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Probabilistic solutions of a variable-mass system under random excitations

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Abstract

The stationary probability density function (PDF) solution of a variable-mass system is calculated under Gaussian white noises and Poisson white noises, respectively. For small mass disturbance, the corresponding Fokker–Planck–Kolmogorov equation and Kolmogorov–Feller equation of the system are derived. The solution procedure based on the exponential–polynomial closure (EPC) method is formulated to obtain and study the probabilistic solutions of the strongly nonlinear variable-mass system subjected to Gaussian white noises and Poisson white noises. Both odd and even nonlinear variable-mass systems are considered. Compared with Monte Carlo simulation results, good agreement is achieved with the EPC method in the case of sixth-order polynomial. For large mass disturbance, the PDFs and logarithmic PDFs of displacement and velocity are numerically calculated via the fourth-order Runge–Kutta algorithm.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 11632008 and 11702119 ), the Natural Science Foundation of Jiangsu Province (No. BK20170565).

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Correspondence to Qin-Sheng Bi.

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Jiang, WA., Han, XJ., Chen, LQ. et al. Probabilistic solutions of a variable-mass system under random excitations. Acta Mech 231, 2815–2826 (2020). https://doi.org/10.1007/s00707-020-02674-y

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  • DOI: https://doi.org/10.1007/s00707-020-02674-y

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