泊松白噪声激励下斜拉索的面内随机振动

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

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。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。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。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。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,获得的理论结果与蒙特卡罗模拟的结果吻合地非常好。

Nonlinear random vibration of stay cables is studied extensively at present, but only in cases of Gaussian random excitation. However, most of random disturbances in reality are non-Gaussian, if Gaussian excitation model is used, great error will be produced. Here, a stay cable system was assumed to be excited by a non-Gaussian excitation, i.e., Poisson white noise, and its in-plane random vibration was studied. Firstly, the stochastic differential equation for its in-plane random vibration under Poisson white noise excitation was derived to establish a generalized Fokker-Plank-Kolmogorov(FPK) equation governing the probability density function(PDF) of the system’s stationary response. Then, the iterative weighted residual method was proposed to solve the fourth-order generalized FPK equation, and obtain the approximate steady state closed solution to the system’s response probability density function. Finally, effects of vertical span ratio, damping coefficient and pulse arrival rate on the system’s in-plane random vibration were examined. Results showed that with increase in vertical span ratio, the cable response becomes more and more asymmetric;with increase in damping ratio, the system response is significantly suppressed;with increase in pulse arrival rate, the cable response increases and is gradually close to that under Gaussian white noise;the results using the proposed method agree well with those using Monte Carlo simulation.