Generating ground motion by two new techniques of adding harmonic wave in the time domain and approximating to response spectrum as a whole

Abstract

In this paper, two new methods are introduced to fit response spectrum in generating earthquake acceleration time history. The first method is Adding Harmonic Wave in Time Domain (AHWTD). In this method, a control point of response spectrum is adjusted by adding a harmonic time history to the adjusted one. Three features of the method are that it has small cross interference, small amount of computation and it can give consideration to the amplitude envelope. The second one is Approximating Response Spectrum as a Whole (ARSW). This method has following feature. When adjust a time history that is decided by amplitude spectrum A k and phase spectrum φ k (k=0, 1, 2,..., n), the mean square root of every relative error E j (j=1, 2,..., M) between response spectrum and object spectrum V r= $$\sqrt {\sum\limits_{J = 1}^M {E_J^2 /M} } $$ is used to decide adjusting direction of any amplitude spectrum A k. Because E j and V r are functions of A k and φ k , the problem of fitting response spectrum in generating earthquake acceleration time history can be changed to a problem of finding minimum pont of V r. Restricted by Nyquist frequency, AHWTD is not suitable for high frequencies of response spectrum. Restricted by frequency distribution of FFT, the density of control points in the low frequency part can’t be too dense for ARSW. But two methods can replenish each other and get such a good fitting effect that we can fit the given peak ground acceleration and peak ground velocity well at the same time.