泊松白噪声激励下斜拉索的面内随机振动

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摘要目前针对斜拉索非线性随机振动的研究已广泛开展，但仅限于高斯随机激励情形。然而，现实中大部分的随机扰动都是非高斯的。若使用高斯激励模型将产生较大误差。本文假设拉索所受非高斯激励为泊松白噪声，研究了泊松白噪声激励下斜拉索面内随机振动。首先，推导了受泊松白噪声激励的斜拉索面内振动的随机微分方程，建立了支配系统平稳响应概率密度函数的广义FPK方程。然后，提出迭代加权残值法求解了四阶广义FPK方程，得到了系统响应概率密度函数的近似稳态闭合解。最后，考察了垂跨比、阻尼系数以及脉冲到达率对拉索面内随机振动响应的影响。结果表明：拉索的响应随着垂跨比的增大，响应呈现不对称现象愈加明显；随阻尼比增加，系统响应得到显著抑制；当脉冲到达率增大，拉索的响应也随之增大，并逐渐接近于高斯白噪声激励的情形。另外，本文获得的理论结果与蒙特卡罗模拟的结果吻合地非常好。

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	刘婧瑞1
	陈林聪1
	2
	赵珧冰1

关键词 ：迭代加权残值法, 拉索振动, 泊松白噪声, 随机振动, 面内振动

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.

Key words： iterative method of weighted residuals cable vibration Poisson white noise random vibration in-plane vibration

收稿日期: 2019-08-01 出版日期: 2020-07-28

引用本文:

刘婧瑞1，陈林聪1,2，赵珧冰1. 泊松白噪声激励下斜拉索的面内随机振动[J]. 振动与冲击, 2020, 39(15): 230-236.
LIU Jingrui1, CHEN Lincong1,2, ZHAO Yaobing1. In-plane random vibration of stay cable system under Poisson white noise excitation. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(15): 230-236.

链接本文:

http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2020/V39/I15/230

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