Stochastic Responses and Stability Analysis of Vibro-Impact Systems With Friction Under Wideband Noise Excitation

MA Lan; TIAN Lili; LIU Li

doi:10.21656/1000-0887.440313

Volume 45 Issue 9

Sep. 2024

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MA Lan, TIAN Lili, LIU Li. Stochastic Responses and Stability Analysis of Vibro-Impact Systems With Friction Under Wideband Noise Excitation[J]. Applied Mathematics and Mechanics, 2024, 45(9): 1235-1242. doi: 10.21656/1000-0887.440313

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Stochastic Responses and Stability Analysis of Vibro-Impact Systems With Friction Under Wideband Noise Excitation

doi: 10.21656/1000-0887.440313

MA Lan^1
,,
TIAN Lili¹,
LIU Li^{1, 2
,
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1.
School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, P.R.China
2.
School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, P.R.China

Received Date: 2023-10-18
Rev Recd Date: 2024-05-12
Publish Date: 2024-09-01

Abstract

Abstract

The stochastic responses and the asymptotic stability with probability 1 of vibro-impact systems with friction under wideband noise excitation were investigated. The Zhuravlev non-smooth transformation and the stochastic averaging method were extended to obtain the steady-state probability density functions of the system. The accuracy of the method was verified through comparison of the theoretical results with those from the Monte Carlo simulations. The effects of the friction force and the vibro-impact restitution coefficient on the system responses were studied. Furthermore, The Lyapunov exponent of the linearized averaged Itô equation was derived and the stability of the trivial solution was determined with the Lyapunov exponent. The results show that, changing the frictional coefficient and the vibro-impact restitution coefficient could adjust the system stochastic stability.
- vibro-impact system with friction,
- stochastic averaging method,
- steady state response,
- stochastic stability

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References(19)

References

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