Free in-plane vibration analysis of rectangular plates by the method of superposition

Gorman, Daniel

doi:10.1016/s0022-460x(03)00421-8

Cited by 101 publications

(45 citation statements)

References 4 publications

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“…With the help of difference formulas of (15) and (17), the nonlinear partial differential equation (10) can be discretized into a set of recurrence formulas…”

Section: Nonlinear Dynamics Of Forced Systemmentioning

confidence: 99%

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Dynamical analysis of axially moving plate by finite difference method

et al. 2011

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The complex natural frequencies for linear free vibrations and bifurcation and chaos for forced nonlinear vibration of axially moving viscoelastic plate are investigated in this paper. The governing partial differential equation of out-of-plane motion of the plate is derived by Newton's second law. The finite difference method in spatial field is applied to the differential equation to study the instability due to flutter and divergence. The finite difference method in both spatial and temporal field is used in the analysis of a nonlinear partial differential equation to detect bifurcations and chaos of a nonlinear forced vibration of the system. Numerical results show that, with the increasing axially moving speed, the increasing excitation amplitude, and the decreasing viscosity coefficient, the equilibrium loses its stability and bifurcates into periodic motion, and then the periodic motion becomes chaotic motion by period-doubling bifurcation.

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“…With the help of difference formulas of (15) and (17), the nonlinear partial differential equation (10) can be discretized into a set of recurrence formulas…”

Section: Nonlinear Dynamics Of Forced Systemmentioning

confidence: 99%

“…Vartik and Wickert paid more attention on parametric instability of torsional vibration of an axially moving plate supported by a laterally moving foundation [14]. Besides with the investigation of out-of-plane vibration, the inplane vibration has been explored analytically or numerically [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of axially moving plate by finite difference method

et al. 2011

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“…The same cases were solved by Wang and Wereley [29], utilising the Kantorovich variational method. Gorman employed a systematic superposition method to study the free inplane vibration of completely free [30] and fully clamped [18] plates. Nefovska-Danilovic et al [31] developed the dynamic stiffness method for isotropic rectangular plates based on Gorman's superposition method.…”

Section: Introductionmentioning

confidence: 99%

A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems

Xiang

Banerjee

2017

Mechanical Systems and Signal Processing

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Citation: Liu, X. and Banerjee, J. R. (2017). A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems. Mechanical Systems and Signal Processing, 87, doi: 10.1016/j.ymssp.2016.10.017 This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent AbstractA highly efficient and accurate analytical spectral dynamic stiffness (SDS) method for modal analysis of plane elastodynamic problems based on both plane stress and plane strain assumptions is presented in this paper. First, the general solution satisfying the governing differential equation exactly is derived by applying two types of one-dimensional modified Fourier series. Then the SDS matrix for an element is formulated symbolically using the exact general solution. The SDS matrices are assembled directly in a similar way to that of the finite element method, demonstrating the method's capability to model complex structures. Any arbitrary boundary conditions are represented accurately in the form of the modified Fourier series. The Wittrick-Williams algorithm is then used as the solution technique where the mode count problem (J 0 ) of a fully-clamped element is resolved. The proposed method gives highly accurate solutions with remarkable computational efficiency, covering low, medium and high frequency ranges. The method is applied to both plane stress and plane strain problems with simple as well as complex geometries. All results from the theory in this paper are accurate up to the last figures quoted to serve as benchmarks.

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“…Many researches [1][2][3][4][5][6] applied different variants of the superposition method to problems of vibrations of rectangular prisms and plates. Dynamic behavior of thin orthotropic plates is studied using the Rayleigh-Ritz method most fully in [7].…”

Section: Introductionmentioning

confidence: 99%

On improvement of the series convergence in the problem of the vibrations of orhotropic rectangular prism

Lyashko

2017

J. Phys.: Conf. Ser.

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Free in-plane vibration analysis of rectangular plates by the method of superposition

Cited by 101 publications

References 4 publications

Dynamical analysis of axially moving plate by finite difference method

Dynamical analysis of axially moving plate by finite difference method

A spectral dynamic stiffness method for free vibration analysis of plane elastodynamic problems

On improvement of the series convergence in the problem of the vibrations of orhotropic rectangular prism

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