Approximate closed-form solution to random response of a SDOF vibro-impact system based on Hertz contact theory

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Journal of Vibration and Shock ›› 2019, Vol. 38 ›› Issue (21) : 6-14.

ZHU Haisheng1, CHEN Lincong1, SUN Jianqiao2,3,ZHAO Yaobing1

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Abstract

Vibro-impact systems exist widely in engineering fields, and studying collision-vibration is of great practical significance.Here, the latest achievement in studying random vibration, i.e., the iterative weighted residual method, was employed to obtain the approximate closed-form solution to random response of a SDOF vibro-impact system based on Hertz contact theory under Gaussian white noise excitation.Firstly, the approximate expression of the steady-state solution to Fokker-Planck-Kolmogorov (FPK) equation was constructed using concepts of the probabilistic circulation and probabilistic potential flow.Then, undetermined coefficients in the approximate expression were obtained using the weighted residual method.Finally, the iterative technique was used to gain the probability density estimation of specific accuracy under specified mean square error.To demonstrate the effectiveness of the proposed method, a Duffing vibro-impact system and a dry friction vibro-impact one were investigated, respectively.The theoretical analytical solutions were compared with the simulation results of Monte Carlo method.It was shown that the theoretical analytical solutions agree well with Monte Carlo simulation results.

Key words

vibro-impact / Hertz contact theory model / iterative method of weighted residual / Gaussian excitation

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ZHU Haisheng1, CHEN Lincong1, SUN Jianqiao2,3,ZHAO Yaobing1. Approximate closed-form solution to random response of a SDOF vibro-impact system based on Hertz contact theory[J]. Journal of Vibration and Shock, 2019, 38(21): 6-14

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