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Shock and Vibration
Volume 2014 (2014), Article ID 795708, 12 pages
http://dx.doi.org/10.1155/2014/795708
Research Article

Approximate Series Solutions for Nonlinear Free Vibration of Suspended Cables

1College of Civil Engineering, Hunan University, Changsha, Hunan 410082, China
2College of Mechanical and Vehicle Engineering, Hunan University, Changsha, Hunan 410082, China

Received 16 October 2013; Accepted 24 February 2014; Published 20 March 2014

Academic Editor: Didier Rémond

Copyright © 2014 Yaobing Zhao 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

This paper presents approximate series solutions for nonlinear free vibration of suspended cables via the Lindstedt-Poincare method and homotopy analysis method, respectively. Firstly, taking into account the geometric nonlinearity of the suspended cable as well as the quasi-static assumption, a mathematical model is presented. Secondly, two analytical methods are introduced to obtain the approximate series solutions in the case of nonlinear free vibration. Moreover, small and large sag-to-span ratios and initial conditions are chosen to study the nonlinear dynamic responses by these two analytical methods. The numerical results indicate that frequency amplitude relationships obtained with different analytical approaches exhibit some quantitative and qualitative differences in the cases of motions, mode shapes, and particular sag-to-span ratios. Finally, a detailed comparison of the differences in the displacement fields and cable axial total tensions is made.