Stochastic responses of nonlinear systems to nonstationary non-Gaussian excitations. (October 2020) - Guo, Siu-Siu; Shi, Qingxuan; Xu, Zhao-Dong
Highlights: Nonlinear oscillator under nonstationary non-Gaussian excitation is investigated. The EPC method is improved for nonlinear systems to non-Gaussian excitations. Response is primarily influenced by the energy content of the modulating function. Non-Gaussian effect has to be considered if impulse arrival rate is infrequent. Abstract: Some random excitations actually demonstrate a strong deviation from Gaussian. They are associated with strong non-Gaussian properties. In this paper, Poisson and filtered Poisson processes are utilized to describe such non-Gaussian excitations. Besides, nonstationarity has to be considered since excitation intensity is actually a varying process. It is modeled by multiplying stationary models with modulating functions. Based on the above, nonstationary responses of single-degree-of-freedom (SDOF) nonlinear systems under non-Gaussian excitations are investigated. Exponential polynomial closure (EPC) approximate method, which is previously proposed for analyzing stationary responses with Gaussian excitations, is further improved by taking time variable or additional state variables into account to determine nonstationary responses with non-Gaussian excitations. Examples of nonlinear systems under nonstationary Poisson and filtered Poisson excitations are analyzed to testify the improved solution procedure. Comparisons between EPC approximates and simulated results evidence that the EPC method is efficient. In addition, non-Gaussian and nonstationary properties of responses are analyzed. Nonationary effects with different modulating function are also discussed.