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Journal articles on the topic 'Rotating Beam Problem'
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1
Stephen, N. G., and P. J. Wang. "Stretching and Bending of Rotating Beam." Journal of Applied Mechanics 53, no. 4 (December 1, 1986): 869–72. http://dx.doi.org/10.1115/1.3171873.
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The effect of uniform high-speed rotation on the simplest representation of a rotating blade is analyzed according to the linear theory of elasticity. The blade is modeled as a uniform prismatic beam of general cross section rotating about a principal section axis perpendicular to the centroidal axis. This quasi-elastostatic three-dimensional problem is reduced to a two-dimensional boundary value problem to which solutions for the amenable circular and elliptic cross sections are given. For sections not possessing two axes of cross-sectional symmetry, the theory predicts curvature of the blade center line.
2
Bauchau, O. A., and C. H. Hong. "Nonlinear Composite Beam Theory." Journal of Applied Mechanics 55, no. 1 (March 1, 1988): 156–63. http://dx.doi.org/10.1115/1.3173622.
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The modeling of naturally curved and twisted beams undergoing arbitrarily large displacements and rotations, but small strains, is a common problem in numerous engineering applications. This paper has three goals: (1) present a new formulation of this problem which includes transverse shearing deformations, torsional warping effects, and elastic couplings resulting from the use of composite materials, (2) show that the small strain assumption must be applied in a consistent fashion for composite beams, and (3) present some numerical results based on this new formulation to assess its accuracy, and to point out some distinguishing feature of anisotropic beam behavior. First, the predictions of the formulation will be compared with experimental results for the large deflections and rotations of an aluminum beam. Then, the distinguishing features of composite beams that are likely to impact the design of rotating blades (such as helicopter blades) will be discussed. A first type of extension-twisting coupling introduced by the warping behavior of a pretwisted beam is discussed, then, a shearing strain squared term, usually neglected in small strain analyses, is shown to introduce a coupling between axial extension and twisting behavior, that can be significant when the ratio E/G is large (E and G are Young’s and shearing moduli of the beam, respectively). Finally, the impact of inplane shearing modulus changes and torsional warping constraints on the behavior of beams exhibiting elastic couplings is investigated.
3
Chen, W. R., and L. M. Keer. "Transverse Vibrations of a Rotating Twisted Timoshenko Beam Under Axial Loading." Journal of Vibration and Acoustics 115, no. 3 (July 1, 1993): 285–94. http://dx.doi.org/10.1115/1.2930347.
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Transverse bending vibrations of a rotating twisted beam subjected to an axial load and spinning about its axial axis are established by using the Timoshenko beam theory and applying Hamilton’s Principle. The equations of motion of the twisted beam are derived in the twist nonorthogonal coordinate system. The finite element method is employed to discretize the equations of motion into time-dependent ordinary differential equations that have gyroscopic terms. A symmetric general eigenvalue problem is formulated and used to study the influence of the twist angle, rotational speed, and axial force on the natural frequencies of Timoshenko beams. The present model is useful for the parametric studies to understand better the various dynamic aspects of the beam structure affecting its vibration behavior.
4
Pozhalostin, A. A., and A. V. Panshina. "Self-oscillations in one-dimensional elastic systems with friction." Izvestiya MGTU MAMI 8, no. 4-4 (August 20, 2014): 71–75. http://dx.doi.org/10.17816/2074-0530-67374.
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The possibility of self-oscillations in the case of transverse vibrations of elastic homogeneous beams is investigated taking into account presence of dry friction in system. The problem is solved using examples of a beam suspended by one end on rotating shaft and a beam articulated at ends. The method of replacing original system by equivalent mechanical oscillation system is used.
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Lee, Sen Yung, and Shueei Muh Lin. "Bending Vibrations of Rotating Nonuniform Timoshenko Beams With an Elastically Restrained Root." Journal of Applied Mechanics 61, no. 4 (December 1, 1994): 949–55. http://dx.doi.org/10.1115/1.2901584.
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Without considering the Coriolis force, the governing differential equations for the pure bending vibrations of a rotating nonuniform Timoshenko beam are derived. The two coupled differential equations are reduced into two complete fourth-order differential equations with variable coefficients in the flexural displacement and in the angle of rotation due to bending, respectively. The explicit relation between the flexural displacement and the angle of rotation due to bending is established. The frequency equations of the beam with a general elastically restrained root are derived and expressed in terms of the four normalized fundamental solutions of the associated governing differential equations. Consequently, if the geometric and material properties of the beam are in polynomial forms, then the exact solution for the problem can be obtained. Finally, the limiting cases are examined. The influence of the coupling effect of the rotating speed and the mass moment of inertia, the setting angle, the rotating speed and taper ratio on the natural frequencies, and the phenomenon of divergence instability (tension buckling) are investigated.
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Bazoune, A. "Effect of Tapering on Natural Frequencies of Rotating Beams." Shock and Vibration 14, no. 3 (2007): 169–79. http://dx.doi.org/10.1155/2007/865109.
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The problem of free vibration of a rotating tapered beam is investigated by developing explicit expressions for the mass, elastic and centrifugal stiffness matrices in terms of the taper ratios. This investigation takes into account the effect of tapering in two planes, the effect of hub radius as well as the stiffening effect of rotation. The equations of motion are derived; the associated generalized eigenvalue problem is defined in conjunction with a suitable Lagrangian form and solved for a wide range of parameter changes. The effect of tapering on the natural frequencies of the beam is examined with all parameter changes present. Results are compared with those available in literature and are found to be in excellent agreement.
7
Yang, Dahao, Zhong-Rong Lu, and Li Wang. "Detection of Structural Damage in Rotating Beams Using Modal Sensitivity Analysis and Sparse Regularization." International Journal of Structural Stability and Dynamics 20, no. 08 (July 2020): 2050086. http://dx.doi.org/10.1142/s0219455420500868.
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Rotating beams are often encountered in the wind turbines and the rotors, and detection of the damages in rotating beams as earlier as possible is central to ensuring the safety and serviceability of practical structures. To this end, a modal sensitivity approach in conjunction with the sparse regularization is proposed in this paper. First, the eigen equations for the flap-wise and chord-wise vibrations of a rotating beam are established upon Hamilton’s principle. Then, damage detection is formulated as a nonlinear least-squares problem that finds the damage coefficients to minimize the error between the measured and calculated data. To solve the nonlinear least-squares problem, the sensitivity method that requires the modal sensitivity analysis is developed. In real applications, damage detection is usually an ill-posed problem and to circumvent the ill-posedness, the sparse regularization is introduced due to the fact that the numbers of actual damage locations are often scarce. Numerical examples are studied and results show that the proposed approach is more accurate than the enhanced sensitivity approach and the flap-wise modal data outperforms the chord-wise modal data in damage detection of rotating beams.
8
Nourifar, Mostafa, Ali Keyhani, and Ahmad Aftabi Sani. "Free Vibration Analysis of Rotating Euler–Bernoulli Beam with Exponentially Varying Cross-Section by Differential Transform Method." International Journal of Structural Stability and Dynamics 18, no. 02 (February 2018): 1850024. http://dx.doi.org/10.1142/s0219455418500244.
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In this paper, the free vibration analysis of non-uniform rotating Euler–Bernoulli beam is carried out. It is assumed that the beam has exponentially decaying circular cross-section. In order to solve the problem, the differential transform method (DTM) is utilized. Based on our knowledge, we claim that the recurrence relation presented herein is an elaborate recurrence relation which has been obtained for ordinary differential equations. Non-dimensional natural frequencies of the beam are obtained and tabulated for different values of the beam parameters such as taper ratio and rotating speed. Furthermore, the finite element method (FEM) is employed to solve the problem. Comparison of the results obtained by DTM and FEM indicates the accuracy of proposed solutions.
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Zolkiewski, Sławomir. "Diagnostics and Transversal Vibrations Control of Rotating Beam by Means of Campbell Diagrams." Key Engineering Materials 588 (October 2013): 91–100. http://dx.doi.org/10.4028/www.scientific.net/kem.588.91.
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The paper concerns problem of diagnostics and transversal vibrations control of rotating beamlike system. The considered system is consisted of a simple prismatic beam. The beam is homogeneous and is being rotated round its end. The beam is fixed on the rotational disk. The most common method of analyzing rotational systems is the Campbell diagram. It gives the short and precise information about resonance points and critical angular velocities. In literature it is a very popular method, but used for shaft systems or rotors rather than for beams rotating round the axis of revolution perpendicular to its own axis of symmetry. In this work the exemplary Campbell diagrams for considered systems derived from the dynamic flexibility of beams are presented. In the used mathematical model the Coriolis forces and centrifugal forces were taken into consideration. Also the different types of boundary conditions were applied in this work. The results after proper adaptation can be used in practical applications such as pumps, turbines or wind power plants.
10
Lu, Tianle, Zhongmin Wang, and Dongdong Liu. "Analysis of Complex Modal Characteristics of Fractional Derivative Viscoelastic Rotating Beams." Shock and Vibration 2019 (October 16, 2019): 1–10. http://dx.doi.org/10.1155/2019/5715694.
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For the transverse vibration problem of a fractional derivative viscoelastic rotating beam, the differential equation of the system is obtained based on the Euler–Bernoulli beam theory and Hamilton principle. Then, introducing dimensionless quantities to differential equations and boundary conditions, the generalized complex eigenvalue equations of the system are obtained by the differential quadrature method. The effects of the slenderness ratio, the viscoelastic ratio, the hub radius-beam length ratio, and dimensionless hub speed and fractional order on the vibration characteristics of fractional derivative viscoelastic rotating beams are discussed by numerical examples. Numerical calculations show that when the dimensionless hub speed is constant, the real part of complex frequency increases with the increase of the fractional order, and the higher-order growth trend is more obvious. Through the study of displacement response at different points on the beam, it can be seen that the closer to the free end, the larger the response amplitude. And, the amplitude of response has been attenuated, which is also consistent with the vibration law of free vibration considering damping.
11
Ren, Yong Sheng, Shuang Shuang Sun, and Chun Jin Zhang. "Nonlinear Natural Frequencies of Rotating Composite Thin-Walled Beam with Geometrical Nonlinear." Advanced Materials Research 683 (April 2013): 779–82. http://dx.doi.org/10.4028/www.scientific.net/amr.683.779.
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The nonlinear governing equations of motion for the rotating composite thin-walled beam are derived using Hamilton’s energy principle and variational-asymptotical method (VAM) on the basis of von Karman’s assumption. The nonlinear vibration of the beam is studied using Galerkin method and harmonic balance method. The large amplitude free vibration of the beam can be expressed as a nonlinear eigenvalue problem and solved using an iterative solution procedure. Numerical results are obtained for Circumferentially Uniform Stiffness (CUS )laminated composite configuration thin-walled beam. The study exhibit the effect of the fiber orientation and rotating speed on nonlinear natural frequency vs. amplitude curves. The developed model can be capable of describing nonlinear free vibration behaviors of rotating composite thin-walled beam with large deformations.
12
Adair, Desmond, and Martin Jaeger. "A power series solution for rotating nonuniform Euler–Bernoulli cantilever beams." Journal of Vibration and Control 24, no. 17 (June 14, 2017): 3855–64. http://dx.doi.org/10.1177/1077546317714183.
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A systematic procedure is developed for studying the dynamic response of a rotating nonuniform Euler–Bernoulli beam with an elastically restrained root. To find the solution, a novel approach is used in that the fourth-order differential equation describing the vibration problem is first written as a first-order matrix differential equation, which is then solved using the power series method. The method can be used to obtain an approximate solution of vibration problems for nonuniform Euler–Bernoulli beams. Specifically, numerical examples are presented here to demonstrate the usefulness of the method in frequency analysis of nonuniform Euler–Bernoulli clamped-free cantilever beams. Results for mode shapes and frequency parameters were found to be in satisfactory agreement with previously published results. The effects of tapering, both equal and unequal, were investigated for both a cantilever wedge and cantilever cone.
13
Cheng, Tian-Yu, Wen-Yue Wang, Jin-Song Li, Ji-Xiang Guo, Shuo Liu, and Jia-Qi Lü. "Rotational Doppler Effect in Vortex Light and Its Applications for Detection of the Rotational Motion." Photonics 9, no. 7 (June 22, 2022): 441. http://dx.doi.org/10.3390/photonics9070441.
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The linear Doppler effect has been widely used to detect the translational motion of objects. However, it suffers difficulties in measuring the angular motion of a rotating target. In recent years, the rotational Doppler effect based on a vortex beam has been helpful to solve the problem of rotational measurement and has attracted extensive attention in remote sensing. This paper expounds the theoretical and experimental basis of the rotational Doppler effect and briefly summarizes its development for the detection of macro and micro targets. Specifically, the properties and analysis methods of a rotational Doppler shift when the vortex beam is misaligned with the rotation axis are described in detail. In addition, the existing problems and further developments in rotation detection based on the rotational Doppler effect are discussed.
14
Artelnyi, V. V., A. A. Rodionov, and A. V. Stulenkov. "Increasing the Frequency Resolution when Measuring Vibrations of Rotating Bodies with Fixed Beam Laser Vibrometry." Acoustical Physics 69, no. 3 (June 2023): 367–71. http://dx.doi.org/10.1134/s1063771022700038.
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AbstractLaser Doppler vibrometry is actively used in experimental studies because of its noncontact measurement technique. When using a stationary laser to measure the vibrations of rotating bodies and Fourier transform to process the results of such measurements, a problem arises, associated with a decrease in the frequency resolution of the spectra with increasing rotation rate of the body. As a result, at sufficiently high rotation rates, closely spaced discrete components may cease to be resolved. This paper proposes a method for solving such a problem using the least squares method. The operability of this processing method has been demonstrated on experimental data.
15
Maleki-Bigdeli, Mohammad-Ali, Majid Baniassadi, Kui Wang, and Mostafa Baghani. "Developing a beam formulation for semi-crystalline two-way shape memory polymers." Journal of Intelligent Material Systems and Structures 31, no. 12 (May 30, 2020): 1465–76. http://dx.doi.org/10.1177/1045389x20924837.
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In this research, the bending of a two-way shape memory polymer beam is examined implementing a one-dimensional phenomenological macroscopic constitutive model into Euler–Bernoulli and von-Karman beam theories. Since bending loading is a fundamental problem in engineering applications, a combination of bending problem and two-way shape memory effect capable of switching between two temporary shapes can be used in different applications, for example, thermally activated sensors and actuators. Shape memory polymers as a branch of soft materials can undergo large deformation. Hence, Euler–Bernoulli beam theory does not apply to the bending of a shape memory polymer beam where moderate rotations may occur. To overcome this limitation, von-Karman beam theory accounting for the mid-plane stretching as well as moderate rotations can be employed. To investigate the difference between the two beam theories, the deflection and rotating angles of a shape memory polymer cantilever beam are analyzed under small and moderate deflections and rotations. A semi-analytical approach is used to inspect Euler–Bernoulli beam theory, while finite-element method is employed to study von-Karman beam theory. In the following, a smart structure is analyzed using a prepared user-defined subroutine, VUMAT, in finite-element package, ABAQUS/EXPLICIT. Utilizing generated user-defined subroutine, smart structures composed of shape memory polymer material can be analyzed under complex loading circumstances through the two-way shape memory effect.
16
Malik, Manash, and Debabrata Das. "Study on free vibration behavior of rotating bidirectional functionally graded nano-beams based on Eringen’s nonlocal theory." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 234, no. 9 (June 9, 2020): 1203–17. http://dx.doi.org/10.1177/1464420720929375.
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Free vibration behavior of rotating bidirectional functionally graded nano-beams is studied based on Eringen’s nonlocal theory. The beam material consists of ceramic and metal constituents, and the material is graded across the length and thickness directions. The mathematical formulation is framed on Euler–Bernoulli beam theory, and the system of governing equations is derived in variational form using Hamilton’s principle. The governing equations are discretized and transformed to an eigen value problem using Ritz method. The model is formulated to study the flapping and lead-lag motions due to free vibration. The model is verified with the available numerical results. The numerical results are presented in non-dimensional frequency-speed plane to study the influence of normalized nonlocal parameter, length gradient parameter, thickness gradient parameter, root radius parameter, and section aspect ratio. Some normalized mode shapes are presented to illustrate the mode switching phenomenon. The mathematical model of a nonlocal rotating bidirectional functionally graded material nano-beam is presented for the first time through this work and the reported results are new of its kind.
17
Lee, Heow-Pueh. "Vibration on an Inclined Rotating Cantilever Beam With Tip Mass." Journal of Vibration and Acoustics 115, no. 3 (July 1, 1993): 241–45. http://dx.doi.org/10.1115/1.2930339.
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The vibration of a rotating cantilever beam with a tip mass is studied with the configuration of the undeformed beam deviating from the radial direction at the clamped end. The equation of motion is formulated based on the Hamilton’s principle and then reduced to the form of a matrix eigenvalue problem for constant rotational speed of the hub. The results of numerical simulations are compared with results from various authors using finite element, Rayleigh-Ritz, and Myklestad methods. The variation of natural frequency with rotational speed of the hub is then presented for various combinations of hub radius, tip mass, and angle of deviation of the undeformed beam from the radial direction.
18
Imregun, M., and A. Tsoutrelis. "Numerical Derivation of FRF Matrices for Curved, Twisted and Rotating Beams." Proceedings of the Institution of Mechanical Engineers, Part C: Mechanical Engineering Science 203, no. 6 (November 1989): 393–401. http://dx.doi.org/10.1243/pime_proc_1989_203_133_02.
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With recent advances in digital computers, frequency response function (FRF) coupling has become a widely used analysis tool for a range of turbomachinery components, such as blades and discs, and this appproach has the distinct advantage of being based on a closed-form solution, thus not requiring a large number of elements to obtain reasonable accuracy. The problem, however, lies in the unavailability of tabulated expressions for geometries more complicated than straight beams or uniform discs, and hence the resulting model is rather too simplistic. This paper deals with the numerical evaluation of FRF matrices for twisted and rotating beams from knowledge of the governing differential equations in an attempt to refine the state-of-the-art stationary multi-stage uniform beam model of turbomachinery blading.
19
Wauer, Jo¨rg. "Dynamics of Cracked Rotating Blades." Applied Mechanics Reviews 44, no. 11S (November 1, 1991): S273—S278. http://dx.doi.org/10.1115/1.3121364.
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The modeling and formulation of equations of motion for a cracked rotating blade are studied. The proposed model is a Bernoulli-Euler beam with a single transverse crack. Two fields are connected by a local spring element characterizing the reduced stiffness of the crack region. First, the governing nonlinear boundary value problem is derived. Next, the stationary deformation state is dealt with. Finally, the linearized equations of motion for small superimposed oscillations are formulated. The paper corresponds with another one of the same author on cracked rotating shafts and shows that several essential modifications are necessary.
20
Volyar, A. V., E. G. Abramochkin, E. V. Razueva, Ya E. Akimova, and M. V. Bretsko. "Structural stability of spiral beams and fine structure of an energy flow." Computer Optics 45, no. 4 (July 2021): 482–89. http://dx.doi.org/10.18287/2412-6179-co-885.
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The problem of structural stability of wave systems with great numbers of degrees of freedom directly concerns the issue of redistribution of energy fluxes in structured vortex beams that ensure their stability under propagating and focusing. A special place in this variety is occupied by spiral vortex beams capable of mapping complex figures, letters and even words. Spiral beams contain an infinite set of Laguerre-Gauss beams with a strong sequence of topological charges and radial numbers, their amplitudes and phases are tightly matched. Therefore, the problem of structural stability plays a special role for their applications. Using a combination of theory and computer simulation, supported by experiment, we ana-lyzed the structure of critical points in energy flows for two main types of spiral beams: triangular beams with zero radial number and triangular beams with complex framing of their faces with both quantum numbers. Structural stability is provided by triads of critical points, both inside and outside the triangle, which direct the light flux along the triangular generatrix and hold the framing when rotating the beam. The experiment showed that a simple triangular spiral beam turns out to be stable even with small alignment inaccuracies, whereas a complex triangular beam with a fram-ing requires careful alignment.
21
Pal, Suman, and Debabrata Das. "Free vibration analysis of functionally graded double-tapered beam rotating in thermal environment considering geometric nonlinearity, shear deformability, and Coriolis effect." Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering 232, no. 12 (June 8, 2017): 2244–62. http://dx.doi.org/10.1177/0954410017711965.
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The present work investigates the free vibration behavior of double-tapered functionally graded beams rotating in thermal environment, using an improved mathematical model. The functional gradation for ceramic–metal compositions, following power-law, is considered to be symmetric with respect to the mid-plane, leading to metal-rich core and ceramic-rich outer surfaces of the beam. The temperature dependence of the material properties are considered using Touloukian model. The nonlinearity in strain–displacement relationships for both the axial and transverse shear strains are considered. Firstly, the governing equations for deformed beam configuration under time-independent centrifugal loading are obtained using minimum total potential energy principle, and the solution is obtained following Ritz method. Then the free vibration problem of the centrifugally deformed beam is formulated employing Lagrange’s principle and considering tangent stiffness of the deformed beam configuration. Coriolis effect is considered in the mathematical model, and the governing equations are transformed to the state-space for obtaining an eigenvalue problem. The results for the first two modes of both chord-wise and flap-wise vibrations are presented in nondimensional plane to show the effects of taperness parameter, root-offset parameter, volume fraction exponent, operating temperature, and functionally graded material composition. The results in comparative form are presented for both temperature-dependent and temperature-independent material properties.
22
Pal, Suman, and Debabrata Das. "A tangent stiffness–based approach to study free vibration of shear-deformable functionally graded material rotating beam through a geometrically non-linear analysis." Journal of Strain Analysis for Engineering Design 52, no. 5 (July 2017): 310–32. http://dx.doi.org/10.1177/0309324717714186.
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An improved mathematical model to study the free vibration behavior of rotating functionally graded material beam is presented, considering non-linearity up to second order for the normal and transverse shear strains. The study is carried out considering thermal loading due to uniform temperature rise and using temperature-dependent material properties. Power law variation is assumed for through-thickness symmetric functional gradation of ceramic–metal functionally graded beam. The effects of shear deformation and rotary inertia are considered in the frame-work of Timoshenko beam theory. First, the rotating beam configuration under time-invariant centrifugal loading and thermal loading is obtained through a geometrically non-linear analysis, employing minimum total potential energy principle. Then, the free vibration analysis of the deformed beam is performed using the tangent stiffness of the deformed beam configuration, and employing Hamilton’s principle. The Coriolis effect is considered in the free vibration problem, and the governing equations are transformed to the state-space to obtain the eigenvalue problem. The solution of the governing equations is obtained following Ritz method. The validation is performed with the available results, and also with finite element software ANSYS. The analysis is carried out for clamped-free beam and for clamped–clamped beam with immovably clamped ends. The results for the first two modes of chord-wise and flap-wise vibration in non-dimensional speed-frequency plane are presented for different functionally graded material compositions, material profile parameters, root offset parameters and operating temperatures.
23
Bornassi, Saeed, and Hossein M. Navazi. "Torsional vibration analysis of a rotating tapered sandwich beam with magnetorheological elastomer core." Journal of Intelligent Material Systems and Structures 29, no. 11 (May 7, 2018): 2406–23. http://dx.doi.org/10.1177/1045389x18770864.
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In this study, the torsional vibration analysis of a rotating tapered sandwich beam with a magnetorheological elastomer core has been investigated. The magnetorheological elastomer material is used as a constrained damping layer embedded between two elastic constraining skins in order to improve the vibrational behavior of the sandwich beam. The three layers of the sandwich beam have rectangular cross-sections with symmetric arrangement. The problem formulation is set up based on the torsional theory of rectangular laminated plates. The assumed modes method and the Lagrange equations are used to derive the governing equations of motion of the system. The validity of the presented formulation is confirmed through comparison of the obtained results with those available in the literature. A detailed parametric study is carried out to investigate the effects of applied magnetic field, tapering ratios, magnetorheological elastomer layer thickness, rotating speed, hub radius, and setting angle on the free vibration characteristics of the sandwich beam. The results show that magnetic field intensity, magnetorheological elastomer layer thickness, and tapering ratio have significant influences on the torsional vibrating characteristics of the sandwich beam, and the effects of rotating speed and hub radius are considerable. The setting angle has no substantial effect on the torsional vibration characteristics.
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Woźniak, J., and M. Firkowski. "Note on the Stability of a Slowly Rotating Timoshenko Beam with Damping." Advances in Applied Mathematics and Mechanics 7, no. 6 (September 9, 2015): 736–53. http://dx.doi.org/10.4208/aamm.2014.m634.
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AbstractThis paper continues the senior author’s previous investigation of the slowly rotating Timoshenko beam in a horizontal plane whose movement is controlled by the angular acceleration of the disk of the driving motor into which the beam is rigidly clamped. It was shown before that this system preserves the total energy. We consider the problem of stability of the system after introducing a particular type of damping. We show that the energy of only part of the system vanishes. We illustrate obtained solution with the critical case of the infinite value of the damping coefficient.
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Fung, E. H. K., J. Q. Zou, and H. W. J. Lee. "Lagrangian Formulation of Rotating Beam With Active Constrained Layer Damping in Time Domain Analysis." Journal of Mechanical Design 126, no. 2 (March 1, 2004): 359–64. http://dx.doi.org/10.1115/1.1649969.
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In this paper, Lagrangian formulation of a horizontal rotating beam with active constrained layer damping (ACLD) treatment is presented. The problem is approached by the Rayleigh-Ritz method. By assuming modal functions as the displacement shape functions and using effective damping model of the visco-elastic material (VEM) layer, the number of degrees of freedom of the system is greatly reduced. The damping of the visco-elastic material is characterized by a shear (storage) modulus and a loss factor. Also the dynamic behavior of the rotating ACLD beam is analyzed in the time domain. The effects of control gains, shear modulus and loss factor of the VEM on the dynamic response are also investigated.
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Subrahmanyam, K. B., and K. R. V. Kaza. "Vibration and Buckling of Rotating, Pretwisted, Preconed Beams Including Coriolis Effects." Journal of Vibration and Acoustics 108, no. 2 (April 1, 1986): 140–49. http://dx.doi.org/10.1115/1.3269314.
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The effects of pretwist, precone, setting angle and Coriolis forces on the vibration and buckling behavior of rotating, torsionally rigid, cantilevered beams are studied in this investigation. The beam is considered to be clamped on the axis of rotation in one case, and off the axis of rotation in the other. Two methods are employed for the solution of the vibration problem: one based upon a finite-difference approach using second-order central differences for solution of the equations of motion, and the other based upon the minimum of the total potential energy functional with a Ritz type of solution procedure making use of complex forms of shape functions for the dependent variables. Numerical results obtained by using these methods are compared to those existing in the literature for specialized simple cases. Results indicating the individual and collective effects of pretwist, precone, setting angle, thickness ratio, and Coriolis forces on the natural frequencies and the buckling boundaries are presented and discussed. Furthermore, it is shown that the inclusion of Coriolis effects is necessary for blades of moderate-to-large thickness ratios while these effects are not so important for small thickness ratio blades. Finally, the results show the possibility of buckling due to centrifugal softening terms for large values of precone and rotation.
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Dong, Shi Min, Wan Sheng Zhang, Guo Hong Chai, Ming Ming Xing, and Hong Zhang. "Simulating Research on Rod String’s Gyro Effect Caused by Eccentric Rotation in Circular Tube." Applied Mechanics and Materials 130-134 (October 2011): 2294–300. http://dx.doi.org/10.4028/www.scientific.net/amm.130-134.2294.
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Based on the influences of eccentrical rotating inertial centrifugal force and axial force on the rod string’s lateral bending deformation, the finite beam element model of rod string’s bending deformation is established. The constraint to rod string’s bending deflection exerted by inwall of circular tube and the distinction of the constraint to rod string’s deflection because of the different gaps between rod string to circular tube and coupling to circular tube are both taken into account. Meanwhile, removable spring elements with two directions are adopted, by which the non-linear contact problem between the rod string and circular tube is well resolved. Combining space beam element and spring elements with two directions, the corresponding finite element simulating program is also developed. Several simulating results can be shown as follows: eccentric rotation of rod string is able to produce gyro effect in vertical circular tube; The shape of the rod string’s deformation is a spiral which is thin on the upper-part and dense on the under-part; Gyro wave numbers are affected obviously by rotating speed, eccentricity, axial concentrated force, axial distributed force and length of the rod string.
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Haering, William. "Bending Dominated Beam Dynamics: Continuous Shape Functions, Boundary Conditions and Internal Loads." Journal of Vibration and Control 10, no. 12 (December 2004): 1813–33. http://dx.doi.org/10.1177/1077546304044210.
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Predicted solutions to flexible beam dynamics problems involving large overall prescribed motion are investigated using two existing continuous shape function approaches. The beam is cantilevered to a rigid rotating table at one end and attached to the table by way of a tether spring at the other end. It is demonstrated that the free-interface component mode approach provides a significantly more accurate solution than the traditional cantilever beam eigenfunction approach. The chief difference between the two approaches is the continuous shape functions used and the handling of the boundary conditions. The beam in this study, in contrast to a previous study, is oriented such that the steady-state response of the beam is dominated by its bending behavior. It is shown that the internal loads acting on the beam must be considered in order to demonstrate the distinctive differences between the two approaches. Finally, it is demonstrated that adding a new static shape function to the existing free-interface component mode synthesis approach yields a significantly more accurate solution to the problem.
29
Piro Barragam, Vinicius, Andre Fenili, and Ijar Milagre da Fonseca. "Dynamics and control of a flexible rotating clamped-free beam by SDRE strategy." Aircraft Engineering and Aerospace Technology 91, no. 7 (July 8, 2019): 1018–26. http://dx.doi.org/10.1108/aeat-11-2017-0240.
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Purpose The purpose of this paper is the dynamic analysis of the coupled rotation and vibration motion of a system containing a central rigid body to which is attached a flexible beam. Design/methodology/approach The methodology includes the Lagrange’s formulation by using the extended Hamilton’s Principle in conjunction with the assumed modes method to describe the system of equations by ordinary differential equations. The first unconstrained mode of vibration was considered as the solution for the transversal displacement. Such mode emerges as the eigenvalue problem solution associated to the dynamics of the system. The control strategy adopted is a nonlinear analogy of the linear quadratic regulator problem as the Riccati equation is solved at every integration step during the numerical solutions. This strategy is known as state-dependent Riccati equation. Findings By means of computational simulations, it was found the relation between controlled motion and inertia ratio. Research limitations/implications This work is limited to planar case and fixed hub. Practical implications Practical implications of this work realize the design of lighter yet dexterous structures. Originality/value The contribution of this paper is the position and vibration control of a flexible beam accounting for nonlinearity effects and the fact that the structure to where it is clamped has a comparable inertia.
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Abouelregal, Ahmed E., Khalil M. Khalil, Wael W. Mohammed, and Doaa Atta. "Thermal vibration in rotating nanobeams with temperature-dependent due to exposure to laser irradiation." AIMS Mathematics 7, no. 4 (2022): 6128–52. http://dx.doi.org/10.3934/math.2022341.
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<abstract> <p>Effective classical representations of heterogeneous systems fail to have an effect on the overall response of components on the spatial scale of heterogeneity. This effect may be critical if the effective continuum subjects' scale differs from the material's microstructure scale and then leads to size-dependent effects and other deviations from conventional theories. This paper is concerned with the thermoelastic behavior of rotating nanoscale beams subjected to thermal loading under mechanical thermal loads based on the non-local strain gradient theory (NSGT). Also, a new mathematical model and governing equations were constructed within the framework of the extended thermoelastic theory with phase delay (DPL) and the Euler-Bernoulli beam theory. In contrast to many problems, it was taken into account that the thermal conductivity and specific heat of the material are variable and linearly dependent on temperature change. A specific operator has been entered to convert the nonlinear heat equation into a linear one. Using the Laplace transform method, the considered problem is solved and the expressions of the studied field variables are obtained. The numerical findings demonstrate that a variety of variables, such as temperature change, Coriolis force due to rotation, angular velocity, material properties, and nonlocal length scale parameters, have a significant influence on the mechanical and thermal waves.</p> </abstract>
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Bhattacharya, Sujash, and Debabrata Das. "Modified couple stress-based free vibration behavior of pre-twisted tapered BFGM rotating micro beam considering spin-softening and Coriolis effects." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 234, no. 1 (August 31, 2019): 21–47. http://dx.doi.org/10.1177/1464420719870822.
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An improved mathematical model of pre-twisted tapered rotating micro beams made of bidirectional functionally graded material (BFGM) is presented to study its free vibration behavior. The effects of spin-softening and Coriolis acceleration are incorporated, and modified couple stress theory is employed to address the size effect. The mathematical formulation is based on first-order shear deformation theory and is developed in a global non-inertial frame incorporating appropriate transformations between the global inertial frame and the local non-inertial frame. Two different but interrelated steps are employed, where the first step determines the centrifugally deformed configuration using minimum potential energy principle, and the second step determines the free vibration behavior through tangent stiffness of the deformed rotating beam using Hamilton's principle. The direct use of tangent stiffness considers the centrifugal stiffening effect through von Kármán non-linearity and bypasses the need of strain energy functional for the vibrating beam. The governing equations are transformed to an eigenvalue problem through state-space approach and solved following Ritz method. The effects of spin-softening, Coriolis acceleration, and pre-twist angle are shown and discussed. The effects of different parameters such as size-dependent parameter, aspect ratio, material gradation indices, operating temperature, FGM constituent, taperness parameters, and slender parameter are discussed.
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Castellini, Paolo, Milena Martarelli, and Enrico Primo Tomasini. "Laser Doppler Vibrometry for Structural Dynamic Characterization of Rotating Machinery." Applied Mechanics and Materials 415 (September 2013): 538–43. http://dx.doi.org/10.4028/www.scientific.net/amm.415.538.
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Laser Doppler Vibrometry (LDV) is a well established technique able to accurately measure vibration velocity of any kind of structure in remote, i.e. non-intrusive way, this allowing to overcome the problem of mass loading, typical of contact sensors as accelerometers and strain-gauges, which has strong influence in case of lightweight structures. Moreover, the possibility of driving automatically the laser beam, by means of moving mirrors controlled with galvanometer servo-actuators, permits to perform scanning measurements at different locations with high spatial resolution and reduced testing time and easily measure the operational deflection shapes (ODS) of the scanned surface. The exploitation of the moving mirrors has allowed to drive the laser beam in a continuous way making it to scan continuously over the structure surface and cover it completely. This way of operation, named Continuous Scanning LDV, permits to perform full-field measurements, the LDV output carrying simultaneously the time-and spatial-dependent information related to the structural vibration. A complementary strategy making use of the LDV coupled with moving mirrors is the so called Tracking LDV, where the laser beam is driven to follow a moving object whose trajectory must be known a priori or measured during operation (e.g. via an encoder in the case of rotating structures). In this paper some applications of the Tracking Laser Doppler Vibrometry (TLDV) and Continuous Scanning Laser Doppler Vibrometry (CSLDV) will be described they concerning, specifically modal and vibrational analysis of rotating structures.
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Sklyar, Grigory M., and Grzegorz Szkibiel. "Controlling a non-homogeneous Timoshenko beam with the aid of the torque." International Journal of Applied Mathematics and Computer Science 23, no. 3 (September 1, 2013): 587–98. http://dx.doi.org/10.2478/amcs-2013-0044.
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Abstract Considered is the control and stabilizability of a slowly rotating non-homogeneous Timoshenko beam with the aid of a torque. It turns out that the beam is (approximately) controllable with the aid of the torque if and only if it is (approximately) controllable. However, the controllability problem appears to be a side-effect while studying the stabilizability. To build a stabilizing control one needs to go through the methods of correcting the operators with functionals so that they have finally the appropriate form and the results on C0-continuous semigroups may be applied.
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Xu, Guangbo. "Small opening cascade synchronous scanning underwater laser fuze using an adaptive backscatter filtering method." Journal of Physics: Conference Series 2478, no. 6 (June 1, 2023): 062012. http://dx.doi.org/10.1088/1742-6596/2478/6/062012.
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Abstract To alleviate the problem of the low spatial utilization rate of underwater single-beam rotating scanning laser fuzes, a multi-beam rotating scanning fuze structure is proposed in this paper. It was used as a platform to study the interference mechanism of underwater pulsed laser backscatter, and Monte Carlo simulations were performed for typical detection situations of the underwater laser fuze. It was found that the interference echoes resulting from backscatter could even drown the actual target echoes and cause severe interference to the target identification of the fuze. To this end, this paper proposes an adaptive filtering algorithm called “VSS-DLMS” suitable for the fuze FPGA platform and simulated using echo data obtained by a real detection environment. The simulation results demonstrate that the algorithm can effectively suppress the backscattered signal of the pulsed laser in seawater and improve the signal-to-noise ratio of fuze detection.
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García-Vallejo, D., H. Sugiyama, and A. A. Shabana. "Finite element analysis of the geometric stiffening effect. Part 2: Non-linear elasticity." Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-body Dynamics 219, no. 2 (June 1, 2005): 203–11. http://dx.doi.org/10.1243/146441905x10050.
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In the first part of this paper, the relationship between the number of finite elements used to model the dynamics of rotating beams and the critical speed at which an incorrect solution is obtained when using linear elasticity theory is discussed. The increase in the number of finite elements leads to an increase in the critical speed when linear elasticity is used and no measures are taken, as recommended in the literature, to account for the effect of the coupling between the bending and axial displacements. In this part of the paper, a non-linear finite element model based on the absolute nodal coordinate formulation is used to study the dynamics of rotating beams. It is shown that, when the non-linear elasticity theory is used, a stable solution is always obtained regardless of the number of finite elements used. Numerical results of various simulations are presented in order to compare the solution of a three-dimensional rotating beam that is obtained using the absolute nodal coordinate formulation with the results previously reported in the literature. A finite element numerical study of the dynamics of a helicopter rotor blade is also presented in this investigation. It is shown that, when the finite element absolute nodal coordinate formulation is used in the analysis of helicopter blades, the problem of ill-conditioning that characterizes many of the existing formulations is not encountered.
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Wu, Qing Hua, and An Qing Zhang. "Research on Beamforming Technique for Communications in Moving of Warship Circular Array Antenna." Applied Mechanics and Materials 241-244 (December 2012): 2295–98. http://dx.doi.org/10.4028/www.scientific.net/amm.241-244.2295.
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Uniform circular antenna array of warship can bring beam and interference null steering from 360° symmetry without rotating. Directional communications can be achieved by UCA geometry. To solve the problem that warship’s stance is changed dynamically in course of sailing, a method was suggested that the electricity phases of UCA elements were changed based on information of stance about longitudinal sway, transverse sway and course. The proposed method can change beam directivity, and ensure providing a very directive pattern with stabilization, so that warships communication in moving each other. An expression of array maximum directivity forming with dynamic is proposed for UCA antenna. The simulation demonstrates that the beam forming method of communications in moving is validity, and is worth using with wide application.
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Ebrahimi, Farzad, Mohammad Reza Barati, and Parisa Haghi. "Wave propagation analysis of size-dependent rotating inhomogeneous nanobeams based on nonlocal elasticity theory." Journal of Vibration and Control 24, no. 17 (June 1, 2017): 3809–18. http://dx.doi.org/10.1177/1077546317711537.
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The present research deals with the wave dispersion behavior of a rotating functionally graded material (FGMs) nanobeam applying nonlocal elasticity theory of Eringen. Material properties of rotating FG nanobeam are spatially graded according to a power-law model. The governing equations as functions of axial force due to centrifugal stiffening and displacements are obtained by employing Hamilton’s principle based on the Euler–Bernoulli beam theory. By using an analytical model, the dispersion relations of the FG nanobeam are derived by solving an eigenvalue problem. Numerical results clearly show that various parameters, such as angular velocity, gradient index, wave number and nonlocal parameter, are significantly effective to characteristics of wave propagations of rotating FG nanobeams. The results can be useful for next generation study and design of nanomachines, such as nanoturbines, nanoscale molecular bearings and nanogears, etc.
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Nayak, D. K., and P. R. Dash. "Parametric Stability Analysis of a Spring Attached, Pre-Twisted, Rotating Sandwich Beam with Tip Mass and Viscoelastic Support." International Journal of Structural Stability and Dynamics 21, no. 10 (June 23, 2021): 2150143. http://dx.doi.org/10.1142/s0219455421501431.
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This paper inspects the influence of a spring attachment provided on the top elastic layer on the stability of a pre-twisted, rotating sandwich beam having viscoelastic supports at the root under the impact of a periodically varying axial load. The spring is deployed on the beam to achieve more strength to weight ratio without compromising the stability. The beam is exponentially tapered, and a tip mass is at the free end to represent the rotating members in various types of machinery as closely as possible. The ruling equations and inter-related boundary conditions are attained by applying Hamilton’s principle. To obtain the solution, a matrix equation was developed through the assumed-mode variational method. The resulting matrix equation was converted to a coupled Hill’s equation of parametric vibration through the modal matrix corresponding to the free vibration problem. Finally, static and dynamic stability graphs were obtained for several system parameters such as position and length of the attached spring on the top elastic layer, the mass of the spring attachment, stiffness of the spring attachment, angle of pre-twist, tip mass, taper parameter, temperature gradient parameter, setting angle, viscoelastic spring stiffness, etc. to analyze their impact on the system’s stability. Saito and Otomi conditions were used to obtain dynamic stability plots. Greater stability is achieved due to the spring attachment on the top of the top elastic layer.
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F. Nitzsche. "Laplace-domain approximation to the transfer functions of a rotor blade in forward flight." Aeronautical Journal 105, no. 1047 (May 2001): 233–40. http://dx.doi.org/10.1017/s0001924000012045.
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Abstract A continuous frequency domain method with roots on the classic Hill’s determinant analysis is presented to approximate the time-varying characteristics of a linear periodic system. The method is particularly useful to derive a time-invariant equivalent form of the time-varying aeroelastic problem of a rotor blade in forward flight. The proposed technique allows methodology usually employed in fixed wing aircraft to obtain closed-loop control laws be extended to rotary wings. The method is first validated solving Mathieu’s equation. Next, the two-degree-of-freedom (flap bending and torsion) problem of rotating beam subject to unsteady and incompressible aerodynamics in forward flight is solved in the laplace domain. As a demonstration of the proposed method, the transfer functions in the ‘s’ plane between a sudden and uniformly distributed input pressure perturbation applied along the beam and the output response of the two elastic degrees of freedom considered are obtained at a set of local sections.
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Kwon, Junhee, Dongwoo Hong, and Byeongil Kim. "Modeling, analysis, and control of shaft transverse vibration from rotating systems through active bearing concept." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 265, no. 7 (February 1, 2023): 649–56. http://dx.doi.org/10.3397/in_2022_0088.
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Rotating parts are widely applied to mechanical systems such as pumped-storage hydroelectricity, nuclear power plant, machining tools and so on. While operating, they can be easily damaged or destroyed by unbalanced mass, bending, torsion and misalignment. In order to solve this problem, rotor vibration control can be conducted through active bearing concept. In this work, active bearing system which consists of piezo actuators and rubber grommets is proposed and applied to a rotating system motivated from a pumped-storage hydroelectricity, for performing active vibration control. The main point of this paper is to prevent damage or failure caused by harsh transverse vibration through active bearings. First, the rotating system is modeled by transfer matrix method (TMM) based on Euler-Bernoulli beam theory and in order to check accuracy of this model, the responses of TMM are compared with the responses from the finite element method (FEM). For implementing active control in real time, normalized least mean square (NLMS) algorithm is utilized. The results show that the proposed active bearing concept shows great performance on the attenuation of shaft transverse vibration.
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Gürgöze, M., and S. Zeren. "On the eigencharacteristics of a centrifugally stiffened, visco-elastic beam." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 223, no. 8 (April 15, 2009): 1767–75. http://dx.doi.org/10.1243/09544062jmes1336.
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The present study is concerned with the out-of-plane vibrations of a rotating, internally damped (Kelvin—Voigt model) Bernoulli—Euler beam carrying a tip mass, which can be thought of as a simplified model of a helicopter rotor blade or a blade of an auto-cooling fan. The differential eigenvalue problem set up is solved by using the Frobenius method of solution in a power series. The developed characteristic equation is then solved numerically. The simulation results are tabulated for a variety of non-dimensional rotational speeds, tip mass, and internal damping parameters. These are compared with the results of conventional finite element (FE) modelling as well and excellent agreement is obtained. Furthermore, it is seen that the numerical calculations according to the proposed solution method need much less computer time as compared to the conventional FE method.
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Apiwattanalunggarn, Polarit, Steven W. Shaw, Christophe Pierre, and Dongying Jiang. "Finite-Element-Based Nonlinear Modal Reduction of a Rotating Beam with Large-Amplitude Motion." Journal of Vibration and Control 9, no. 3-4 (March 2003): 235–63. http://dx.doi.org/10.1177/107754603030751.
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A nonlinear one-dimensional finite-element model representing the axial and transverse motions of a cantilevered rotating beam is reduced to a single nonlinear normal mode using invariant manifold techniques. This system is an idealized representation for large-amplitude vibrations of a rotorcraft blade. Although this model is relatively simple, it possesses the essential nonlinear coupling effects between the axial and transverse degrees of freedom. The nature of this coupling leads to the fact that we must use many degrees of freedom, whether based on finite elements or modal expansions, in order to accurately represent the beam vibrations. In this work, the slow modal convergence problem is overcome by nonlinear modal reduction that makes use of invariant manifold based nonlinear modes. This reduction procedure generates a single-degree-of-freedom reduced-order model that systematically accounts for the dynamics of all the linear modes, or finite elements, considered in the original model. The approach is used to study the dynamic characteristics of the finite-element model over a wide range of vibration amplitudes. Using extensive simulations, it is shown that the response of the reduced-order model is nearly identical to a reference system which is based on a large-scale representation of the finite-element model, and to a reduced-order Rayleigh-Ritz model. All of the procedures presented here have been computationally automated. Hence, in this study we demonstrate that it is feasible and practical to interface nonlinear finite-element methods with nonlinear modal reduction.
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Ding, Hu, Minghui Zhu, Zhen Zhang, Ye-Wei Zhang, and Li-Qun Chen. "Free Vibration of a Rotating Ring on an Elastic Foundation." International Journal of Applied Mechanics 09, no. 04 (May 16, 2017): 1750051. http://dx.doi.org/10.1142/s175882511750051x.
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In the present paper, free vibration of a rotating ring supported by an elastic foundation is studied by analytical method, finite element (FE) simulation and experiment. By adopting the ring analogy of Timoshenko beam theory, the nonlinear vibration of the rotating ring on an elastic foundation is modeled based on Hamilton’s principle. Radial and tangential deformation are considered. By solving the generalized eigenvalue problem, natural frequencies and flexural modes are obtained. Furthermore, the Euler–Bernoulli (E–B) theory is also employed to investigate the free vibration. For determining the necessity of the Timoshenko theory, the flexural vibration frequencies from two theories are compared. Specifically, the effects of the radius and the radial height (the thickness) of the ring on the difference between the two models are studied. In order to confirm the analytical results, finite element analysis and experiments on three test specimens are used to verify the natural frequency and flexural mode predictions. Overall, this work shows the necessity of the Timoshenko theory for studying free vibration of an elastic ring.
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Ren, Wen, Xia Wen, and Sencai Lai. "Digital Real-Time Rotating Speed Measuring and Fuzzy PID Control Algorithm Design for the Multi-Speed Electronic Let-Off System." Fibres and Textiles in Eastern Europe 29, no. 4(148) (August 31, 2021): 48–55. http://dx.doi.org/10.5604/01.3001.0014.8231.
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Aiming at the warp knit fabric horizontal strip problem faced by the multi-speed electronic let-off process of warp knitting machines, a design scheme of a fully digital intelligent multi-speed electronic system is proposed. A wide-range digital speed measurement method is proposed which solves the problem that the traditional analog circuit speed measurement method cannot measure the real-time warp beam speed, and also eliminates the problem of the low-speed feedback blind zone. According to the characteristics of the electronic let-off system of warp knitting machines, the hardware structure and software algorithm of the fuzzy PI control system were designed which can adjust the control parameters of the traditional PI controller in real time according to the fuzzy control table, and realise stable multi-speed electronic let-off. The effectiveness of the design method was verified by simulation.
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Zhi, Fengyao, Fajie Duan, Jie Li, Guangyue Niu, and Qi Zhou. "Parameters Identification of Blade Multi-mode Coupled Vibration Based on Blade Tip Timing." Journal of Physics: Conference Series 2437, no. 1 (January 1, 2023): 012076. http://dx.doi.org/10.1088/1742-6596/2437/1/012076.
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Abstract Health monitoring is crucial for the safe operation of rotating machinery. As an effective technique for measuring the vibration of rotating blades, blade tip timing (BTT) is widely used since its advantages of non-contact and low intervention. During the operation of high-speed blades, the multi-mode coupled synchronous vibration will occur. However, the existing BTT-based methods cannot identify the multi-mode coupled vibration parameters. To solve the problem, a multi-mode coupled vibration model of the blade based on a slender cantilever beam is established, and the contribution of each mode to the blade vibration response is considered. A new Circumferential Fourier Fit (CFF) method for parameters identification of blade multi-mode coupled synchronous vibration is proposed. According to the proposed method, the reconstruction of multi-mode coupled synchronous vibration signals can be realized. Finally, the accuracy of the proposed method is verified by simulation data.
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Choura, S. "Finite-Time Settling Control of a Flexible Arm." Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 208, no. 2 (May 1994): 79–87. http://dx.doi.org/10.1243/pime_proc_1994_208_312_02.
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This paper considers the position control of a flexible beam attached to a rotating rigid hub. The control torque is applied at the hub through a motor. A state-space model describing the motion of the flexible beam is developed and is employed in the design of the control law. The finite-time settling control strategy that combines feedback and feedforward is applied to the beam problem. The feedback part is separately designed to resolve the issues of asymptotic stability and robustness to uncertainties. The feedforward part simultaneously suppresses the rigid-body mode and a finite set of flexible modes at the end of manoeuvre and, therefore, it is the part responsible for the finite-time settling of the beam to its final configuration. It is shown that if the finite-time settling control is compared with previously developed control strategies under the same input bound constraint, it leads to a better suppression of vibrations at the end of manoeuvre, provided that a sufficient number of flexible modes are incorporated in the computation of the feedforward control law. A robustness test is carried out to show the viability of the control strategy supported by computer simulations.
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Othman, Mohamed I. A., Magda E. M. Zidan, and Mohamed I. M. Hilal. "Effect of magnetic field on a rotating thermoelastic medium with voids under thermal loading due to laser pulse with energy dissipation." Canadian Journal of Physics 92, no. 11 (November 2014): 1359–71. http://dx.doi.org/10.1139/cjp-2013-0689.
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This investigation deals with the rotation of magneto-thermoelastic solid with voids subjected to thermal loading due to laser pulse. The bounding plane surface is heated by a non-Gaussian laser beam. The entire porous medium is rotated with a uniform angular velocity. The problem is studied in the context of Green–Naghdi (GN) theory of types II and III, with the effect of rotation, magnetic field, thermal loading and voids. Normal mode analysis is used to solve the physical problem to obtain the exact expressions for the displacement components, stresses, temperature distribution, and change in the volume fraction field, which have been shown graphically by comparison between two types of GN theory (types II and III) in the presence and the absence of rotation and magnetic field and for two values of time on thermoelastic material with voids.
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Haefner, Stephan, and Reiner Thomä. "High Resolution Estimation of AoA, AoD and TdoA from MIMO Channel Sounding Measurements with Virtual Antenna Arrays: Maximum-Likelihood vs. Unitary Tensor-ESPRIT." International Journal of Advances in Telecommunications, Electrotechnics, Signals and Systems 7, no. 2 (June 28, 2018): 27. http://dx.doi.org/10.11601/ijates.v7i2.254.
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Estimating the parameters of a geometric propagation model from MIMO channel sounding measurements will be considered, which requires the solution of an inverse problem. Thus, a model of the measured data is derived, which incorporates a model of the measurement system as well as the parameters of interest. Based on the data model a maximum-likelihood estimator will be derived to infer the model parameters. Because virtual antenna arrays are considerer, formed by step-wise rotating directive antennas at transmitter and receiver side, the MIMO measurements are conducted in the beam-space. Hence, the data model can be described by a multidimensional convolution of the measurement system and the propagation channel. Based on the convolutional modelling, the parameter estimation problem is transformed into a harmonic retrieval problem, which can be solved by an Unitary Tensor-ESPRIT algorithm. The maximum-likelihood and ESPRIT estimator are compared by Monte-Carlo simulations according to their root-mean-square estimation error.
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Jouve, Laurène, and Gordon I. Ogilvie. "Direct numerical simulations of an inertial wave attractor in linear and nonlinear regimes." Journal of Fluid Mechanics 745 (March 19, 2014): 223–50. http://dx.doi.org/10.1017/jfm.2014.63.
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AbstractIn a uniformly rotating fluid, inertial waves propagate along rays that are inclined to the rotation axis by an angle that depends on the wave frequency. In closed domains, multiple reflections from the boundaries may cause inertial waves to focus onto particular structures known as wave attractors. These attractors are likely to appear in fluid containers with at least one boundary that is neither parallel nor normal to the rotation axis. A closely related process also applies to internal gravity waves in a stably stratified fluid. Such structures have previously been studied from a theoretical point of view, in laboratory experiments, in linear numerical calculations and in some recent numerical simulations. In the present paper, two-dimensional direct numerical simulations of an inertial wave attractor are presented. By varying the amplitude at which the system is forced periodically, we are able to describe the transition between the linear and nonlinear regimes as well as the characteristic properties of the two situations. In the linear regime, we first recover the results of the linear calculations and asymptotic theory of Ogilvie (J. Fluid Mech., vol. 543, 2005, pp. 19–44) who considered a prototypical problem involving the focusing of linear internal waves into a narrow beam centred on a wave attractor in a steady state. The velocity profile of the beam and its scalings with the Ekman number, as well as the asymptotic value of the dissipation rate, are found to be in agreement with the linear theory. We also find that, as the beam builds up around the wave attractor, the power input by the applied force reaches its limiting value more rapidly than the dissipation rate, which saturates only when the beam has reached its final thickness. In the nonlinear regime, the beam is strongly affected and becomes unstable to a subharmonic instability. This instability transfers energy to secondary waves possessing shorter wavelengths and lower frequencies. The onset of the instability of a narrow inertial wave beam is investigated by means of a separate linear analysis and the results, such as the onset of the instability, are found to be consistent with the global simulations of the wave attractor. The excitation of such secondary waves described theoretically in this work has also been seen in recent laboratory experiments on internal gravity waves.
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Balthazar, Jose M., Jorge L. Palacios Felix, and Reyolando M. L. R. F. Brasil. "Short Comments on Self-Synchronization of Two Non-Ideal Sources Supported by a Flexible Portal Frame Structure." Journal of Vibration and Control 10, no. 12 (December 2004): 1739–48. http://dx.doi.org/10.1177/1077546304041754.
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A practical problem of synchronization of a non-ideal (i.e. when the excitation is influenced by the response of the system) and non-linear vibrating system was posed and investigated by means of numerical simulations. Two rotating unbalanced motors compose the mathematical model considered here with limited power supply mounted on the horizontal beam of a simple portal frame. As a starting point, the problem is reduced to a four-degrees-of-freedom model and its equations of motion, derived elsewhere via a Lagrangian approach, are presented. The numerical results show the expected phenomena associated with the passage through resonance with limited power. Further, for a two-to-one relationship between the frequencies associated with the first symmetric mode and the sway mode, by using the variation of torque constants, the control of the self-synchronization and synchronization (in the system) are observed at certain levels of excitations.