Random Response and Crossing Rate of Fractional Order Nonlinear System with Impact
The random response and mean crossing rate of the fractional order nonlinear system with impact are investigated through the equivalent nonlinearization technique. The random additive excitation is Gaussian white noise, while the impact is described by a phenomenological model, which is developed fr...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2021/6666843 |
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| _version_ | 1850163872742244352 |
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| author | Yang Zheng Jiayin Wu Ming Xu |
| author_facet | Yang Zheng Jiayin Wu Ming Xu |
| author_sort | Yang Zheng |
| collection | DOAJ |
| description | The random response and mean crossing rate of the fractional order nonlinear system with impact are investigated through the equivalent nonlinearization technique. The random additive excitation is Gaussian white noise, while the impact is described by a phenomenological model, which is developed from the actual impact process experiments. Based on the equivalent nonlinearization technique, one class of random nonlinear system with exact probability density function (PDF) solution of response is selected. The criterion of the appropriate equivalent nonlinear system is the similarity with the original system on the damping, stiffness, and inertia. The more similar, the higher the precision. The optimal unknown parameters of the equivalent random nonlinear system in the damping and stiffness terms are determined by the rule of smallest mean-square difference. In the view of equivalent nonlinearization technique, the response of the original system is the same as that of the equivalent system with the optimal unknown parameters in analytical solution manner. Then, the mean crossing rate is derived from stationary PDF. The consistence between the results from proposed technique and Monte Carlo simulation reveals the accuracy of the proposed analytical procedure. |
| format | Article |
| id | doaj-art-e9645676c3ce43b3b1a91f58b67c4dcd |
| institution | OA Journals |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-e9645676c3ce43b3b1a91f58b67c4dcd2025-08-20T02:22:06ZengWileyShock and Vibration1070-96221875-92032021-01-01202110.1155/2021/66668436666843Random Response and Crossing Rate of Fractional Order Nonlinear System with ImpactYang Zheng0Jiayin Wu1Ming Xu2Institute of Fluid Mechanics, China Jiliang University, Hangzhou 310018, ChinaHangzhou Hikrobot Intelligent Technology Co., Ltd., Hangzhou 310052, ChinaInstitute of Fluid Mechanics, China Jiliang University, Hangzhou 310018, ChinaThe random response and mean crossing rate of the fractional order nonlinear system with impact are investigated through the equivalent nonlinearization technique. The random additive excitation is Gaussian white noise, while the impact is described by a phenomenological model, which is developed from the actual impact process experiments. Based on the equivalent nonlinearization technique, one class of random nonlinear system with exact probability density function (PDF) solution of response is selected. The criterion of the appropriate equivalent nonlinear system is the similarity with the original system on the damping, stiffness, and inertia. The more similar, the higher the precision. The optimal unknown parameters of the equivalent random nonlinear system in the damping and stiffness terms are determined by the rule of smallest mean-square difference. In the view of equivalent nonlinearization technique, the response of the original system is the same as that of the equivalent system with the optimal unknown parameters in analytical solution manner. Then, the mean crossing rate is derived from stationary PDF. The consistence between the results from proposed technique and Monte Carlo simulation reveals the accuracy of the proposed analytical procedure.http://dx.doi.org/10.1155/2021/6666843 |
| spellingShingle | Yang Zheng Jiayin Wu Ming Xu Random Response and Crossing Rate of Fractional Order Nonlinear System with Impact Shock and Vibration |
| title | Random Response and Crossing Rate of Fractional Order Nonlinear System with Impact |
| title_full | Random Response and Crossing Rate of Fractional Order Nonlinear System with Impact |
| title_fullStr | Random Response and Crossing Rate of Fractional Order Nonlinear System with Impact |
| title_full_unstemmed | Random Response and Crossing Rate of Fractional Order Nonlinear System with Impact |
| title_short | Random Response and Crossing Rate of Fractional Order Nonlinear System with Impact |
| title_sort | random response and crossing rate of fractional order nonlinear system with impact |
| url | http://dx.doi.org/10.1155/2021/6666843 |
| work_keys_str_mv | AT yangzheng randomresponseandcrossingrateoffractionalordernonlinearsystemwithimpact AT jiayinwu randomresponseandcrossingrateoffractionalordernonlinearsystemwithimpact AT mingxu randomresponseandcrossingrateoffractionalordernonlinearsystemwithimpact |