Academic literature on the topic 'Linear motion (oscillation)'
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Journal articles on the topic "Linear motion (oscillation)"
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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).
Dissertations / Theses on the topic "Linear motion (oscillation)"
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Renneflott, Anette Cathrine. "Spatial and Temporal Aspects of the Jitter Aftereffect." Thesis, Griffith University, 2014. http://hdl.handle.net/10072/366835.
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The spatial and temporal parameters determining the duration of the jitter aftereffect (JAE) were examined. Experiment one showed the JAE is a luminance-based effect. Experiment two showed that element sizes 0.084 square (≈7 cpd) and temporal frequencies above 18 Hz were optimal. Experiment three showed that the JAE is dependent on the rate of change during adaptation, not the number of changes. Experiment four compared directional noise: linear, circular, and radial to adirectional dynamic random noise (DRN). Linear noise was better than circular or radial, but random noise was best. Experiment five tested horizontal and vertical oscillation of various peak-to-peak amplitudes, frequencies and velocities. Velocity had a significant effect on JAE duration; amplitude did not. Murakami and Cavanagh’s (1998) proposal that the region of least instantaneous motion becomes the new baseline for perceived zero motion was tested. A motion energy difference between regions is necessary for the JAE. A difference in motion directions between regions at the same energy level is not sufficient. The JAE required one region above 18 Hz, and one below it. Experiment six compared Brownian motion to DRN of identical energy levels. DRN always produced a stronger JAE. Contrast was tested and found to be effective only during adaptation. A dynamic theory where miniature eye movements facilitate relative motion perception was proposed to account for the JAE.Thesis (PhD Doctorate)
Doctor of Philosophy in Clinical Psychology (PhD ClinPsych)
School of Applied Psychology
Griffith Health
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Pancieri, José Guilherme Pelição. "Análise de movimentos periódicos em sistemas bi-linear com folga simétrica." Universidade Federal do Espírito Santo, 2012. http://repositorio.ufes.br/handle/10/6256.
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Previous issue date: 2012-03-27O presente trabalho apresenta a modelagem matemática de um sistema vibracional com excitação harmônica da base. Esse tipo de sistema tem sido estudado por vários pesquisadores que exploraram muitos aspectos da dinâmica global. No entanto, na grande parte dos sistemas estudados, o sistema era modelado para uma característica de vibroimpacto. No sistema aqui estudado, os impactos são substituídos por outro conjunto visco-elástico e os instantes de transição são considerados como condição de periodicidade. As condições de periodicidade são aplicadas sobre o estado nos instantes de transição a fim de obter um mapa da próxima transição baseada no estado da anterior. Este mapa não-linear é aplicado para obter as condições de existência dos movimentos periódicos com padrões específicos. Assim, aplicando as condições de existência, a estabilidade do movimento pode ser realizada por meio da análise dos autovalores do mapa linearizado, tendo em conta estas restrições
This work presents the mathematical modeling of a vibrational system with the harmonically excited base. The system has been investigated by several researchers exploring many aspects of the global dynamics. However, in most of the systems studied, the systems were modeled for a vibro-impact feature. In this system, the impacts are replaced by another visco-elastic set and the moment of transition is considered as a condition of periodicity. Periodicity conditions are applied on the state at the moment of transition in order to obtain a map of the next transition based on the state of the previous one. This nonlinear map is used to obtain the conditions of existence of periodic motions with specific patterns. Applying the existence conditions, the stability of the motion can be achieved by analyzing the eigenvalues of the linearized map while taking these conditions into account
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Ozen, Onder Garip. "Influence Of Filtering On Linear And Nonlinear Single Degree Of Freedom Demands." Master's thesis, METU, 2006. http://etd.lib.metu.edu.tr/upload/12607842/index.pdf.
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Ground-motion data processing is a necessity for most earthquake engineering related studies. Important engineering parameters such as the peak values of ground motion and the ordinates of the response spectra are determined from the strong ground-motion data recorded by accelerometers. However, the raw data needs to be processed since the recorded data always contains high- and low-frequency noise from different sources.
Low-cut filters are the most popular ground-motion data processing scheme for removing long-period noise. Removing long-period noise from the raw accelogram is important since the displacement spectrum that provides primary information about deformation demands on structural systems is highly sensitive to the long-period noise.
The objective of this study is to investigate the effect of low-cut filtering period on linear and nonlinear deformation demands. A large number of strong ground motions from Europe and the Middle East representing different site classes as well as different magnitude and distance ranges are used to conduct statistical analysis. The statistical results are used to investigate the influence of low-cut filter period on spectral displacements.
The results of the study are believed to be useful for future generation ground-motion prediction equations on deformation demands that are of great importance in performance-based earthquake engineering.
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Kramář, Ondřej. "Návrh lineárního oscilačního pohonu s vnitřním buzením." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2009. http://www.nusl.cz/ntk/nusl-228880.
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This thesis deals with design of linear internal excitation drive with oscillative motion. Here is shown the survey area of linear drives, as well as the field of patents which are involved in this issue. This work is proposed specific conception of linear internal excitation drive with oscillative motion which is verified by simulation of dynamic behavior and for which is also proposed a control. Design of linear internal excitation drive with oscillative motion, that meet the specified input parameters is a goal of this thesis.
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Švrček, Jakub. "Třísítný vibrační třídič." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2020. http://www.nusl.cz/ntk/nusl-416620.
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This diploma thesis deals with the design of an inclined three-sided vibrating screen, which is designed for sorting bulk aggregates. The aim of the diploma thesis is primarily to make a construction design with a specific comparison of various design solutions, considering the calculated operating parameters. In the construction design, is used not only the experience of the manufacturer of this type of machine, but also recommendations based on the manu-facturers of screens component. The design also includes a comparison of two types of flex-ible mounting, which is one of the basic structural units of the entire vibrating screen. The thesis is conceived from the basics, with emphasis on the simplicity and functionality of the device.
Books on the topic "Linear motion (oscillation)"
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1938-, Trubetskov D. I., ed. Oscillations and waves in linear and nonlinear systems. Dordrecht: Kluwer Academic Publishers, 1989.
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Mann, Peter. Near-Equilibrium Oscillations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0012.
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In this chapter, the theory of near-equilibrium oscillations is developed and normal mode analysis is performed. This topic requires a little bit of linear algebra when dealing with matrices, as well as an understanding of differential equations. The chapter explores small perturbations (small nudges or tiny shifts) to a stable equilibrium point in configuration space and introduces the characteristic equation. Interdisciplinary examples are then investigated, including a surface science example in which the bond frequencies of surface adsorbates are calculated, an example in which the motion of atoms in a triatomic molecule is examined and an example in which the molecular physics of atomic force microscopy is analysed. The properties of the eigenvalue problem for small oscillations are also investigated.
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Nobre, Anna C. (Kia), and Gustavo Rohenkohl. Time for the Fourth Dimension in Attention. Edited by Anna C. (Kia) Nobre and Sabine Kastner. Oxford University Press, 2014. http://dx.doi.org/10.1093/oxfordhb/9780199675111.013.036.
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This chapter takes attention into the fourth dimension by considering research that explores how predictive information in the temporal structure of events can contribute to optimizing perception. The authors review behavioural and neural findings from three lines of investigation in which the temporal regularity and predictability of events are manipulated through rhythms, hazard functions, and cues. The findings highlight the fundamental role temporal expectations play in shaping several aspects of performance, from early perceptual analysis to motor preparation. They also reveal modulation of neural activity by temporal expectations all across the brain. General principles of how temporal expectations are generated and bias information processing are still emerging. The picture so far suggests that there may be multiple sources of temporal expectation, which can bias multiple stages of stimulus analysis depending on the stages of information processing that are critical for task performance. Neural oscillations are likely to provide an important medium through which the anticipated timing of events can regulate neuronal excitability.
Book chapters on the topic "Linear motion (oscillation)"
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Maisser, P., and U. Jungnickel. "Stability of Controlled Motion of a Gymnast in High-Speed Mid Air Maneuvers." In IUTAM Symposium on Recent Developments in Non-linear Oscillations of Mechanical Systems, 121–29. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-011-4150-5_13.
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Thomas, Michael E. "Electrodynamics I: Macroscopic Interaction of Light and Matter." In Optical Propagation in Linear Media. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780195091618.003.0008.
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Thus far, we have developed the properties of the electromagnetic field at optical frequencies, based on Maxwell’s equations. These equations further give a classical macroscopic perspective on the coupling of the propagation media to the field, as presented in Chapter 2. The macroscopic properties of a medium are based on averaged microscopic properties. The microscopic energy structure of matter was presented in Chapter 3, covering gases, solids, and liquids by employing mostly quantum models. We now proceed to the next level of development, the dynamic description of the interaction between the optical field and the propagation medium as a function of the field frequency and propagation media variables (e.g., energy structure, temperature, and pressure). In this chapter, the classical electromagnetic field is coupled to discrete frequency oscillators via Newton’s equation of motion. This approach leads to the popular classical oscillator model, often presented in introductory books on lasers. The classical oscillator model is an incomplete theory and can be only a semiempirical model. In the next chapter, a more detailed and comprehensive approach, which also includes statistical and quantum mechanics, is used leading to robust semiclassical and quantum oscillator models. This chapter and the next are the basis for the applied models presented in Part II of this book. Classical electrodynamics is based on Maxwell’s equations, as given in Chapter 2, and the Lorentz force relation, as given below: . . . F = q[E + (v × B)]. (4.1) . . . These equations cover the classical description of the interaction of light and matter. The first term in Eq. 4.1 represents coupling of the electric field to the medium. As discussed in Chapter 2 (Section 2.2), the leading mechanism for this is the electric dipole moment. To see that this is the coupling mechanism in the first term, consider the potential function driving this force, F = −∇V(r) = −∇(−qr · E). The above expression contains the dipole moment, as defined in Chapter 2. The second term in Eq. 4.1 represents coupling of the magnetic field to the medium.
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Autschbach, Jochen. "Quantized Rotational Motion in a Plane." In Quantum Theory for Chemical Applications, 306–12. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780190920807.003.0015.
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The angular momentum for the simplified case of a particle rotating in a fixed plane is treated. The ‘perimeter model’ is the analogue of the one-dimensional particle in a box (PiaB), with the particle moving on a circle with fixed radius. This requires cyclic – or periodic – boundary conditions. It is shown that the quantum perimeter model results can be obtained by re-interpreting the coordinate of the linear PiaB and by considering the periodic boundary conditions. The eigenvalue pattern leads to a 4n+2 Huckel rule. Next, the chapter discusses hindered rotations, such as the rotation of a methyl group around a C-C bond. The solutions to the hindered rotation problem combine features of the harmonic oscillator at low energies, with features of the perimeter model at high energies.
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Nitzan, Abraham. "The Spin–Boson Model." In Chemical Dynamics in Condensed Phases. Oxford University Press, 2006. http://dx.doi.org/10.1093/oso/9780198529798.003.0018.
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In a generic quantum mechanical description of a molecule interacting with its thermal environment, the molecule is represented as a few level system (in the simplest description just two, for example, ground and excited states) and the environment is often modeled as a bath of harmonic oscillators. The resulting theoretical framework is known as the spin–boson model, a term that seems to have emerged in the Kondo problem literature (which deals with the behavior of magnetic impurities in metals) during the 1960s, but is now used in a much broader context. Indeed, it has become one of the central models of theoretical physics, with applications in physics, chemistry, and biology that range far beyond the subject of this book. Transitions between molecular electronic states coupled to nuclear vibrations, environmental phonons, and photon modes of the radiation field fall within this class of problems. The present chapter discusses this model and some of its mathematical implications. The reader may note that some of the subjects discussed in Chapter 9 are reiterated here in this more general framework. In Sections 2.2 and 2.9 we have discussed the dynamics of the two-level system and of the harmonic oscillator, respectively. These exactly soluble models are often used as prototypes of important classes of physical system. The harmonic oscillator is an exact model for a mode of the radiation field and provides good starting points for describing nuclear motions in molecules and in solid environments. It can also describe the short-time dynamics of liquid environments via the instantaneous normal mode approach. In fact, many linear response treatments in both classical and quantum dynamics lead to harmonic oscillator models: Linear response implies that forces responsible for the return of a system to equilibrium depend linearly on the deviation from equilibrium—a harmonic oscillator property! We will see a specific example of this phenomenology in our discussion of dielectric response in Section 16.9.
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Milonni, Peter W. "Fluctuations, Dissipation, and Noise." In An Introduction to Quantum Optics and Quantum Fluctuations, 325–408. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780199215614.003.0006.
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General concepts in the theory of fluctuations and dissipation are reviewed and applied to examples in quantum optics. Brownian motion, Fokker-Planck and Langevin equations, and the Wiener-Khintchine theorem are reviewed, followed by a derivation and discussion of the fluctuation-dissipation theorem. The general problem of an oscillator coupled to a heat bath is revisited, as is the nonrelativistic theory of radiation reaction. The general ideas about fluctuations and dissipation developed in the first part of the chapter are then applied to the theory of the fundamental laser linewidth, the photon statistics of linear amplifiers and attenuators, the noise figure, amplified spontaneous emission, and the quantum theory of the beam slitter and homodyne detection.
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Kennel, Charles F. "The Bell-Like Magnetosphere." In Convection and Substorms. Oxford University Press, 1996. http://dx.doi.org/10.1093/oso/9780195085297.003.0006.
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The fact that the geomagnetic field “pulsates” was known a century before the space age opened. The century of ground-based observations did lead to an effective empirical classification of the pulsations based on period, wave form, and geographical distribution (Section 3.1), but why the magnetic field of an astronomical body should oscillate on short time scales was a first-class scientific puzzle that could only by solved in the space age. Low-frequency hydromagnetic waves were first observed in the distant magnetosphere on Explorer 6 (Judge and Coleman, 1962). The task for space research was to relate the oscillations of plasma and fields in deep space to the ground observations using the refined theoretical languages of magnetohydrodynamics and plasma physics. There have been two critical issues. The first was to understand how plasma instabilities generate some of the observed pulsations. The second, the subject of this chapter, has been to understand how motions of the magnetopause induced by the variability of the solar wind are communicated to the interior of the magnetosphere. The breakthrough came when it was understood that the MHD fast mode can cross field lines and couple resonantly to localized standing Alfven waves. What is seen on the ground is due primarily to the resonant Alfven waves (Section 3.3). In Section 3.4, we provide basic theoretical information about the eigenmodes of the “MHD box” as a conceptual framework for the observations of oscillating fields and particles in the magnetospheric cavity. Space observations provided convincing evidence for the existence of standing Alfven waves shortly after the fast-wave coupling theory was proposed (Section 3.5). The next issue was which standing wave harmonics are excited (Section 3.6). Multiharmonic excitations now seem to be a semipermanent feature of the dayside magnetosphere, attesting to the constant activity at the magnetopause. There have been a few observations of the “global mode,” the low-frequency, radially standing compressional wave that may be responsible for discrete frequency resonant oscillations (Section 3.7).
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Newnham, Robert E. "Nonlinear optics." In Properties of Materials. Oxford University Press, 2004. http://dx.doi.org/10.1093/oso/9780198520757.003.0031.
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In most dielectrics, the linear relation between electric polarization and applied electric field is accurately obeyed even for fairly large fields of 107 V/m. The reason is that the atomic displacements are extremely small, in the range of nuclear sizes—millions of times smaller than the size of atoms. Though nonlinear effects such as electrostriction have been known for some time, it was not until the invention of the laser that sufficiently large optical fields became available to produce sizeable nonlinear optical effects. The induced polarization P can be written as a power series in an electric field, . . . P = χE + dE2 +· · · , . . . where χ is the linear electric susceptibility, and the higher-order terms lead to nonlinear effects such as second harmonic generation. The electric field associated with the incident light is sinusoidal, E = E0 sin ωt, and when E is substituted in the expression for P, a power series in sin ωt results. The second term is dE20 sin2 ωt = 1/2dE20 (1 − cos 2ωt), which includes a component of polarization with twice the frequency of the impressed field E. This rapidly oscillating induced dipole moment is the source of second harmonic light. The intensity of the light depends on the size of d, the second order coefficient. Crystal symmetry is a major factor in the second-order effect. The one-dimensional polar chain in Fig. 29.2 illustrates the origin of the quadratic term. When the applied field is directed to the left, the ions and bonding electrons are in very close contact and the displacements will be small because of short range repulsive forces. These forces do not oppose motion in the opposite direction, so that fields directed to the right give larger motions and larger polarizations. A centric chain does not show this effect. Such a chain can give rise to odd-order terms producing saturation but not to even power terms in the P(E) relation. This means that centric crystals are useless as second harmonic generators.
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Aspray, Silvianne. "Conclusion." In Metaphysics in the Reformation, 137–46. British Academy, 2021. http://dx.doi.org/10.5871/bacad/9780197266939.003.0006.
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This conclusion considers the hermeneutical implications of the finding that Vermigli’s work is metaphysically complex with a view to what it means for understanding the Reformation more broadly. It argues that the metaphysical complexity underlying Reformation theology helps to make sense of radically diverging contemporary readings of reformers like Luther and Calvin. It moreover contends that if the Reformation was not characterised by a univocal metaphysics only, it becomes problematic to hold a line of argument which makes of the Reformation a motor of modernity, while predicating modernity on univocal structures of being. Finally, it argues that it is historically and philosophically significant that Vermigli’s work, and Reformation theology more broadly, sustains an unresolved tension by oscillating between a participatory and a univocal metaphysical model.
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Krishnamurti, T. N., H. S. Bedi, and V. M. Hardiker. "Initialization Procedures." In An Introduction to Global Spectral Modeling. Oxford University Press, 1998. http://dx.doi.org/10.1093/oso/9780195094732.003.0011.
Full textAbstract:
In this chapter we describe two of the most commonly used initialization procedures. These are the dynamic normal mode initialization and the physical initialization methods. Historically, initialization for primitive equation models started from a hierarchy of static initialization methods. These include balancing the mass and the wind fields using a linear or nonlinear balance equation (Charney 1955; Phillips 1960), variational techniques for such adjustments satisfying the constraints of the model equations (Sasaki 1958), and dynamic initialization involving forward and backward integration of the model over a number of cycles to suppress high frequency gravity oscillations before the start of the integration (Miyakoda and Moyer 1968; Nitta and Hovermale 1969; Temperton 1976). A description of these classical methods can be found in textbooks such as Haltiner and Williams (1980). Basically, these methods invoke a balanced relationship between the mass and motion fields. However, it was soon realized that significant departures from the balance laws do occur over the tropics and the upperlevel jet stream region. It was also noted that such departures can be functions of the heat sources and sinks and dynamic instabilities of the atmosphere. The procedure called nonlinear normal mode initialization with physics overcomes some of these difficulties. Physical initialization is a powerful method that permits the incorporation of realistic rainfall distribution in the model’s initial state. This is an elegant and successful initialization procedure based on selective damping of the normal modes of the atmosphere, where the high-frequency gravity modes are suppressed while the slow-moving Rossby modes are left untouched. Williamson (1976) used the normal modes of a shallow water model for initialization by setting the initial amplitudes of the high frequency gravity modes equal to zero. Machenhauer (1977) and Baer (1977) developed the procedure for nonlinear normal mode initialization (NMI), which takes into account the nonlinearities in the model equations. Kitade (1983) incorporated the effect of physical processes in this initialization procedure. We describe here the normal mode initialization procedure. Essentially following Kasahara and Puri (1981), we first derive the equations for vertical and horizontal modes of the linearized form of the model equations.
Conference papers on the topic "Linear motion (oscillation)"
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Su, D. N., Q. Song, Y. X. Dou, and K. M. Zhong. "Light-Load Linear Reciprocating Motion Device Based on Servo Motor and Small Eccentricity Crank Mechanism." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-11241.
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Here designs innovatively a kind of NC light-load straight reciprocating motion device which has relative fully technical function. It is driven by a low-power servo motor to actuate small eccentricity crank mechanism to rotate or swing. The rotation or swing drives piston to move linearly short distance. With the help of the simple and functional device, the internal-reflux area-differential hydraulic stroke amplifying device, the small linear displacement of the piston can be amplified dozens times or even more than one hundred times, so the output plunger can obtain relative large linear displacement to meet the required output force and motion. This device of hydrau-electromechanial integration has the following advantages: (1) easy to control the frequency of straight reciprocating motion by editing the program to control the rotating/swing frequency of the servo motor; (2) easy to get the needed stroke of the output plunger by editing program to control the oscillation angle of the servo motor; (3) higher precision in motion and displacement than pneumatic/hydraulic transmission device while the same good buffering as in pneumatic/hydraulic transmission device.
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Nihei, Yasunori, Takeshi Kinoshita, and Weiguang Bao. "Non-Linear Wave Forces Acting on a Body of Arbitrary Shape Slowly Oscillating in Waves." In ASME 2005 24th International Conference on Offshore Mechanics and Arctic Engineering. ASMEDC, 2005. http://dx.doi.org/10.1115/omae2005-67486.
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In the present study, non-linear wave loads such as the wave drift force, wave drift damping and wave drift added mass, acting on a moored body is evaluated based on the potential theory. The body is oscillating at a low frequency under the non-linear excitation of waves. The problem of interaction between the low-frequency oscillation of the body and ambient wave fields is considered. A moving coordinate frame following the low frequency motion is adopted. Two small parameters, which measure the wave slope and the frequency of slow oscillations (compared with the wave frequency) respectively, are used in the perturbation analysis. So obtained boundary value problems for each order of potentials are solved by means of the hybrid method. The fluid domain is divided into two regions by an virtual circular cylinder surrounding the body. Different approaches, i.e. boundary element method and eigen-function expansion, are applied to these two regions. Calculated nonlinear wave loads are compared to the semi-analytical results to validate the present method.
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Kastengren, A. L., C. F. Powell, Z. Liu, K. Fezzaa, and J. Wang. "High-Speed X-Ray Imaging of Diesel Injector Needle Motion." In ASME 2009 Internal Combustion Engine Division Spring Technical Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/ices2009-76032.
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Phase-enhanced x-ray imaging has been used to examine the geometry and dynamics of four diesel injector nozzles. The technique uses a high-speed camera, which allows the dynamics of individual injection events to be observed in real time and compared. Moreover, data has been obtained for the nozzles from two different viewing angles, allowing for the full three-dimensional motions of the needle to be examined. This technique allows the needle motion to be determined in situ at the needle seat and requires no modifications to the injector hardware, unlike conventional techniques. Measurements of the nozzle geometry have allowed the average nozzle diameter, degree of convergence or divergence, and the degree of rounding at the nozzle inlet to be examined. Measurements of the needle lift have shown that the lift behavior of all four nozzles consists of a linear increase in needle lift with respect to time until the needle reaches full lift and a linear decrease as the needle closes. For all four nozzles, the needle position oscillates at full lift with a period of 170–180 μs. The full-lift position of the needle changes as the rail pressure increases, perhaps reflecting compression of the injector components. Significant lateral motions were seen in the two single-hole nozzles, with the needle motion perpendicular to the injector axis resembling a circular motion for one nozzle and linear oscillation for the other nozzle. The two VCO multihole nozzles show much less lateral motion, with no strong oscillations visible.
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Mahalatkar, Kartikeya, Jeff Litzler, Urmila Ghia, Karman Ghia, and Arun Ramchandani. "Application of CFD to Study Performance of Hydrofoil-Based Ship-Stabilization Systems." In ASME 2006 2nd Joint U.S.-European Fluids Engineering Summer Meeting Collocated With the 14th International Conference on Nuclear Engineering. ASMEDC, 2006. http://dx.doi.org/10.1115/fedsm2006-98451.
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Computational Fluid Dynamics is used for simulating the flow over an oscillating hydrofoil found in a typical active-fin ship stabilization system. The hydrofoils oscillate through large angles of attack well above the static stall angle to generate large lift forces. Lift forces are calculated on the hydrofoil by using a simple sinusoidal motion at mean frequency of fin oscillation. The lift data is used in a linear system model created to simulate the active-fin ship-stabilization system. A Proportional Integral Derivative (PID) control system has also been developed for the purpose of controlling the fin motion. The simulation provides the typical motion experienced by a hydrofoil used in a ship stabilization system. This motion is fed back to a CFD solver to understand the effect of non-sinusoidal oscillation on Lift, Drag and Moment of the hydrofoil. The aerodynamics of the non-sinusoidally oscillating hydrofoil is analyzed so as to find the effect of pitch rate of the hydrofoil on the lift forces and hence on the performance of the ship stabilizer.
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Ananthakrishnan, Palaniswamy. "Effects of Viscosity and Free-Surface Nonlinearity on the Wave Motion Generated by an Oscillating Twin Hull." In ASME 2012 31st International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/omae2012-83171.
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The hydrodynamics of a rectangular, floating twin hull under heave oscillation is analyzed to determine viscous and nonlinear effects on the radiation hydrodynamics of multi-hulls, in particular, at the resonant frequency corresponding to the piston (Helmholtz) mode of wave motions. A second-order finite-difference method based on boundary-fitted coordinates is used for the solution of the incompressible Navier-Stokes equations together with exact nonlinear viscous boundary conditions. To separate the viscosity effects from the nonlinear free-surface effects, through comparison of results, nonlinear inviscid results are also obtained using a boundary-fitted curvilinear coordinates based finite difference method. The nonlinear inviscid algorithm is based on the Eulerian-Lagrangian formulation of the nonlinear free-surface flow. The nonlinear results are compared with the linear potential-flow results obtained by Yeung and Seah [20] to quantify the combined nonlinear and viscous effects on the wave forces. The present results show the overall behavior of the wave motion to be similar to that predicted by the linear potential-flow theory [20]. Our results show that the effects of nonlinearity and viscosity on the wave motion can be significant for the Helmholtz mode, particularly for small separation distance between the hulls, which result in large vertical oscillation of the mean surface between the hulls. For small amplitudes of oscillation, the hydrodynamic pressure forces computed in the present analysis are in striking agreement with that given by the linear potential-flow analysis of Yeung and Seah [20].
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Wang, Yigang, Kevin C. Chu, and Tsu-Chin Tsao. "Analysis and Control of Halbach Linear Motor for Nanopositioning." In ASME 2009 Dynamic Systems and Control Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/dscc2009-2765.
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This paper presents control of a Halbach linear motor for nano-precision positioning. Using an FPGA based decoding scheme and sensor signal processing, a 0.23nm root-mean-square (RMS) sensor noise level has been obtained from a 4 micrometer period sinusoidal quadrature encoder. Disturbances to the linear motor are studied at nanometer scale. When the motor is supported by the air bearing without feedback control, the mechanical motion measured by the sensor shows substantial low frequency oscillation around 10Hz. Under a PID digital servo feedback control, the stage can be brought to a regulated state of 11.14nm RMS error at 10kHz sampling rate, otherwise not achieved by lower sampling rate. Although PID servo loop substantially reduces the 10Hz motion, a 60Hz vibration and its harmonics begin to dominate at nanometer level. It is suspected and confirmed by experiments to be due to the coupling of the DC power supply/amplifier and control computer to the AC power source. A robust repetitive control scheme is employed to reject the 60Hz disturbance and its harmonics and bring the regulated state to 1.78nm RMS value.
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Bae, Jae-Sung, and In Lee. "Nonlinear Aeroelastic Characteristics of a Fighter-Type Wing With Control Surface." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-33066.
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The nonlinear aeroelastic characteristics of a fighter-type wing with control surface have been investigated. The fictitious mass modal approach is used to reduce the problem size and the computation time in the linear and nonlinear flutter analyses. A Doublet-Hybrid method are used for the computation of subsonic unsteady aerodynamic forces. Structural nonlinearity of the control surface hinge is represented by a free-play spring. The linear and nonlinear flutter analyses indicate that the flapping mode of control surface and the hinge stiffness have significant effects on the flutter characteristics. The nonlinear flutter analysis shows that limit cycle oscillation and chaotic motion are observed in the wide range of air speed below the linear flutter boundary and the jump of limit cycle oscillation amplitude is observed. The nonlinear flutter characteristics and the nonlinear flutter boundary of limit cycle oscillation and chaotic motion have been investigated.
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Lee, Young S., Gae¨tan Kerschen, Alexander F. Vakakis, Panagiotis Panagopoulos, Lawrence A. Bergman, and D. Michael McFarland. "Surprisingly Complicated Dynamics of a Single-Degree-of-Freedom Linear Oscillator Coupled to a Nonlinear Attachment." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84688.
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We study the dynamics of a two-degree-of-freedom nonlinear system consisting of a linear oscillator with an essentially nonlinear attachment. For the undamped system, we perform a numerical study based on non-smooth temporal transformations to determine its periodic solutions in a frequency-energy plot. It turns out that there is a sequence of periodic solutions bifurcating from the main backbone curve of the plot. We then study analytically the periodic orbits of the undamped system using the complexification / averaging technique in order to determine the frequency contents of the various branches of solutions, and to understand the types of oscillation performed by the system at the different regimes of the motion. The transient responses of the weakly damped system are then examined, and numerical wavelet transforms are used to study the time evolutions of their harmonic components. We show that the structure of periodic orbits of the undamped system greatly influences the damped dynamics, as it causes complicated transitions between modes in the damped transient motion. In addition, there is the possibility of strong passive energy transfer from the linear oscillator to the nonlinear attachment if certain periodic orbits of the undamped dynamics are excited by the initial conditions.
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Sharma, Sheshadri, and Richard Rodrigues Jettappa. "A Method to Determine the Exact Time Period of Oscillations of a Bifilar Pendulum." In ASME Turbo Expo 2010: Power for Land, Sea, and Air. ASMEDC, 2010. http://dx.doi.org/10.1115/gt2010-23531.
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A novel method to determine the exact time period of oscillations of a class of non-linear systems is presented. Taking the bifilar pendulum as an example, and employing the conservation of total energy concept, the free oscillations of the system is studied. The governing equation of motion of a bifilar pendulum is non-linear. The integration of this equation to obtain the time period of oscillation is highly complicated and only numerical solution is available. This is because the integral is singular at the extremities of the motion where the velocity will be zero. But, what cannot be achieved by integral calculus can be obtained easily by employing the definition of velocity taught in the high school curriculum. By employing this simple mathematical trick, this intractable equation is recast in a different but exact form. This leads to the identification of what is called the “Geometric Inertia” in bifilar pendulums. This Geometric Inertia is the additional inertia displayed by the system due to the constraint imposed by the two filaments as a result of the geometry of the pendulum. In the proposed method, the total displacement of the system is considered and divided into small equal segments. At the end points of each such segment, the corresponding velocity is calculated from the energy equation. Noting that the velocities are zero at the extremities of the system, an average velocity to each segment is calculated, and this average velocity is positive in each segment. The “delta” time spent by the system in each segment is now calculated by dividing the segment length by the average velocity of that segment. (From, time = displacement/velocity). The linear sum of such “delta” times gives the time period of oscillation. As the number of segments is increased, thereby reducing the segment length, the estimate becomes increasingly accurate. The proposed approach avoids a direct integration of complex, and often singular expressions that complicate the determination of time periods of oscillations of non-linear systems.
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Masuda, Arata, and Chisato Sawai. "Stick-Slip Energy Harvesting: A Preliminary Study." In ASME 2017 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/smasis2017-3994.
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In this paper, a design of an energy harvesting device which converts a translational relative motion to an oscillatory motion via stick-slip phenomenon is presented. In this design, an L-shape cantilever is used as an energy converter, the tip of which is rubbed by a linearly moving rubber pad. The induced stick-slip motion produces a relatively high frequency oscillation in the middle part of the cantilever during the stick phase, which is then converted to the electrical energy via a piezoelectric element attached on the cantilever surface. Testing of a proof-of-concept prototype reveals how the linear relative motion induces the stick-slip motion and the high frequency oscillation of the cantilever. The dependence of the stick-slip frequency on the design parameters is preliminary studied. Then, the load resistance optimization and the maximum output power are discussed, and the energy efficiency which is defined as the ratio of the output electrical energy to the input mechanical work during the rubbing motion is evaluated.