It is a well-known fact that a non-stationary nature of earthquake motion is intensely controlled by phase spectrum. However, it has not yet been verified how the uncertainty of phase spectrum of earthquake motion affects the response of a structure. We, therefore, modeled stochastic characteristics of phase spectrum and derived a theoretical solution for mean and R.M.S response time histories of a SDOF system exited by a non-stationary input ground motion controlled by the stochastic phase characteristics. We also derived a methodology to estimate the peak response value using the concept of a complex envelope function.

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