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Stochastic response analysis of multi-degree-of-freedom vibro-impact system undergoing Markovian jump

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Abstract

The paper treats stationary response of a stochastically excited multi-degree-of-freedom (multi-DOF) vibro-impact system undergoing Markovian jump. The vibro-impact system with sudden abrupt changes in substructures or external excitations is modeled as a continuous-discrete Markovian jump system, which is essentially different from the traditional vibro-impact model. It is demonstrated that the random jump factors switch between a finite number of modes. This salient feature allows us to identify this type of dynamic behaviors as response of hybrid vibro-impact systems undergoing Markovian jump. Utilizing a two-step approximate technique, we can reduce the considered multi-DOF hybrid system to one-dimensional averaged Itô equation of the form of system’s total energy. The approximate analytical solution of the associated Fokker–Planck–Kolmogorov (FPK) equation of system’s energy is derived to predict the stationary response of original hybrid systems.

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Acknowledgements

This work was supported by the Natural Science Foundation of China through the Grant Nos. 11872307, 11972293, Natural Science Basic Research Plan in Shaanxi Province of China, No. 2018JQ1086 and “Research Funds for Interdisciplinary subject, NWPU”.

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  1. Department of Engineering Mechanics, MIIT Key Laboratory of Dynamics and Control of Complex Systems, Northwestern Polytechnical University, Xi’an, 710129, China

    Rongchun Hu, Xudong Gu & Zicheng Deng

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  1. Rongchun Hu
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  2. Xudong Gu
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Correspondence to Rongchun Hu.

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Hu, R., Gu, X. & Deng, Z. Stochastic response analysis of multi-degree-of-freedom vibro-impact system undergoing Markovian jump. Nonlinear Dyn 101, 823–834 (2020). https://doi.org/10.1007/s11071-020-05823-z

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