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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 642782, 14 pages
http://dx.doi.org/10.1155/2014/642782
Research Article

Transverse Vibration and Waves in a Membrane: Frequency Domain Spectral Element Modeling and Analysis

Department of Mechanical Engineering, Inha University, 100 Inharo, Nam-gu, Incheon 402-751, Republic of Korea

Received 23 June 2014; Revised 12 August 2014; Accepted 13 August 2014; Published 9 September 2014

Academic Editor: Gen Qi Xu

Copyright © 2014 Jungho Park et al. 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.

Abstract

Although the spectral element method (SEM) has been well recognized as an exact continuum element method, its application has been limited mostly to one-dimensional (1D) structures, or plates that can be transformed into 1D-like problems by assuming the displacements in one direction of the plate in terms of known functions. We propose a spectral element model for the transverse vibration of a finite membrane subjected to arbitrary boundary conditions. The proposed model is developed by using the boundary splitting method and the waveguide FEM-based spectral super element method in combination. The performance of the proposed spectral element model is numerically validated by comparison with exact solutions and solutions using the standard finite element method (FEM).