A simple and unified displacement field for three-dimensional vibration analysis of prestressed circular plates

Liu, Chorng-Fuh; Chen, Ting-Jung

doi:10.1177/1077546311430245

Cited by 2 publications

(1 citation statement)

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“…In their study, the polynomial-Ritz method was utilized to solve the eigenvalue problem. A simple and unified method for three-dimensional vibration analysis of prestressed circular plates was proposed by Liu and Chen (2013).…”

Section: Introductionmentioning

confidence: 99%

A unified method for free vibration analysis of circular, annular and sector plates with arbitrary boundary conditions

Shi

et al. 2014

Journal of Vibration and Control

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The vibrations of circular, annular, and sector plates are traditionally considered as different boundary value problems and often treated using different solution algorithms and procedures. This problem is further compounded by the fact that the solution for each type of plate typically needs to be adapted to different boundary conditions. In this paper, a simple solution method is proposed for a unified vibration analysis of annular, circular and sector plates with arbitrary boundary conditions. Regardless of the shapes of the plates and the types of boundary conditions, the displacement solutions are invariably expressed as a new and simple form of trigonometric series expansion with an accelerated convergence rate. The unification of seemingly different boundary value problems for the circular and annular plates and their sector counterparts is physically accomplished by applying a set of coupling springs to ensure appropriate continuity conditions along the radial edges. 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. It should be noted that the current method can be easily applied to sector plates with an arbitrary inclusion angle up to 2 π.

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Section: Introductionmentioning

confidence: 99%