摘要
考虑一个具有卷积型非粘滞阻尼特性的多自由度系统响应的时程分析问题。非粘滞阻尼模型假设阻尼力与质点速度的时间历程相关,数学表达式为阻尼力等于质点速度与某一核函数的卷积,该模型为常用的粘滞阻尼模型的一般化形式。以一种在特定区间内求解第二类Volterra方程的Taylor展开法为基础,对所分析时段中各时间点的响应函数逐步作Taylor展开,代入卷积核来消去运动方程的积分项,通过求解推导出的时变线性方程组完成对卷积型阻尼模型系统的时程响应分析。数值算例验证了该方法的有效性。该方法增大时间步长可以大幅减少计算量,计算精度有所下降。
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.
出处
《应用力学学报》
CAS
CSCD
北大核心
2018年第2期261-266,共6页
Chinese Journal of Applied Mechanics
基金
国家自然科学基金(51378155)
