Vibration analysis of moderately thick skew plates by a variational approach
About: This article is published in Journal of Sound and Vibration.The article was published on 1985-07-01. It has received 13 citations till now. The article focuses on the topics: Skew.
Citations
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TL;DR: The first known three-dimensional study of skewed cantilevered thick plates was performed in this article, where the assumed displacement functions are in the form of algebraic polynomials which satisfy the fixed face conditions exactly, and which are mathematically complete.
72 citations
TL;DR: In this article, the authors examined the accuracy and convergence behaviors of polynomial basis function differential quadrature (PDQ) and harmonic basis function DQ for free vibration analysis of variable thickness skew plates.
49 citations
TL;DR: In this article, the free vibration characteristics of skew thick plates with arbitrary boundary conditions have been studied based on the three-dimensional, linear and small strain elasticity theory, and the actual skew plate domain is mapped onto a basic cubic domain and the eigenvalue equation is derived from the energy functional of the plate by using the Ritz method.
42 citations
TL;DR: In this paper, the effect of the skew angle and chord ratio on a series of trapezoidal and triangular planforms has been investigated for C0 continuous, Lagrangian isoparametric plate finite element analyses.
24 citations
TL;DR: In this article, the spline element method based on the Mindlin plate theory was applied to analyze the vibration of skew Mindlin plates with varying thickness in the longitudinal direction, and several examples were solved, and results were compared with those obtained by other numerical methods.
20 citations
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4,554 citations
TL;DR: In this article, the Rayleigh-Ritz method is applied to the prediction of the natural frequencies of flexural vibration of square plates having general boundary conditions, based on the use of Mindlin plate theory so that the effects of shear deformation and rotary inertia are included.
162 citations
TL;DR: In this paper, an isoparametric quadrilateral plate bending element is used for the free and forced vibration analysis of both thick and thin plates, and the element performance is assessed by comparison with analytical solutions based on Mindlin's thick plate theory, three-dimensional elasticity solutions and solution based on thin plate theory.
Abstract: An isoparametric quadrilateral plate bending element is used for the free and forced vibration analysis of both thick and thin plates. Plates of rectangular, circular and triangular planform are analysed and excellent results are obtained. The element performance is assessed by comparison with analytical solutions based on Mindlin's thick plate theory, three-dimensional elasticity solutions and solutions based on thin plate theory.
69 citations
TL;DR: In this paper, a finite strip analysis of the vibration of rectangular Mindlin plates with general boundary conditions is described, where the normal modes of vibration of Timoshenko beams are used to represent the spatial variation along a strip of the deflection and the two cross-sectional rotations.
58 citations
TL;DR: In this paper, an isoparametric quadrilateral plate bending element is introduced and its use for the free vibration analysis of both thick and thin plates is examined and excellent results are obtained.
54 citations