Stochastic dynamic analysis of nonlinear MDOF systems under combined Gaussian and Poisson noise excitation based on DPIM

被引:16
作者
Chen, Hanshu [1 ]
Chen, Guohai [1 ]
Meng, Zeng [2 ]
Zhang, Yahui [1 ]
Yang, Dixiong [1 ]
机构
[1] Dalian Univ Technol, Int Res Ctr Computat Mech, Dept Engn Mech, State Key Lab StrucOal Anal Ind Equipment, Dalian 116024, Peoples R China
[2] Hefei Univ Technol, Sch Civil Engn, Hefei 230009, Peoples R China
基金
中国国家自然科学基金;
关键词
Random vibration; Nonlinear MDOF system; Combined Gaussian and Poisson white noise; excitation; Probability density integral equation; Direct probability integral method; WHITE-NOISE; HAMILTONIAN-SYSTEMS; NONSTATIONARY RESPONSE; PATH-INTEGRATION; RELIABILITY; STABILITY; EVOLUTION;
D O I
10.1016/j.ymssp.2022.109163
中图分类号
TH [机械、仪表工业];
学科分类号
0802 ;
摘要
Random vibration analysis of structures subjected to combined Gaussian and Poisson white noise excitation is a challenging issue. In this paper, a novel direct probability integral method (DPIM) is suggested to address stochastic responses and dynamic reliability of nonlinear multi-degree-offreedom (MDOF) systems under combined excitation. Firstly, probability density integral equation (PDIE) of MDOF system under combined excitation is derived based on the principle of probability conservation. Then, DPIM is proposed to achieve the probability density function of stochastic response by solving deterministic motion equation of MDOF system and PDIE in sequence. To solve PDIE, two techniques, i.e., partition of input probability space and smoothing of Dirac delta function, are introduced. From the perspective of probability conservation, furthermore, the equivalent relationship between the PDIE and the corresponding probability density differential equation of a Markov system under combined Gaussian and Poisson noise is established. Since Dirac delta function is analytically integrated as Heaviside function, the firstpassage dynamic reliability of MDOF system under combined excitation is readily evaluated by introducing the extreme value mapping of stochastic response. Finally, two nonlinear MDOF systems, including multiple-span bridge under combined vehicle load and non-stationary seismic excitation, are solved. Results demonstrate that the proposed DPIM is effective for random vibration and dynamic reliability analyses of MDOF structures excited by combined Gaussian and Poisson noise, and considering the randomness of vehicle load and seismic excitation simultaneously in the bridge design benefits the safe operation of bridge.
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页数:22
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