弹性圆拱在非平稳水平随机地震作用下的伽辽金法

Galerkin Method in Nonstationary Analysis of Horizontal Seismic Response of Elastic Circular Arch

应用虚拟激励法与伽辽金法相结合,分析弹性圆拱在非平稳水平随机地震作用下的随机响应问题.在建立圆拱动力平衡微分方程的基础上,通过选取适当的试函数,将动力平衡方程转化为线性常微分方程组.通过设定虚拟荷载,按确定性方法求解响应量的时变功率谱密度的近似解,并进一步求出响应的方差和各阶谱矩.由于采用较少的试函数就能获得较高的精度,大大提高了计算效率.

The nonstationary random response of elastic circular arch under horizontal seismic excitation was studied by the method combining the pseudo-excitation algorithm with Galerkin algorithm. On the basis of establishing the dynamical equilibrium differential equations of circular arch which can be transformed into system of linear ordinary differential equations by choosing appropriate trial functions, the approximate solution of evolutionary power spectrum density, variance and random spectral moment of response were solved by assuming pseudo-excitation load. The method is highly efficient owing to only using few trial functions.