In-plane random vibration of stay cable system under Poisson white noise excitation

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Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (15) : 230-236.

LIU Jingrui1, CHEN Lincong1,2, ZHAO Yaobing1

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Abstract

The nonlinear random vibration of stay cables has been studied extensively so far, but it appeared to be limited to Gaussian white noise excited cases. However, the random disturbances in reality are non-Gaussian excitations. There will be large errors if Gaussian excitations are replaced by non-Gaussian excitations. In this paper, the stay cable system is supposed to be excited by Poisson white noise, and the in-plane random vibration of stay cable system under non-Gaussian stochastic excitation is studied. First, the stochastic differential equation of the in-plane vibration of stay cable system under Poisson white noise excitation is formulated, and the corresponding reduced generalized Fokker-Plank-Kolmogorov (FPK) equation governing the probability density function (PDF) of stationary response is established. Then, the iterative method of weighted residuals is proposed to solve the fourth-order generalized FPK equation to yield the approximate stationary PDF of system. Finally, the effects of sag ratio, damped coefficient and pulse arrival rate on the in-plane stochastic vibration of cable are examined. The results show that the asymmetric appearance of response is becoming much obvious while the sag ratio increases; the response is then suppressed obviously as the coefficient of damping increases; the response of stay cable system increases rapidly with the increase of pulse arrival rate, and is getting closer to the Gaussian white noise excited case. Besides, the feasibility of the method is compared with the Monte Carlo simulation. The results show that the analytical solutions are in good agreement with Monte Carlo simulation data.

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iterative method of weighted residuals / cable vibration / Poisson white noise / random vibration / in-plane vibration

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LIU Jingrui1, CHEN Lincong1,2, ZHAO Yaobing1. In-plane random vibration of stay cable system under Poisson white noise excitation[J]. Journal of Vibration and Shock, 2020, 39(15): 230-236

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