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Mathematical Problems in Engineering
Volume 2010, Article ID 561364, 17 pages
Research Article

L-P Perturbation Solution of Nonlinear Free Vibration of Prestressed Orthotropic Membrane in Large Amplitude

1College of Civil Engineering, Chongqing University, Chongqing 400045, China
2Key Laboratory of the Three Gorges Reservoir Region's Eco-Environment, Ministry of Education, Chongqing 400045, China

Received 25 May 2010; Accepted 30 September 2010

Academic Editor: Jaromir Horacek

Copyright © 2010 Liu Chang-jiang 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.


This paper reviewed the research on the nonlinear free vibration of pre-stressed orthotropic membrane, which is commonly applied in building membrane structures. We applied the L-P perturbation method to solve the governing equations of large amplitude nonlinear free vibration of rectangular orthotropic membranes and obtained a simple approximate analytical solution of the frequency and displacement function of large amplitude nonlinear free vibration of rectangular membrane with four edges simply supported. By giving computational examples, we compared and analyzed the frequency results. In addition, vibration mode of the membrane and displacement and time curve of each feature point on the membrane surface were analyzed in the computational example. Results obtained from this paper provide a simple and convenient method to calculate the frequency and lateral displacement of nonlinear free vibration of rectangular orthotropic membranes in large amplitude. Meanwhile, the results provide some theoretical basis for solving the response of membrane structures under dynamic loads and provide some computational basis for the vibration control and dynamic design of building membrane structures.