Non-stationary response of MDOF dynamical systems under combined Gaussian and Poisson white noises by the generalized cell mapping method

• Published in: Probabilistic engineering mechanics Vol. 55; pp. 102 - 108
• Main Authors: Yue, Xiaole, Xu, Wei, Xu, Yong, Sun, Jian-Qiao
• Format: Journal Article
• Language: English
• Published: Barking Elsevier Ltd 01.01.2019; Elsevier Science Ltd
• Subjects: Block matrix analysis; Cell mapping method; Computer simulation; Degrees of freedom; Dynamical systems; Engineering; Matrix; Matrix methods; MDOF dynamical system; Non-stationary response; Nonlinear analysis; Nonlinear response; Nonlinear systems; Parameter estimation; Poisson distribution; Poisson white noise; Probability; Probability density functions; Stationary response; Stochastic models; Non-stationary response; MDOF dynamical system; Block matrix analysis; Poisson white noise; Cell mapping method
• ISSN: 0266-8920; 1878-4275
• DOI: 10.1016/j.probengmech.2019.01.001

A block matrix analysis procedure of the generalized cell mapping (GCM) method is proposed in this paper. The proposed method solves the storage problem in the response analysis of nonlinear stochastic dynamical system with the GCM method, and makes it possible to compute the non-stationary and stationary probability density functions (PDFs) of multi-degree-of-freedom (MDOF) nonlinear systems without using supercomputing. Two examples of two-degree-of-freedom systems under external or parametric excitations of combined Gaussian and Poisson white noises are presented to demonstrate the efficiency of the proposed method. Monte Carlo (MC) simulations are used to verify the accuracy of the solutions obtained with the proposed method. •The generalized cell mapping method based on block matrix analysis is presented.•Probability density functions of response of MDOF dynamical system can be obtained.•Non-stationary response of systems under Gaussian and Poisson white noises is studied.•The accuracy of the solutions is verified by the Monte Carlo (MC) simulations.