摘要
本文在简要总结了计算单自由度系统地震反应频域方法和时域方法的特点之后,按照统一的递归公式,系统地对计算单自由度体系的四种时域方法即中心差分方法、Newmark方法、Z变换方法、Duhamel逐步积分法进行了对比研究。通过递归系数b1和b2的不变性、传递函数的低频约束条件和相位特性以及数值分析等几个方面说明了上述方法各自的优缺点、相对精度和适用的范围。根据动力平衡方程的算子不变性,研究了上述方法的共性特征,揭示了相对位移、相对速度、相对加速度递归公式的内在联系,这表明只要知道相对位移的递归公式,相对速度、相对加速度的递归公式也就随之确定。在此基础上推荐了一套计算单自由度系统相对位移、相对速度、相对加速度地震反应的递归公式。
The main characteristics of numerical methods for calculating dynamic response of singledegree offreedom (SDOF) system in frequencydomain and timedomain are briefly reviewed in this paper. Based on the uniform recursive formula, four methods (central difference method, Newmark′s method, Z-transform method and Duhamel′s step integral method) are systematically studied. The advantages, disadvantages, relative precision and usage range of the four methods are pointed out through analyzing the invariance of recursive parameters b1 and b2 which are related to the poles of the transfer function of system, the constraint condition of the system transform function at low frequency and the phase properties of the digital filter in theory and numerical calculation have been presented. Based on the invariance of operators in dynamic equation common characteristics of the four methods and the interrelation among recursive equation of relative displacement, relative velocity and relative acceleration are also obtained. This means that if the recursive algorithm of relative displacement is known, the corresponding recursive algorithm of relative velocity or acceleration will be obtained easily. Finally, a set of new algorithms for calculating displacement, velocity and acceleration response of SDOF system to arbitrary ground motion are suggested.
出处
《地震工程与工程振动》
CSCD
北大核心
2003年第1期18-30,共13页
Earthquake Engineering and Engineering Dynamics
基金
国家自然科学基金项目(59895410)
中国地震局"十五"项目
