Response Analysis of the Three-Degree-of-Freedom Vibroimpact System with an Uncertain Parameter
The inherent non-smoothness of the vibroimpact system leads to complex behaviors and a strong sensitivity to parameter changes. Unfortunately, uncertainties and errors in system parameters are inevitable in mechanical engineering. Therefore, investigations of dynamical behaviors for vibroimpact syst...
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MDPI AG
2023-09-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/9/1365 |
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| author | Guidong Yang Zichen Deng Lin Du Zicheng Lin |
| author_facet | Guidong Yang Zichen Deng Lin Du Zicheng Lin |
| author_sort | Guidong Yang |
| collection | DOAJ |
| description | The inherent non-smoothness of the vibroimpact system leads to complex behaviors and a strong sensitivity to parameter changes. Unfortunately, uncertainties and errors in system parameters are inevitable in mechanical engineering. Therefore, investigations of dynamical behaviors for vibroimpact systems with stochastic parameters are highly essential. The present study aims to analyze the dynamical characteristics of the three-degree-of-freedom vibroimpact system with an uncertain parameter by means of the Chebyshev polynomial approximation method. Specifically, the vibroimpact system model considered is one with unilateral constraint. Firstly, the three-degree-of-freedom vibroimpact system with an uncertain parameter is transformed into an equivalent deterministic form using the Chebyshev orthogonal approximation. Then, the ensemble means responses of the stochastic vibroimpact system are derived. Numerical simulations are performed to verify the effectiveness of the approximation method. Furthermore, the periodic and chaos motions under different system parameters are investigated, and the bifurcations of the vibroimpact system are analyzed with the Poincaré map. The results demonstrate that both the restitution coefficient and the random factor can induce the appearance of the periodic bifurcation. It is worth noting that the bifurcations fundamentally differ between the stochastic and deterministic systems. The former has a bifurcation interval, while the latter occurs at a critical point. |
| first_indexed | 2024-03-10T22:47:02Z |
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| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T22:47:02Z |
| publishDate | 2023-09-01 |
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| spelling | doaj.art-2c8a36e70ae548e2aa81109d165bbca42023-11-19T10:36:36ZengMDPI AGEntropy1099-43002023-09-01259136510.3390/e25091365Response Analysis of the Three-Degree-of-Freedom Vibroimpact System with an Uncertain ParameterGuidong Yang0Zichen Deng1Lin Du2Zicheng Lin3Department of Engineering Mechanics, Northwestern Polytechnical University, Xi’an 710129, ChinaDepartment of Engineering Mechanics, Northwestern Polytechnical University, Xi’an 710129, ChinaSchool of Mathematics and Statistics, Northwestern Polytechnical University, Xi’an 710129, ChinaSchool of Mathematics and Statistics, Xidian University, Xi’an 710071, ChinaThe inherent non-smoothness of the vibroimpact system leads to complex behaviors and a strong sensitivity to parameter changes. Unfortunately, uncertainties and errors in system parameters are inevitable in mechanical engineering. Therefore, investigations of dynamical behaviors for vibroimpact systems with stochastic parameters are highly essential. The present study aims to analyze the dynamical characteristics of the three-degree-of-freedom vibroimpact system with an uncertain parameter by means of the Chebyshev polynomial approximation method. Specifically, the vibroimpact system model considered is one with unilateral constraint. Firstly, the three-degree-of-freedom vibroimpact system with an uncertain parameter is transformed into an equivalent deterministic form using the Chebyshev orthogonal approximation. Then, the ensemble means responses of the stochastic vibroimpact system are derived. Numerical simulations are performed to verify the effectiveness of the approximation method. Furthermore, the periodic and chaos motions under different system parameters are investigated, and the bifurcations of the vibroimpact system are analyzed with the Poincaré map. The results demonstrate that both the restitution coefficient and the random factor can induce the appearance of the periodic bifurcation. It is worth noting that the bifurcations fundamentally differ between the stochastic and deterministic systems. The former has a bifurcation interval, while the latter occurs at a critical point.https://www.mdpi.com/1099-4300/25/9/1365vibroimpact systembifurcationChebyshev polynomialuncertain parameter |
| spellingShingle | Guidong Yang Zichen Deng Lin Du Zicheng Lin Response Analysis of the Three-Degree-of-Freedom Vibroimpact System with an Uncertain Parameter Entropy vibroimpact system bifurcation Chebyshev polynomial uncertain parameter |
| title | Response Analysis of the Three-Degree-of-Freedom Vibroimpact System with an Uncertain Parameter |
| title_full | Response Analysis of the Three-Degree-of-Freedom Vibroimpact System with an Uncertain Parameter |
| title_fullStr | Response Analysis of the Three-Degree-of-Freedom Vibroimpact System with an Uncertain Parameter |
| title_full_unstemmed | Response Analysis of the Three-Degree-of-Freedom Vibroimpact System with an Uncertain Parameter |
| title_short | Response Analysis of the Three-Degree-of-Freedom Vibroimpact System with an Uncertain Parameter |
| title_sort | response analysis of the three degree of freedom vibroimpact system with an uncertain parameter |
| topic | vibroimpact system bifurcation Chebyshev polynomial uncertain parameter |
| url | https://www.mdpi.com/1099-4300/25/9/1365 |
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