The objective of this study is to estimate the statistics of the maximum values of the structural response when the system is excited by a non-stationary process. To provide basic information for the design of structures, the response of a one degree-of-freedom (1DOF) system subjected to a non-stationary Gaussian white noise is considered. For this purpose, we derive the probabilistic properties of the maximum values of non-stationary and zero-mean white noise, whose standard deviation varies temporally under some limited conditions. Then, using the obtained properties, a method is proposed to estimate the stochastic properties of the maximum response of a given 1DOF system excited by a non-stationary white noise whose time-varying standard deviation are known. Furthermore, the response spectra can be estimated easily using the proposed method and the appropriateness of the obtained results is con?rmed through Monte Carlo simulation.
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