水平地震时具有非线性阻尼的薄壁梁桥弯扭振动的渐近解

Asymptotic Solutions for Twisting and Bending Vibration of Thin-Walled Beam Bridge under Horizontal Seismic Force with Nonlinear Damping

本文采用非线性瑞利阻尼,它包括了运动初期低速时有激发,当速度达到极大值时又开始衰减。应用摄动方法把非线性控制方程组化为以无量纲的衰减系数为小参数的各阶线性渐近控制方程组,得出它们的每一个渐近方程组的解都是一个双重杜哈米积分。用一个具体例题说明本文方法的应用。

Abstract in this study,the nonlinear Rayleigh damping is adopted to depict the initial exciting state in low vibrational velocity and the decaying state at maximum velocity Perturbation method is adopted to deduce the nonlinear governing equa- tions into linear asymptotic governing equations for each order with non- dimensional small pamameter Analytical solutions are obtained in form of a two fold Duhamel integral for each asymptotic governing equation and an example is given to illustrate the approach.