Vibration of moderately thick square orthotropic stepped thickness plates
TL;DR: In this article, the frequency of vibration analysis of orthorhombic material properties of aragonite was performed using the finite element method to compute frequencies and determine mode shapes for simply supported and clamped square Mindlin plates.
About: This article is published in Applied Acoustics.The article was published on 2003-07-01. It has received 20 citations till now. The article focuses on the topics: Vibration of plates & Plate theory.
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TL;DR: In this paper, the free vibration analysis of multilayered laminated composite and sandwich plates using various methods available for the analysis of plates is presented and compared with other higher order shear deformation theories.
284 citations
Additional excerpts
...Hull and Buchanan [148] presented vibration analysis of square orthotropic stepped plates based on finite element method....
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TL;DR: A semi-analytical differential quadrature element method (DQEM) based on first-order shear deformation theory for free vibration analysis of thick plates is introduced in this paper.
52 citations
TL;DR: In this paper, a variational principle of minimum total energy and the extended Kantorovich method were used to investigate the vibration behaviors of stepped plates. But the results from the proposed approach are in good agreement with results from past studies and those of the finite element method.
Abstract: In this study, vibration behaviors of stepped plates are investigated based on the variational principle of minimum total energy and the extended Kantorovich method. The out-of-plane displacement is represented by a separable function of parameters x and y. A set of governing equations, boundary conditions, and continuity conditions in the form of ordinary differential equations are derived from the energy condition. The natural frequency and out-of-plane displacement function can be determined numerically from the derived equations and conditions. Solutions from the proposed approach are in good agreement with results from past studies and those of the finite element method.
17 citations
Cites methods from "Vibration of moderately thick squar..."
...In addition to thin plate problems, Hull and Buchanan [18] applied Mindlin plate theory to vibration problems of isotropic and orthotropic stepped thickness plates....
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TL;DR: In this paper, an analytical solution for the vibration response of a beam-stiffened Mindlin plate using a modal expansion solution approach was presented, which was utilized to evaluate the prediction discrepancy using a thin (ribbed) plate model.
14 citations
TL;DR: In this article, a comparative study on advances in the shear deformation theory for analyzing the statics and dynamics of different plates with the use of numerical examples is performed, and shape functions for the displacement field across the plate thickness are compared, and then, the stresses, deflections, and natural frequencies of laminated composite plates are also compared.
Abstract: An attempt has been made to perform a comparative study on advances in the shear deformation theory for analyzing the statics and dynamics of different plates with the use of numerical examples. Initially, shape functions for the displacement field across the plate thickness are compared, and then, the stresses, deflections, and natural frequencies of laminated composite plates are also compared.
13 citations
Cites methods from "Vibration of moderately thick squar..."
...[121] analyzed the vibration parameter of LCPs resting on elastically restrained edges by the FEA....
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References
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TL;DR: In this article, a unified exact analysis for the statics and dynamics of a class of thick laminates is presented, which leads to simple infinite series for stresses and displacements in flexure, forced vibration and "beam-column" type problems and to closed form characteristic equations for free vibration and buckling problems.
770 citations
TL;DR: In this paper, the authors present analytical solutions for the free vibration analysis of laminated composite and sandwich plates based on two higher order re,ned theories already developed by the,rst author for which analytical formulations and solutions were not reported earlier in the literature.
133 citations
TL;DR: In this paper, a Rayleigh-Ritz approach for the study of the free vibration of systems comprised of rectangular plates is presented; the choice of the deflection functions for the component plates is simplified through the use of the concept of artificial springs being introduced at the joints between the plates and at the system boundaries; the shape functions for each component are thus those for a fully free plate.
122 citations
Book•
01 Jul 1988
TL;DR: A detailed survey of elasticity theory can be found in this article, with a discussion of the basic equations and associated boundary conditions of the elasticity of transversely loaded and initially stressed plates.
Abstract: Mathematical preliminaries survey of elasticity theory fundamentals of plate theory basic equations and associated boundary conditions static deformation of transversely loaded plates dynamics of plates initially stressed plates - elastic instability numerical methods nonlinear considerations laminated plates.
119 citations
TL;DR: In this article, the vibration characteristics of stepped thickness plates of rectangular geometry with simply supported edges are investigated through an exact analysis, and numerical calculations have been made for various combinations of thickness step, step-length ratio and side ratio.
74 citations