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Shock and Vibration
Volume 15 (2008), Issue 3-4, Pages 425-434

On the Modeling of Beam Reinforced Thin Plates Using the Spectral Element Method

N.B.F. Campos and J.R.F. Arruda

State University of Campinas, Computational Mechanics Department, Rua Mendeleiev, 200, Cidade Universitária, Caixa Postal 6122, 13083-970 Campinas, SP, Brazil

Received 29 April 2007; Revised 29 April 2007

Copyright © 2008 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Modeling beam reinforced thin plates at mid and high frequencies through the most commonly used methods such as finite and boundary element methods frequently leads to unsatisfactory results, since the accuracy of these methods depends on the relation between the dimensions of the elements in which the structure was discretized and the wavelength. Due to this characteristic, the modeling using these techniques will require that the size of the elements becomes smaller as the frequency increases, while its number needs to be increased. For structures that are usual in some areas, like the aerospace industry, this will be possible only with an unreasonable computational effort, which is responsible for restricting the use of these methods practically to low-frequency applications. Semi-analytical methods such as the spectral element method do not need mesh refinement at higher frequencies, but they were very limited in the geometries and boundary conditions that can be treated. This paper presents a spectral element for rectangular thin plates reinforced symmetrically along the sides with Euler beams, which can be used to model plates with arbitrary boundary conditions. The method was verified by comparing its results with those obtained from a Finite Element model.