Energy-based formulation for nonlinear normal modes in cable-stayed beam

Based on Hamilton’s variational principle, the governing equations for in-plane dynamics of the model are obtained. Nonlinear normal modes for composite structure cable-stayed beam have been studied extensively in the literature. When all particles of the system reach their extremum values at the sa...

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Bibliographic Details
Published in:Applied mathematics and computation 2015-08, Vol.265, p.176-186
Main Authors: Wang, Zhiqian, Yi, Zhuangpeng, Luo, Yingshe
Format: Article
Language:English
Subjects:
Beams (structural)
Cable stayed beams
Cable-stayed beam
Dynamical systems
Mathematical analysis
Mathematical models
Nonlinear coupling term
Nonlinear dynamics
Nonlinear normal mode
Nonlinearity
Partial differential equations
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Summary:Based on Hamilton’s variational principle, the governing equations for in-plane dynamics of the model are obtained. Nonlinear normal modes for composite structure cable-stayed beam have been studied extensively in the literature. When all particles of the system reach their extremum values at the same instant of time, there are free periodic motions. A partial differential equation related to the modal function has been constructed by means of conservation of energy, which can be solved using a perturbation methodology. Most studies have been limited to uncoupling nonlinear terms of the system. This work investigated the nonlinear normal modes in the system that contains coupling nonlinear terms. The results of the two classes of nonlinear terms are also compared in this study.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2015.05.011