Generation of Time History Compatible with Multi-Damping Response Spectra

Based on the method developed by M. Hirasawa and M. Watabe (1992), the authors deduced the related mathematical formulas. Taking an artificial ground motion compatible with single-damping as the original time history, a small corrected time history was calculated by solving linear equations using a singular value decomposition method. We performed iteration to obtain the simulated earthquake motion compatible with multi-damping within a certain accuracy. The influences of selective matching frequencies are discussed preliminarily. Although the current criterion still has no explicit demand on different numbers of matching frequencies for various damping factors, it should be taken into account in practice.