Comparison of Four Numerical Methods for Calculating Seismic Dynamic Response of Sdof System

The main characteristics of the numerical methods for dynamic response analysis of single degree of freedom (SDOF) system in both frequency-domain and time-domain are briefly reviewed in this paper. Based on the uniform recursive formula, four methods (Central difference method, Newmark’s method, Ztransform method and Duhamel’s step integral method) are systematically studied. The advantages, disadvantages, relative precision and applicability 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 calculating 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 if the recursive algorithm of relative displacement is known, the corresponding recursive equation of relative velocity or acceleration will be obtained easily. At last, a series of new algorithms for calculating displacement, velocity and acceleration response of SDOF system to arbitrary under ground motion are suggested.