弹性半空间上弹性扁壳非线性动力响应解析解

用非线性瑞雷阻尼描述包括激发和衰减的地震运动,首先导出问题的控制方程组及定解条件,然后用摄动方法,得到线性的各阶渐近控制方程组及定解条件假定未知函数为只含时间变量的待定函数乘上满足边界条件的富氏级数,得出各阶的渐近解为双重杜哈米积分,最后,通过一个具体算例说明本文方法的应用。

Analytical Solutions for Nonlinear Dynamic Response of Shallow Shell Foundation on Elastical Half Space

In this paper,we adopt the nonlinear Rayleigh Damping which describes the damping and the decaying processes.First,the governing equations are derived, then, the linearized asymptotical governing equations for each order of the nondimensional small parameter of the nonlinear term in each equation by perturbation technique are obtained.By assuming the unknown functions to be double Fourier series with unknown functions of time only, we deduce the linearized governing equations of each order to be ordinary differential equation of order four, and the Solution is expressed by a double Duhamel integral.An example is given to illustrate our method.