the polymer. By using the polymer, self-oscillation only in the existence of biorelated organic acid was actually achieved.
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Wang, Z. H., and M. L. Du. "Asymptotical Behavior of the Solution of a SDOF Linear Fractionally Damped Vibration System." Shock and Vibration 18, no. 1-2 (2011): 257–68. http://dx.doi.org/10.1155/2011/253130.
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Fractional-order derivative has been shown an adequate tool to the study of so-called "anomalous" social and physical behaviors, in reflecting their non-local, frequency- and history-dependent properties, and it has been used to model practical systems in engineering successfully, including the famous Bagley-Torvik equation modeling forced motion of a rigid plate immersed in Newtonian fluid. The solutions of the initial value problems of linear fractional differential equations are usually expressed in terms of Mittag-Leffler functions or some other kind of power series. Such forms of solutions are not good for engineers not only in understanding the solutions but also in investigation. This paper proves that for the linear SDOF oscillator with a damping described by fractional-order derivative whose order is between 1 and 2, the solution of its initial value problem free of external excitation consists of two parts, the first one is the 'eigenfunction expansion' that is similar to the case without fractional-order derivative, and the second one is a definite integral that is independent of the eigenvalues (or characteristic roots). The integral disappears in the classical linear oscillator and it can be neglected from the solution when stationary solution is addressed. Moreover, the response of the fractionally damped oscillator under harmonic excitation is calculated in a similar way, and it is found that the fractional damping with order between 1 and 2 can be used to produce oscillation with large amplitude as well as to suppress oscillation, depending on the ratio of the excitation frequency and the natural frequency.
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Markeev, A. P., and T. N. Chekhovskaya. "On Nonlinear Oscillations and Stability of Coupled Pendulums in the Case of a Multiple Resonance." Nelineinaya Dinamika 16, no. 4 (2020): 607–23. http://dx.doi.org/10.20537/nd200406.
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The points of suspension of two identical pendulums moving in a homogeneous gravitational field are located on a horizontal beam performing harmonic oscillations of small amplitude along a fixed horizontal straight line passing through the points of suspension of the pendulums. The pendulums are connected to each other by a spring of low stiffness. It is assumed that the partial frequency of small oscillations of each pendulum is exactly equal to the frequency of horizontal oscillations of the beam. This implies that a multiple resonance occurs in this problem, when the frequency of external periodic action on the system is equal simultaneously to two its frequencies of small (linear) natural oscillations. This paper solves the nonlinear problem of the existence and stability of periodic motions of pendulums with a period equal to the period of oscillations of the beam. The study uses the classical methods due to Lyapunov and Poincaré, KAM (Kolmogorov, Arnold and Moser) theory, and algorithms of computer algebra. The existence and uniqueness of the periodic motion of pendulums are shown, its analytic representation as a series is obtained, and its stability is investigated. For sufficiently small oscillation amplitudes of the beam, depending on the value of the dimensionless parameter which characterizes the stiffness of the spring connecting the pendulums, the found periodic motion is either Lyapunov unstable or stable for most (in the sense of Lebesgue measure) initial conditions or formally stable (stable in an arbitrarily large, but finite, nonlinear approximation).
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Mouro, João, Paolo Paoletti, Michele Basso, and Bruno Tiribilli. "Measuring Viscosity Using the Hysteresis of the Non-Linear Response of a Self-Excited Cantilever." Sensors 21, no. 16 (August 19, 2021): 5592. http://dx.doi.org/10.3390/s21165592.
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A self-oscillating microcantilever in a feedback loop comprised of a gain, a saturator, and an adjustable phase-shifter is used to measure the viscosity of Newtonian fluids. Shifting the signal of the loop with the adjustable phase-shifter causes sudden jumps in the oscillation frequency of the cantilever. The exact position of these jumps depends on whether the shift imposed by the phase-shifter is increasing or decreasing and, therefore, the self-excited cantilever exhibits a hysteretic non-linear response. This response was studied and the system modeled by a delay differential equation of motion where frequency-dependent added mass and damping terms accounted for the density and the viscosity of the medium. Experimental data were obtained for solutions with different concentrations of glycerol in water and used to validate the model. Two distinct sensing modalities were proposed for this system: the sweeping mode, where the width of the observed hysteresis depends on the viscosity of the medium, and the threshold mode, where a sudden jump of the oscillation frequency is triggered by an arbitrarily small change in the viscosity of the medium.
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Al-Hussein, Abdul-Basset A., Fadhil Rahma Tahir, and Karthikeyan Rajagopal. "Chaotic Power System Stabilization Based on Novel Incommensurate Fractional-Order Linear Augmentation Controller." Complexity 2021 (September 29, 2021): 1–13. http://dx.doi.org/10.1155/2021/3334609.
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The nonlinear dynamics of an incommensurate fractional-order single-machine infinite-bus (SMIB) power system benchmark model are explored and studied by means of modern nonlinear analysis theories, such as bifurcation, chaos, power spectral density (PSD), and bicoherence methods. The effect of incommensurate order derivatives on power system dynamics is presented. The study reveals that the power system undergoes interesting dynamics such as periodic motion, chaotic oscillations, and multistability whenever the system parameter values fall into particular ranges. A new fractional-order linear augmentation-based control scheme is applied to damp out the power system’s chaotic oscillation, change the stability of the coexisting states, and drive the system from multistability to monostability. The stability of the proposed control system is derived using Lyapunov theory. Simulation results confirmed the effectiveness and robustness of the proposed control scheme in damping power system oscillations and achieving good overall performance. The results in this paper will give a better understanding of the nonlinear dynamic behaviors of the incommensurate fractional-order SMIB power system.
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Blesbois, Olivier, Sergei I. Chernyshenko, Emile Touber, and Michael A. Leschziner. "Pattern prediction by linear analysis of turbulent flow with drag reduction by wall oscillation." Journal of Fluid Mechanics 724 (May 8, 2013): 607–41. http://dx.doi.org/10.1017/jfm.2013.165.
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AbstractA turbulent flow past a transverse-oscillating wall is considered. The oscillation parameters correspond to the regime where drag reduction is observed. Streak spacing and streak angle obtained from the generalized optimal perturbation approach are compared with results from direct numerical simulations. Other flow features of the generalized optimal perturbation are compared with conditionally-averaged data extracted from numerical simulations. The generalized optimal perturbation at a given instant in time is found to consist of an infinitely long structure at a certain angle to the main flow direction. This angle varies slowly with time for half a period, and then suddenly jumps to a different value, changing both sign and magnitude. The angle variation is shown to be slow, because there is a short time interval in the oscillation period when a small perturbation of a certain angle grows strongly and then remains dominant for almost the entire half-period. The transient growth mechanism of the generalized optimal perturbation is found to be a combination of the Orr mechanism due to the cross-flow shear, acting at the initial stage, followed by the lift-up mechanism of the velocity component directed along the structure by the wall-normal motion also oriented in the same direction.
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Koslucher, Frank, Eric Haaland, Amy Malsch, Jennifer Webeler, and Thomas A. Stoffregen. "Sex Differences in the Incidence of Motion Sickness Induced by Linear Visual Oscillation." Aerospace Medicine and Human Performance 86, no. 9 (September 1, 2015): 787–93. http://dx.doi.org/10.3357/amhp.4243.2015.
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Wall, C., A. Assad, G. Aharon, P. S. Dimitri, and L. R. Harris. "The human oculomotor response to simultaneous visual and physical movements at two different frequencies." Journal of Vestibular Research 11, no. 2 (July 1, 2001): 81–89. http://dx.doi.org/10.3233/ves-2001-11203.
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In order to investigate interactions in the visual and vestibular systems' oculomotor response to linear movement, we developed a two-frequency stimulation technique. Thirteen subjects lay on their backs and were oscillated sinusoidally along their z-axes at between 0.31 and 0.81 Hz. During the oscillation subjects viewed a large, high-contrast, visual pattern oscillating in the same direction as the physical motion but at a different, non-harmonically related frequency. The evoked eye movements were measured by video-oculography and spectrally analysed. We found significant signal level at the sum and difference frequencies as well as at other frequencies not present in either stimulus. The emergence of new frequencies indicates non-linear processing consistent with an agreement-detector system that have previously proposed.
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Haris, Muhammad, Muhammad Shafiq, Adyda Ibrahim, and Masnita Misiran. "Nonlinear feedback controller for the synchronization of (chaotic) systems with known parameters." Journal of Mathematics and Computer Science 23, no. 02 (October 22, 2020): 124–35. http://dx.doi.org/10.22436/jmcs.023.02.05.
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This paper proposes, designs, and analyses a novel nonlinear feedback controller that realizes fast, and oscillation free convergence of the synchronization error to the equilibrium point. Oscillation free convergence lowers the failure chances of a closed-loop system due to the reduced chattering phenomenon in the actuator motion, which is a consequence of low energy sm ooth control signal. The proposed controller has a novel structure. This controller does not cancel nonlinear terms of the plant in the closed-loop; this attribute improves the robustness of the loop. The controller consists of linear and nonlinear parts; each part executes a specific task. The linear term in the controller keeps the closed-loop stable, while the nonlinear part of the controller facilitates the fast convergence of the error signal to the vicinity of the origin. Then the linear controller synthesizes a smooth control signal that moves the error signals to zero without oscillations. The nonlinear term of the controller does not contribute to this synthesis. The collaborative combination of linear and nonlinear controllers that drive the synchronization errors to zero is innovative. The paper establishes proof of global stability and convergence behavior by describing a detailed analysis based on the Lyapunov stability theory. Computer simulation results of two numerical examples verify the performance of the proposed controller approach. The paper also provides a comparative study with state-of-the-art controllers.
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Buffa, Gianluca, Davide Campanella, Antonello D'Annibale, Antoniomaria di Ilio, and Livan Fratini. "Experimental and Numerical Study on Linear Friction Welding of AA2011 Aluminum Alloy." Key Engineering Materials 611-612 (May 2014): 1511–18. http://dx.doi.org/10.4028/www.scientific.net/kem.611-612.1511.
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Linear Friction Welding (LFW) is a solid-state joining process used for non-axisymmetric components. LFW involves joining of materials through the relative motion of two components undergoing an axial force. In the process, the heat source is given by the frictional forces work decaying into heat and determining a local softening of the material and eventually the needed bonding conditions. In the paper, an experimental and numerical campaign is proposed for AA2011 aluminum alloys welding. Different case studies are considered with fixed oscillation frequency and varying pressure at the interface between the specimens. Constant oscillation amplitude and specimens geometry is used. The calculated results permitted to highlight the effects of the process parameters on the material flow determining the soundness of the weld.
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PANDA, J. "Shock oscillation in underexpanded screeching jets." Journal of Fluid Mechanics 363 (May 25, 1998): 173–98. http://dx.doi.org/10.1017/s0022112098008842.
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The periodic oscillation of the shock waves in screeching, underexpanded, supersonic jets, issuing from a choked, axisymmetric, nozzle at fully expanded Mach numbers (Mj) of 1.19 and 1.42, is studied experimentally and analytically. The experimental part uses schlieren photography and a new shock detection technique which depends on a recently observed phenomenon of laser light scattering by shock waves. A narrow laser beam is traversed from point to point in the flow field and the appearance of the scattered light is sensed by a photomultiplier tube (PMT). The time-averaged and phase-averaged statistics of the PMT data provide significant insight into the shock motion. It is found that the shocks move the most in the jet core and the least in the shear layer. This is opposite to the intuitive expectation of a larger-amplitude shock motion in the shear layer where organized vortices interact with the shock. The mode of shock motion is the same as that of the emitted screech tone. The instantaneous profiles of the first four shocks over an oscillation cycle were constructed through a detailed phase averaged measurement. Such data show a splitting of each shock (except for the first one) into two weaker ones through a ‘moving staircase-like’ motion. During a cycle of motion the downstream shock progressively fades away while a new shock appears upstream. Spark schlieren photographs demonstrate that a periodic convection of large organized vortices over the shock train results in the above described behaviour. An analytical formulation is constructed to determine the self-excitation of the jet column by the screech sound. The screech waves, while propagating over the jet column, add a periodic pressure fluctuation to the ambient level, which in turn perturbs the pressure distribution inside the jet. The oscillation amplitude of the first shock predicted from this linear analysis shows reasonable agreement with the measured data. Additional reasons for shock oscillation, such as a periodic perturbation of the shock formation mechanism owing to the passage of the organized structures, are also discussed.
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Hack, M. J. Philipp, and Tamer A. Zaki. "The influence of harmonic wall motion on transitional boundary layers." Journal of Fluid Mechanics 760 (November 3, 2014): 63–94. http://dx.doi.org/10.1017/jfm.2014.591.
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AbstractThe influence of harmonic spanwise wall motion on bypass transition in boundary layers is investigated using direct numerical simulations. It is shown that the appropriate choice of the forcing parameters can achieve a substantial stabilization of the laminar flow regime. However, an increase of the forcing amplitude or period beyond their optimal values diminishes the stabilizing effect, and leads to breakdown upstream of the unforced case. For the optimal wall-oscillation parameters, the reduction in propulsion power substantially outweighs the power requirement of the forcing. The mechanism of transition delay is examined in detail. Analysis of the pre-transitional streaks shows that the wall oscillation substantially reduces their average amplitude, and eliminates the most energetic streaks. As a result, the secondary instabilities that precede breakdown to turbulence are substantially weakened – an effect demonstrated by linear stability analyses of flow fields from direct numerical simulations. The outcome is transition delay owing to a significant reduction in the frequency of occurrence of turbulent spots and a downstream shift in their average inception location. Finally, it is shown that the efficiency of the forcing can be further improved by replacing the sinusoidal time dependence of the wall oscillation with a square wave.
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Darelius, E., I. Fer, T. Rasmussen, C. Guo, and K. M. H. Larsen. "On the modulation of the periodicity of the Faroe Bank Channel overflow instabilities." Ocean Science Discussions 12, no. 3 (May 21, 2015): 823–61. http://dx.doi.org/10.5194/osd-12-823-2015.
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Abstract. The Faroe Bank Channel (FBC) is one of the major pathways where dense, cold water formed in the Nordic Seas flows southward towards the north Atlantic. The plume region downstream of the FBC sill is characterized by high mesoscale variability, quasi-regular oscillations and intense mixing. Here, one year-long time series of velocity and temperature from eight moorings deployed in May 2012 in the plume region is analyzed to describe variability in the strength and period of the oscillations. The eddy kinetic energy (EKE) associated with the oscillations is modulated with a factor of ten during the year and the dominant period of the oscillations changes between three to four and six days, where the shorter period oscillations are more energetic. The dense water is observed on a wider portion of the slope (both deeper and shallower) during periods with energetic, short period oscillations. The observations are complemented by results from a regional, high resolution model that shows a similar variability in EKE and a gradual change in oscillation period between three and four days. The observed variability in oscillation period is directly linked to changes in the volume transport across the sill: the oscillation period decreases with about six days Sv−1 both in the observations and in the model. This is in agreement with results from linear instability analysis which suggests that the period and growth rate decrease for decreased plume thickness. The changes in oscillation period can partly be explained by variability in the upper layer, background flow and advection of the oscillations past the stationary moorings, but the changes in the fraction of the EKE that is derived from the cross isobath motion suggests that the intrinsic period of the instability is modulated. It is further shown that about 50% of the transport variability across the sill is explained by changes in the local barotropic forcing, which is obtained from satellite altimetry.
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Tanaka, Toshiharu, Takaaki Oiwa, and Hashim Syamsul. "Positioning behavior resulting from the application of ultrasonic oscillation to a linear motion ball bearing during step motion." Precision Engineering 51 (January 2018): 362–72. http://dx.doi.org/10.1016/j.precisioneng.2017.09.007.
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Saha, Asit, and Amiya Das. "Dynamical behavior of nonlinear wave solutions of the generalized Newell–Whitehead–Segel equation." International Journal of Modern Physics C 31, no. 04 (February 27, 2020): 2050059. http://dx.doi.org/10.1142/s012918312050059x.
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Dynamical behavior of nonlinear wave solutions of the perturbed and unperturbed generalized Newell–Whitehead–Segel (GNWS) equation is studied via analytical and computational approaches for the first time in the literature. Bifurcation of phase portraits of the unperturbed GNWS equation is dispensed using phase plane analysis through symbolic computation and it shows stable oscillation of the traveling waves. Chaotic behavior of the perturbed GNWS equation is obtained by applying different computational tools, like phase plot, time series plot, Poincare section, bifurcation diagram and Lyapunov exponent. A period-doubling bifurcation behavior to chaotic behavior is shown for the perturbed GNWS equation and again it shows chaotic to periodic motion through inverse period-doubling bifurcation. The perturbed GNWS equation also shows chaotic motion through a sequence of periodic motions (period-1, period-3 and period-5) depending on the variation of the parameter of linear coefficient. Thus, the parameter of linear coefficient plays the role of a controlling parameter in the chaotic dynamics of the perturbed GNWS equation.
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Li, Xinglu, Zongxia Jiao, Yang Li, and Yuan Cao. "Adaptive Repetitive Control of A Linear Oscillating Motor under Periodic Hydraulic Step Load." Sensors 20, no. 4 (February 19, 2020): 1140. http://dx.doi.org/10.3390/s20041140.
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A linear oscillating motor has a direct and efficient linear motion output and is widely used in linear actuation systems. The motor is often applied to compact hybrid electrohydraulic actuators to drive a linear pump. However, the periodic switch of the rectification valve in the pump brings the hydraulic step load to the linear motor, which causes periodic oscillation waveform distortions. The distortion results in the reduction of pumping capacity. The conventional feedback proportional-integral-derivative control is applied to the pump, however, this solution cannot handle the step load as well as resolving nonlinear properties and uncertainties. In this paper, we introduce a nonlinear model to identify periodic hydraulic load. Then, the loads are broken up into a set of simple terms by Fourier series approximation. The uncertain terms and other modeling uncertainties are estimated and compensated by the practical adaptive controller. A robust control term is also developed to handle uncertain nonlinearities. The controller overcame drawbacks of conventional repetitive controllers, such as heavy memory requirements and noise sensitivity. The controller can achieve a prescribed final tracking accuracy under periodic hydraulic load via Lyapunov analysis. Finally, experimental results on the linear oscillating motor-pump are provided for validation of the effectiveness of the scheme.
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Pelekasis, N. A., J. A. Tsamopoulos, and G. D. Manolis. "Nonlinear oscillations of liquid shells in zero gravity." Journal of Fluid Mechanics 230 (September 1991): 541–82. http://dx.doi.org/10.1017/s0022112091000897.
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It has been shown experimentally (Lee et al. 1982) that water drops with injected air bubbles inside them may be forced dynamically to assume the spherosymmetric shape. Linear analysis is unable to predict a centring mechanism, but provides two distinct modes of oscillation. Weakly nonlinear theory (Tsamopoulos & Brown 1987) indicates that centring of the bubble inside the drop occurs when the two interfaces move out of phase. A hybrid boundary element-finite element schemes is used here to study the complete effect of nonlinearity on the dynamics of the motion. The gas inside the liquid shell may be considered either incompressible or compressible by using a polytropic relation. In both cases, the present calculations show that besides the fast oscillation of the shell due to an initial disturbance, a slow oscillatory motion of the centres of the bubble and the drop is induced around the concentric configuration. This occurs in both modes of oscillation and is a direct result of Bernoulli's law. Furthermore, when this slow oscillation is damped by viscous forces, it is anticipated that it will lead to a spherosymmetric shape.