The objective of the current paper is to study and extend the exponential-polynomial-closure (EPC) method in analyzing the non-stationary response probabilistic solutions of nonlinear stochastic oscillators excited by combined deterministic harmonic and Gaussian white noise excitations. The probabilistic solution of the non-stationary responses of nonlinear stochastic oscillator is expressed as an exponential function of polynomial with time-variant coefficients and then the Fokker–Planck–Kolmogorov equation is solved approximately. Two validation examples are presented. The results obtained by Monte Carlo simulation (MCS) and EPC method are presented to show their good agreement, which confirms the effectiveness of the EPC method for the probabilistic solutions to nonlinear stochastic oscillators. The advantage of the EPC method for analyzing the oscillators with strong nonlinearities is investigated by comparison with Equivalent Linearization method. Furthermore, compared with MCS, the computational efficiency by using the EPC method is increased by about 56 times in the first example and 44 times in the second example.
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