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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 140173, 9 pages
http://dx.doi.org/10.1155/2013/140173
Research Article

Nontrivial Periodic Solutions of an -Dimensional Differential System and Its Application

School of Mathematical Science, Yangzhou University, Yangzhou 225002, China

Received 29 March 2013; Accepted 3 August 2013

Academic Editor: Pei Yu

Copyright © 2013 F. B. Gao. 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

Two criteria are constructed to guarantee the existence of periodic solutions for a second-order -dimensional differential system by using continuation theorem. It is noticed that the criteria established are found to be associated with the system’s damping coefficient, natural frequency, parametrical excitation, and the coefficient of the nonlinear term. Based on the criteria obtained, we investigate the periodic motions of the simply supported at the four-edge rectangular thin plate system subjected to the parametrical excitation. The effectiveness of the criteria is validated by corresponding numerical simulation. It is found that the existent range of periodic solutions for the thin plate system increases along with the increase of the ratio of the modulus of nonlinear term’s coefficient and parametric excitation term, which generalize and improve the corresponding achievements given in the known literature.