斜拉索在平面内的非线性固有振动特性分析

研究斜拉索在平面内的非线性固有振动特性。从考虑抗弯刚度和垂度影响的斜拉索在平面内发生横向振动的非线性自由振动方程出发,对斜拉索发生单模态振动进行了分析,将拉索运动微分方程简化为带平方项的Du ffing方程,用摄动法求取反映该平方项影响的近似解析解,然后通过求解派生系统的特征值问题来分析拉索模态之间的耦合作用对拉索非线性动力学性质的影响,并与单模态振动分析结果进行了对比和验证。最后结合工程实例讨论分析了斜拉索重量、抗弯刚度、拉伸刚度、张力和倾斜角度对其非线性固有振动特性的影响。

Nonlinearly Natural Vibration Characteristic Analysis of Inclined Cable in Plane

The governing equations of free nonlinear transverse vibration inplane of the stayed cable are presented considering the effects of the flexural rigidity and the sag,the nonlinearly natural vibration characteristic is studied.When single mode vibration occurs,the governing equation is simplified as a traditional Duffing equation with a quadratic term.The perturbation method is used to solve approximately the Duffing equation.The influence of internal nonlinear couplings between the cable modes on nonlinear dynamics properties of stayed cable is studied by solving the eigenvalue problem of the derived system and a comparison is made with solution to single mode vibration analysis for the taut cable.Combined with engineering practice,an example is provided to study the influence of the weight,the flexural rigidity,the elongation rigidity,the tension,and the inclination angle on nonlinearly natural vibration characteristic of an inclined cable in plane.