论文部分内容阅读
该文提出一种计算基础阻抗力的时域算法。通过引入一个辅助变量并执行逆傅里叶变换,将基础动力刚度的连续时间有理近似实现为时域高阶常微分方程;进一步定义不同时刻的辅助变量为多个不同的辅助变量,将高阶微分方程等价地转化为以状态空间描述的一阶常微分方程组。微分方程组的稳定性和精度等价于连续时间有理近似的稳定性和精度。之后采用四阶龙格-库塔公式数值地求解获得的一阶微分方程组。典型基础振动问题的分析表明了该文方法的有效性。
This paper presents a time-domain algorithm for calculating the fundamental impedance. By introducing an auxiliary variable and performing inverse Fourier transform, the continuous time of fundamental dynamic stiffness can be reasonably approximated as a high-order ordinary differential equation in time domain. Further, the auxiliary variables at different moments are defined as a number of different auxiliary variables, Differential equations are equivalently transformed into first-order ordinary differential equations described in state space. The stability and accuracy of the system of differential equations is equivalent to the stability and accuracy of rational approximation of continuous time. Afterwards, the first-order differential equations obtained by numerical solution of the fourth-order Runge-Kutta formula are obtained. The analysis of typical foundation vibration problems shows the effectiveness of the method.