Approximate Series Solutions for Nonlinear Free Vibration of Suspended Cables
Approximate Series Solutions for Nonlinear Free Vibration of Suspended Cables
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DOI：
10.1155/2014/795708
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发表时间：
2014-03
影响因子：
1.6
通讯作者：
Yaobing Zhao;Ceshi Sun;Zhiqian Wang;Lianhua Wang
中科院分区：
文献类型：
--
作者：
Yaobing Zhao;Ceshi Sun;Zhiqian Wang;Lianhua Wang
本文分别用Lindstedt-Poincare法和同伦分析法给出了悬索非线性自由振动的近似级数解。首先，考虑悬索的几何非线性和准静态假设，建立了悬索的数学模型。其次，介绍了非线性自由振动情况下的近似级数解的两种解析方法。此外，还分别选取了小矢跨比和大矢跨比两种初始条件，利用这两种分析方法对结构的非线性动力响应进行了研究。数值结果表明，频率振幅关系与不同的分析方法得到的运动，振型，和特定的垂跨比的情况下表现出一些定量和定性的差异。最后，对位移场和索轴向总拉力的差异进行了详细的比较。
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.