随机横桥向激励下斜拉索面内耦合振动特性研究

IN-PLANE COUPLED VIBRATION OF INCLINED CABLES UNDER RANDOM TRANSVERSE EXCITATION

研究了横桥向零均值高斯白噪声随机激励下斜拉索面内耦合振动特性。基于牛顿运动定律及Galerkin模态截断原理,考虑拉索的垂度、大位移引起的几何非线性及初始静平衡特性,推导了拉索空间三维非线性随机振动平衡微分方程,采用等价随机线性化法推出了14维拉索面内、面外横向振动状态向量一阶均方微分方程组,利用Runge-Kutta数值积分法求解该方程组的均方根响应特性。研究表明,当拉索承受面外横向激励超过一定值时,由于耦合振动项的耦合作用,拉索面内横向振动也将被激起,发生面内耦合振动所需的临界激励均方值随着拉索阻尼比的增大而增大,在此运动状态下,即使激励为平稳荷载,拉索振动也将呈现非平稳特性。最后,采用Lyaponov指数判断系统在耦合振动过程中的稳定性特性,分析了阻尼比对稳定性的影响。

In-plane coupled stochastic vibration behaviors of inclined cables subjected to Gaussian zero mean stationary white noise excitation in transverse bridge orientation were investigated. Based on Newton’s laws of motion and Galerkin’s modal truncation principle, and taking the influences of geometry nonlinearity induced by the sags and big displacements of cables and the initial equilibrium states into account, the three-dimensional non-linear coupled differential motion equations of inclined cables were deduced. The equivalent stochastic linearization method was applied to derive the 14 dimensions first-order nonlinear differential equations of state vectors of inclined cables, and the Runge-Kutta integration method was utilized to obtain the RMS response characteristics. The results show that when the transverse random excitation acting on the stayed-cable exceeds a critical value, the in-plane transverse vibration of the cable will be excited due to the coupling nonlinear items, and the critical value of random excitation increases as the damping ratio of cable increases. The cable response is of non-stationary characteristics, even though the loading is a stationary random process. The Lyaponov exponent was applied to investigate the stability property of the coupled vibration under random excitations, and the effects of the damping on the stability were also concerned.