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Stochastic response of nonlinear oscillators under non-homogeneous Poisson white noise excitations
https://orcid.org/0000-0003-1218-7741
Abstract Poisson white noise is a typical non-Gaussian process. It is generally utilized to model stationary loadings by the assumed constant impulse arrival rate. Much research work has been done on that. However, the actual impulse arrival times of some discrete loadings are not uniform in the given time duration. The resulting arrival rate is a time-varying function instead of a constant one. Corresponding Poisson process is non-homogeneous. Less work in the literature has been found. In this paper, a Poisson white noise process with a time-varying impulse arrival rate is considered in the excitation model. Under such excitation the response of nonlinear system is a Markov process. The resulting generalized time-dependent Fokker–Planck equation becomes more complicated. The perturbation method, combined with the exponential-polynomial closure (EPC) method, is utilized to solve this equation. Examples of typical nonlinear systems under non-homogeneous Poisson white noise excitations are investigated. The effect of time-varying impulse arrival rate on the response is illustrated. Numerical results show that the response statistical characteristics depend strongly on the impulse arrival rate. Large errors would generate if the arrival rate varies fast over time and is still treated as an average constant.
Highlights Stochastic response of nonlinear oscillators under non-homogeneous Poisson white noise excitation is investigated. The improved perturbation method, combined with the EPC method, is utilized to solve the FPK equation. The obtained approximate results agree well with the simulated ones, which has verified the efficiency of the proposed method. Response statistical characteristics depends strongly on the impulse arrival rate, which indicates the non-Gaussianity of excitation cannot be ignored.
Stochastic response of nonlinear oscillators under non-homogeneous Poisson white noise excitations
https://orcid.org/0000-0003-1218-7741
Abstract Poisson white noise is a typical non-Gaussian process. It is generally utilized to model stationary loadings by the assumed constant impulse arrival rate. Much research work has been done on that. However, the actual impulse arrival times of some discrete loadings are not uniform in the given time duration. The resulting arrival rate is a time-varying function instead of a constant one. Corresponding Poisson process is non-homogeneous. Less work in the literature has been found. In this paper, a Poisson white noise process with a time-varying impulse arrival rate is considered in the excitation model. Under such excitation the response of nonlinear system is a Markov process. The resulting generalized time-dependent Fokker–Planck equation becomes more complicated. The perturbation method, combined with the exponential-polynomial closure (EPC) method, is utilized to solve this equation. Examples of typical nonlinear systems under non-homogeneous Poisson white noise excitations are investigated. The effect of time-varying impulse arrival rate on the response is illustrated. Numerical results show that the response statistical characteristics depend strongly on the impulse arrival rate. Large errors would generate if the arrival rate varies fast over time and is still treated as an average constant.
Highlights Stochastic response of nonlinear oscillators under non-homogeneous Poisson white noise excitation is investigated. The improved perturbation method, combined with the EPC method, is utilized to solve the FPK equation. The obtained approximate results agree well with the simulated ones, which has verified the efficiency of the proposed method. Response statistical characteristics depends strongly on the impulse arrival rate, which indicates the non-Gaussianity of excitation cannot be ignored.
Stochastic response of nonlinear oscillators under non-homogeneous Poisson white noise excitations
https://orcid.org/0000-0003-1218-7741
Abstract Poisson white noise is a typical non-Gaussian process. It is generally utilized to model stationary loadings by the assumed constant impulse arrival rate. Much research work has been done on that. However, the actual impulse arrival times of some discrete loadings are not uniform in the given time duration. The resulting arrival rate is a time-varying function instead of a constant one. Corresponding Poisson process is non-homogeneous. Less work in the literature has been found. In this paper, a Poisson white noise process with a time-varying impulse arrival rate is considered in the excitation model. Under such excitation the response of nonlinear system is a Markov process. The resulting generalized time-dependent Fokker–Planck equation becomes more complicated. The perturbation method, combined with the exponential-polynomial closure (EPC) method, is utilized to solve this equation. Examples of typical nonlinear systems under non-homogeneous Poisson white noise excitations are investigated. The effect of time-varying impulse arrival rate on the response is illustrated. Numerical results show that the response statistical characteristics depend strongly on the impulse arrival rate. Large errors would generate if the arrival rate varies fast over time and is still treated as an average constant.
Highlights Stochastic response of nonlinear oscillators under non-homogeneous Poisson white noise excitation is investigated. The improved perturbation method, combined with the EPC method, is utilized to solve the FPK equation. The obtained approximate results agree well with the simulated ones, which has verified the efficiency of the proposed method. Response statistical characteristics depends strongly on the impulse arrival rate, which indicates the non-Gaussianity of excitation cannot be ignored.
Stochastic response of nonlinear oscillators under non-homogeneous Poisson white noise excitations
Meng, Fei-Fan (Autor:in) / Shi, Qingxuan (Autor:in) / Guo, Siu-Siu (Autor:in)
Engineering Structures ; 303
09.01.2024
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
Nonlinear Systems With Poisson White Noise
| British Library Conference Proceedings | 1997
Nonlinear Systems with Poisson White Noise
| British Library Conference Proceedings | 1996