On free vibration analysis of circular annular plates with non-uniform thickness by the differential quadrature method

Wang, X.; Yang, Jie; Xiao, Jun

doi:10.1006/jsvi.1995.0332

Cited by 35 publications

(11 citation statements)

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“…A final example of a numerical method is by Wang [22], who uses a differential quadrature (DQ) method to evaluate the natural frequencies of vibration of a plate whose thickness varies from m = ±1. This method allows highly accurate solutions to differential equations to be found using only a small number of grid points.…”

Section: Existing Solutions For Cylindrical Platesmentioning

confidence: 99%

Damping of flexural vibrations in circular plates with tapered central holes

O'Boy

Krylov

2011

Journal of Sound and Vibration

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The paper develops a numerical approach to the calculation of mobilities for a circular plate with a tapered central hole of power-law profile. The exact solution of the corresponding flexural wave equation that exists for m = 2 has been used in the process of the numerical solution of the corresponding boundary problem. Note that this value of m belongs to the power-law range m ≥ 2 associated with zero reflection of quasi-plane waves from a tapered hole in geometrical acoustics approximation. Two cases of added damping in the central hole area have been considered: a thin absorbing layer and a constrained layer. Cross and point mobilities have been calculated for both these cases. The obtained results for point and cross mobilities show a substantial suppression of resonant peaks (up to 17 dB), in comparison with the cases of a plate with an uncovered hole of the same power-law profile and of a reference circular plate of constant thickness covered or uncovered by a thin absorbing layer. Further theoretical and experimental research is needed to examine applications of the obtained numerical results to more practical situations, e.g. to rectangular plates or other structures with arbitrary locations of tapered holes.

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Section: Existing Solutions For Cylindrical Platesmentioning

confidence: 99%

Damping of flexural vibrations in circular plates with tapered central holes

O'Boy

Krylov

2011

Journal of Sound and Vibration

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“…Mcgee et al [4] analyzed free vibration of sectorial plates with complete free boundary conditions by a novel Ritz method. Then, the differential quadrature method was developed by Wang et al [5] to study the free vibration of circular annular plates with classical boundary conditions and non-uniform thickness. Moreover, Wang [6] also extended the differential quadrature method to research the free vibration of thin sector plates with various sector angles and six combinations of classical boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

A unified solution for free vibration of orthotropic circular, annular and sector plates with general boundary conditions

Shi¹,

Liang²,

Wang³

et al. 2016

J. vibroeng.

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This paper adopts a modified Fourier-Ritz approach to study the free vibration characteristics of orthotropic circular, annular and sector thin plates subjected to general boundary conditions. For the arbitrary plate forms and the boundary conditions, the displacements can be written in the form of a standard Fourier cosine series supplemented with several auxiliary functions. The auxiliary functions, which are closed-form and introduced to remove all the potential discontinuities of the original displacement function and its derivatives in the whole domain, can be usefully employed in improving the convergence of the results. The artificial boundary spring technique and artificial coupling spring technique are adopted to simulate the arbitrary boundary conditions and to ensure appropriate continuity conditions along the radial edges, respectively. Because the displacement field is sufficiently smooth in the whole solution domain, the accurate solution can be obtained by using the Ritz procedure on the basis of the energy functions. The accuracy, reliability and versatility of the current method are fully demonstrated and verified through numerical examples involving plates with various shapes and boundary conditions.

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“…Tomasiello [19] applied the differential quadrature method to initialboundary-value problems. Wang et al [20] presented the free vibration analysis of circular annular plates with nonuniform thickness by the differential quadrature method. Wang and Gu [21] presented the static analysis of frame structures by the differential quadrature element method.…”

Section: The Differential Quadrature Methodsmentioning

confidence: 99%

The Effect of Residual Stress on the Electromechanical Behavior of Electrostatic Microactuators

Hsu

2008

Active and Passive Electronic Components

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This work simulates the nonlinear electromechanical behavior of different electrostatic microactuators. It applies the differential quadrature method, Hamilton's principle, and Wilson-θ integration method to derive the equations of motion of electrostatic microactuators and find a solution to these equations. Nonlinear equation difficulties are overcome by using the differential quadrature method. The stresses of electrostatic actuators are determined, and the residual stress effects of electrostatic microactuators are simulated.

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On free vibration analysis of circular annular plates with non-uniform thickness by the differential quadrature method

Cited by 35 publications

References 0 publications

Damping of flexural vibrations in circular plates with tapered central holes

Damping of flexural vibrations in circular plates with tapered central holes

A unified solution for free vibration of orthotropic circular, annular and sector plates with general boundary conditions

The Effect of Residual Stress on the Electromechanical Behavior of Electrostatic Microactuators

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