摘要
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。
A time-domain method for computing foundation impedance force is proposed in this paper.The high-order ordinary differential equations in time are first obtained from a stable and accurate continuous-time rational approximation（CRA） of foundation dynamic stiffness by introducing an auxiliary variable and performing inverse Fourier transform.The equivalent first-order system of ordinary differential equations in time as a state-space description is then obtained by defining above auxiliary variable in different instants as some different new auxiliary variables,whose stability and accuracy are identical with those of the CRA.The fourth-order Runge-Kutta formula is finally applied to solve the resulting first-order system.The effectiveness of the proposed method is indicated by analyzing several foundation vibration problems.
出处
《工程力学》
EI
CSCD
北大核心
2010年第3期62-66,共5页
Engineering Mechanics
基金
国家重点基础研究发展计划项目(2007CB714203)
国家自然科学基金项目(90715041
90715035
90510011)
关键词
基础阻抗
时域算法
辅助变量
常微分方程
龙格-库塔公式
foundation impedance
time-domain method
auxiliary variable
ordinary differential equation
Runge-Kutta formula
