薄壁梁桥的强非线性弯扭耦合振动解析解

采用非线性Rayleigh阻尼描述在运动初期有激发使运动加速至最大速度后开始衰减直到运动停止。本文的控制方程组是两个耦连的非线性偏微分方程，选用适合所有边界条件的两个振型函数代入控制方程组，应用Fourier级数的运算，得出两个无穷系列耦连的以时间为自变量的未知函数的二阶非线性常微分方程组，用迭代加法每次只取一个未知函数而化为一个van der Pol方程，得出其头两次的渐近解，讨论了解的跳跃特性，最后代入具体数据，得出数值结果。本文是文献（7）的深入，因（7）是弱非线性。

Coupled Bending and Twisting Vibration of Thin Walled Beam Bridges Excited by Horizontal Seismic Force with Nonlinear Damping

The nonlinear Rayleigh damping is adopted to depict exciting in the initial stage as well as decaying in the later stage.The governing equations are two coupled nonlinear PDEs which are deduced into two infinite systems of nonlinear ODEs by assuming the unknown functions fulfilling all the boundary conditions.Substituting them into the governing equations,applying the calculation of fourier series, and apppling the interatine method to solve the coupled nonlinear ODEs for each time to choose only one unknown function which is a van der Pol equation,the analytical solution is obtained finally.