Probabilistic solutions of a variable-mass system under random excitations
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 deri...
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| Veröffentlicht in: | Acta mechanica 2020-07, Vol.231 (7), p.2815-2826 |
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| creator | Jiang, Wen-An Han, Xiu-Jing Chen, Li-Qun Bi, Qin-Sheng |
| description | 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. |
| doi_str_mv | 10.1007/s00707-020-02674-y |
| format | Article |
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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.</description><identifier>ISSN: 0001-5970</identifier><identifier>EISSN: 1619-6937</identifier><identifier>DOI: 10.1007/s00707-020-02674-y</identifier><language>eng</language><publisher>Vienna: Springer Vienna</publisher><subject>Algorithms ; Classical and Continuum Physics ; Comparative analysis ; Computer simulation ; Control ; Distribution (Probability theory) ; Dynamical Systems ; Engineering ; Engineering Fluid Dynamics ; Engineering Thermodynamics ; Heat and Mass Transfer ; Monte Carlo method ; Monte Carlo simulation ; Nonlinear systems ; Original Paper ; Polynomials ; Probability density functions ; Runge-Kutta method ; Solid Mechanics ; Statistical analysis ; Theoretical and Applied Mechanics ; Variable mass systems ; Vibration</subject><ispartof>Acta mechanica, 2020-07, Vol.231 (7), p.2815-2826</ispartof><rights>Springer-Verlag GmbH Austria, part of Springer Nature 2020</rights><rights>COPYRIGHT 2020 Springer</rights><rights>Springer-Verlag GmbH Austria, part of Springer Nature 2020.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c358t-fd22d13a6a0312f07e95d49fd28e5cd42ab97c61e440833ef2e2847b77f15283</citedby><cites>FETCH-LOGICAL-c358t-fd22d13a6a0312f07e95d49fd28e5cd42ab97c61e440833ef2e2847b77f15283</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00707-020-02674-y$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00707-020-02674-y$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Jiang, Wen-An</creatorcontrib><creatorcontrib>Han, Xiu-Jing</creatorcontrib><creatorcontrib>Chen, Li-Qun</creatorcontrib><creatorcontrib>Bi, Qin-Sheng</creatorcontrib><title>Probabilistic solutions of a variable-mass system under random excitations</title><title>Acta mechanica</title><addtitle>Acta Mech</addtitle><description>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. 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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.</abstract><cop>Vienna</cop><pub>Springer Vienna</pub><doi>10.1007/s00707-020-02674-y</doi><tpages>12</tpages></addata></record> |
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| subjects | Algorithms Classical and Continuum Physics Comparative analysis Computer simulation Control Distribution (Probability theory) Dynamical Systems Engineering Engineering Fluid Dynamics Engineering Thermodynamics Heat and Mass Transfer Monte Carlo method Monte Carlo simulation Nonlinear systems Original Paper Polynomials Probability density functions Runge-Kutta method Solid Mechanics Statistical analysis Theoretical and Applied Mechanics Variable mass systems Vibration |
| title | Probabilistic solutions of a variable-mass system under random excitations |
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