A non-stationary stochastic model for periodic excitation with random phase modulation

The paper presents a non-stationary stochastic model for periodic excitation with random phase modulation, where the phase modulation is modeled as a modulated stationary. Gaussian process. Applications of the model are demonstrated by analysis of response of a single-degree-of-freedom (SDOF) system under such an excitation. The response is, in general, non-Gaussian. Cases of step, rectangular, and exponential envelopes are considered in the present study. The nonstationary second and fourth order moments are calculated by numerically solving the transient moment equations. Non-Gaussianity of the response is studied in terms of the non-stationary excess factor. Some numerical results are presented. The influences of system parameters, build-up and decay rates as well as duration of random phase modulation on the moment response of the SDOF system are discussed.