Novel method for random vibration analysis of single-degree-of-freedom vibroimpact systems with bilateral barriers

doi:10.1007/s10483-019-2543-5

Abstract

Abstract: The vibroimpact systems with bilateral barriers are often encountered in practice. However, the dynamics of the vibroimpact system with bilateral barriers is full of challenges. Few closed-form solutions were obtained. In this paper, we propose a novel method for random vibration analysis of single-degree-of-freedom (SDOF) vibroimpact systems with bilateral barriers under Gaussian white noise excitations. A periodic approximate transformation is employed to convert the equations of the motion to a continuous form. The probabilistic description of the system is subsequently defined through the corresponding Fokker-Planck-Kolmogorov (FPK) equation. The closed-form stationary probability density function (PDF) of the response is obtained by solving the reduced FPK equation and using the proposed iterative method of weighted residue together with the concepts of the circulatory probability flow and the potential probability flow. Finally, the versatility of the proposed approach is demonstrated by its application to two typical examples. Note that the solution obtained by using the proposed method can be used as the benchmark to examine the accuracy of approximate solutions obtained by other methods.

Key words: bilateral barrier, vibroimpact system, weighted residue method, iterative, random vibration

2010 MSC Number:

Lincong CHEN, Haisheng ZHU, J. Q. SUN. Novel method for random vibration analysis of single-degree-of-freedom vibroimpact systems with bilateral barriers. Applied Mathematics and Mechanics (English Edition), 2019, 40(12): 1759-1776.

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References 39

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