Effect of uncertain evolutionary PSD function of seismic excitation on peak response of MDOF systems

Abstract

Seismic excitation is inherently nonstationary with respect to time and frequency. The nonstationary excitation or process is commonly characterized by the evolutionary power spectral density (PSD) function, which may be represented by a time modulating function and a PSD function of a stationary process. This chapter describes an analysis procedure for evaluating probability that the peak response of a multi-degree-of-freedom (MDOF) system to nonstationary excitation exceeds a specified level. The analysis considers that the parameters controlling the evolutionary PSD function are uncertain. This uncertain arises from the consideration that a structural system is designed to withstand all potential earthquake threats. The model used for the PSD function of the stationary process is the Kanai–Tajimi model and the exponential modulating function is employed for the time modulating function. The first-passage probability distribution is used to represent the probability distribution of the peak responses. Using the obtained uniform hazard spectra (UHS), the probability associated with the peak responses of MDOF systems to nonstationary ground motions evaluated by the complete quadratic combination (CQC) rule is assessed. The results show that the use of CQC rule with the modal responses obtained from the UHS is adequate if the peak responses of MDOF system are dominated by the response of one mode.