Journal ArticleDOI
A Finite Element Approach to Plate Vibration Problems
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In this paper, a method of computing the natural frequencies of vibration of flat plates of arbitrary shape is outlined in which the plate is considered as an assemblage of elements and stiffness and inertia matrices are derived for a rectangular isotropic plate element of uniform thickness.Abstract:Â
A method of computing the natural frequencies of vibration of flat plates of arbitrary shape is outlined in which the plate is considered as an assemblage of elements.Both stiffness and inertia matrices are derived for a rectangular isotropic plate element of uniform thickness, and these matrices are used to find the natural frequencies of square plates subject to various boundary conditions. Comparison of finite element frequencies with known exact, experimental and energy solutions shows the method to give good results even for relatively few elements.read more
Citations
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Book
Introduction to finite element vibration analysis
TL;DR: In this article, the finite element displacement method was used for the analysis of free vibration of plates and shells, and for the simulation of forced response and forced response analysis of rigid and flexible plates.
Journal ArticleDOI
A review and catalogue of plate bending finite elements
M.M. Hrabok,T.M. Hrudey +1 more
TL;DR: A brief review of developments in the field of plate finite elements is presented in this article, followed by an extensive tabular listing of plate bending elements and their applications in the literature.
Journal ArticleDOI
The buckling and frequency of flexural vibration of rectangular isotropic and orthotropic plates using rayleigh's method
TL;DR: In this paper, a simple approximate formula for the natural frequencies of flexural vibration of isotropic plates, originally developed by Warburton using characteristic beam functions in Rayleigh's method, is modified to apply to specially orthotropic plates and extended to include the effect of uniform, direct inplane forces.
References
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Journal ArticleDOI
The Vibration of Rectangular Plates
TL;DR: In this article, the free transverse vibrations of rectangular plates with all possible boundary conditions obtained by combining free, freely-supported, and fixed edges were considered, and the effect on frequency of an edge being supported and partially restrained is discussed.
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A Stiffness Matrix for the Analysis of Thin Plates in Bending
TL;DR: In this article, a stiffness matrix for an isotropic rectangular plate panel of uniform thickness was developed for application to the analysis of thin plates of variable thickness in bending, and the convergence characteristics of this matrix were demonstrated on simple problems with known exact, analog, and experimental solutions.
Journal ArticleDOI
The Effect of Lumped Parameters on Beam Frequencies
F. A. Leckie,G. M. Lindberg +1 more
TL;DR: In this article, an investigation into the errors involved in using certain lumped parameter methods for the solution of beam frequencies has been made and a new dynamic stiffness matrix has been formulated, which gives consistently good results for even a few elements.
Journal ArticleDOI
Natural Frequencies of Uniform and Non-Uniform Rectangular Cantilever Plates:
TL;DR: In this article, various methods of calculating the natural frequencies of flat rectangular cantilever plates are discussed, and it is shown both analytically and experimentally that relatively simple expressions b...