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Journal of Applied Mathematics
Volume 2014, Article ID 183257, 6 pages
Research Article

Nonlinear Dynamical Analysis for the Cable Excited with Parametric and Forced Excitation

College of Civil Engineering and Architecture, Xiamen University of Technology, Xiamen, Fujian 361024, China

Received 10 April 2014; Revised 20 August 2014; Accepted 7 September 2014; Published 19 October 2014

Academic Editor: Ali R. Ashrafi

Copyright © 2014 C. Z. Qian 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.


Considering the deck vibration effect on the cable in cable-stayed bridge, using nonlinear structure dynamics theory, the nonlinear dynamical equation for the stayed cable excited with deck vibration is proposed. Research shows that the vertical vibration of the deck has a combined parametric and forced excitation effect on the cable when the angle of the cable is taken into consideration. Using multiscale method, the 1/2 principle parametric resonance is studied and the bifurcation equation is obtained. Despite the parameters analysis, the bifurcation characters of the dynamical system are studied. At last, by means of numerical method and software MATHMATIC, the effect rules of system parameters to the dynamical behavior of the system are studied, and some useful conclusions are obtained.