基于Volterra积分方程Taylor展开的卷积型非粘滞阻尼系统响应的时程分析方法

Time-history analysis of a multiple-degree-of-freedom system with convolutional type non-viscous damping is considered. In the non-viscously damped system, the damping force relates with the velocity time history by a convolution integral between the velocity and a decaying kernel function in its mathematical formulation. The damping model of this kind is a further generalization of the familiar viscous damping. Based on the Taylor expansion method for the second kind Volterra integral equation in a specific interval, the response function at different time points is Taylor expanded, which is substituted to the convolution integral kernel to eliminate the integral term in the equation, and the time-history response of the convolutional type damping model system is obtained by solving the time-varying linear equations. Numerical example demonstrates the effectiveness of the method. It is found that increasing the time step can greatly reduce the computation, but the accuracy will decrease slightly.