An approximate method is presented for obtaining analytical solutions for the conditional first passage probability of systems under modulated white noise excita- tion. As the method is based on VanMarcke's approximation, with normalization of the response introduced, the expected decay rates can be evaluated from the second-moment statistics instead of the correlation functions or spectrum density functions of the re- sponse of considered structures. Explicit solutions to the second-moment statistics of the response are given. Accuracy, effciency and usage of the proposed method are demon- strated by the first passage analysis of single-degree-of-freedom (SDOF) linear systems under two special types of modulated white noise excitations.
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