A new type of bilateral vibro-impact model: random vibration analysis


In this work, a novel class of bilateral vibro-impact model is proposed. Unlike the traditional impact model, the energy dissipation of the novel bilateral system is measured by the model of the restitution coefficient dependent with velocity. Then the random vibration of the system is investigated in the presence of Gaussian white noise excitations. The motions of the unperturbed impact system are firstly considered and grouped into two categories. Then, the mean drift and diffusion coefficients of the two kinds of motion are calculated with the stochastic averaging methodology for energy envelope under the assumed condition that the impact vibration system is quasi-conservative. Subsequently, the probability density functions of stationary responses are computed with solving the averaged Fokker-Plank-Kolmogorov equation. Finally, two illustrations are chosen to demonstrate the reliability of the presented technique. And, the validation of analytical results is verified by the simulation data generated by Monte Carlo.

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Code availability

The code that support the findings of this study are available from the corresponding author upon reasonable request.


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The National Natural Science Foundation of China (No. 11672111, No. 12072118), the Program for New Century Excellent Talents in Fujian Province University, the Natural Science Foundation of Fujian Province of China (No. 2019J01049).

Author information




JQ: Investigation, Data curation, Writing—original draft. LC: Conceptualization, Methodology, Supervision, Project administration. SL: Data Collation, textual corrigendum.

Corresponding author

Correspondence to Lincong Chen.

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The authors declare that they have no conflict of interest.

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The data and material that support the findings of this study are available from the corresponding author upon reasonable request.

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Qian, J., Chen, L. & Liu, S. A new type of bilateral vibro-impact model: random vibration analysis. Int. J. Dynam. Control (2021). https://doi.org/10.1007/s40435-021-00759-7

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  • Bilateral vibro-impact systems
  • Velocity-dependent restitution coefficient
  • Stochastic averaging
  • Random vibration