First passage of stochastically dynamical system with fractional derivative and power-form restoring force under Gaussian excitation
First passage problem in a dynamical system with power-form restoring force and fractional derivative is studied in this paper. At first, the original system is transformed into an diffusion differential equation by way of generalized Van der Pol transformation and stochastic averaging method. After...
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| Format: | Article |
| Language: | English |
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University of Belgrade - Faculty of Mechanical Engineering, Belgrade
2014-01-01
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| Series: | FME Transactions |
| Subjects: | |
| Online Access: | https://scindeks-clanci.ceon.rs/data/pdf/1451-2092/2014/1451-20921404277W.pdf |
| _version_ | 1818109151552733184 |
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| author | Wei Li Trišović Nataša Cvetković Aleksandar |
| author_facet | Wei Li Trišović Nataša Cvetković Aleksandar |
| author_sort | Wei Li |
| collection | DOAJ |
| description | First passage problem in a dynamical system with power-form restoring force and fractional derivative is studied in this paper. At first, the original system is transformed into an diffusion differential equation by way of generalized Van der Pol transformation and stochastic averaging method. After that , according to the definition of first passage, BK equation and GP equation are constructed and solved. The numerical results tell us that the reliability probabilities are decreased monotonously with respect to time. Higher order of fractional derivative can lead to higher reliability of the system. Boundary value of safe domain can affect the reliability probability greatly. The larger it is, the higher probability value is. |
| first_indexed | 2024-12-11T02:26:42Z |
| format | Article |
| id | doaj.art-6e1ddf5a7cff4d5abadf5fff5c63fd85 |
| institution | Directory Open Access Journal |
| issn | 1451-2092 2406-128X |
| language | English |
| last_indexed | 2024-12-11T02:26:42Z |
| publishDate | 2014-01-01 |
| publisher | University of Belgrade - Faculty of Mechanical Engineering, Belgrade |
| record_format | Article |
| series | FME Transactions |
| spelling | doaj.art-6e1ddf5a7cff4d5abadf5fff5c63fd852022-12-22T01:23:54ZengUniversity of Belgrade - Faculty of Mechanical Engineering, BelgradeFME Transactions1451-20922406-128X2014-01-014242772801451-20921404277WFirst passage of stochastically dynamical system with fractional derivative and power-form restoring force under Gaussian excitationWei Li0Trišović Nataša1https://orcid.org/0000-0003-1043-5780Cvetković Aleksandar2School of Mathematics and Statistics, Xidian University, Xi'an, Shaanxi, ChinaUniversity of Belgrade, Faculty of Mechanical Engineering, Department of MechanicsUniversity of Belgrade, Faculty of Mechanical Engineering, Department of MechanicsFirst passage problem in a dynamical system with power-form restoring force and fractional derivative is studied in this paper. At first, the original system is transformed into an diffusion differential equation by way of generalized Van der Pol transformation and stochastic averaging method. After that , according to the definition of first passage, BK equation and GP equation are constructed and solved. The numerical results tell us that the reliability probabilities are decreased monotonously with respect to time. Higher order of fractional derivative can lead to higher reliability of the system. Boundary value of safe domain can affect the reliability probability greatly. The larger it is, the higher probability value is.https://scindeks-clanci.ceon.rs/data/pdf/1451-2092/2014/1451-20921404277W.pdffractional derivativedynamical systemrestoring forcegaussian excitationreliability |
| spellingShingle | Wei Li Trišović Nataša Cvetković Aleksandar First passage of stochastically dynamical system with fractional derivative and power-form restoring force under Gaussian excitation FME Transactions fractional derivative dynamical system restoring force gaussian excitation reliability |
| title | First passage of stochastically dynamical system with fractional derivative and power-form restoring force under Gaussian excitation |
| title_full | First passage of stochastically dynamical system with fractional derivative and power-form restoring force under Gaussian excitation |
| title_fullStr | First passage of stochastically dynamical system with fractional derivative and power-form restoring force under Gaussian excitation |
| title_full_unstemmed | First passage of stochastically dynamical system with fractional derivative and power-form restoring force under Gaussian excitation |
| title_short | First passage of stochastically dynamical system with fractional derivative and power-form restoring force under Gaussian excitation |
| title_sort | first passage of stochastically dynamical system with fractional derivative and power form restoring force under gaussian excitation |
| topic | fractional derivative dynamical system restoring force gaussian excitation reliability |
| url | https://scindeks-clanci.ceon.rs/data/pdf/1451-2092/2014/1451-20921404277W.pdf |
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