风激拉索的张弛振荡分析

为了研究斜拉索在横向风激励下的多模态张弛振荡特性,获得临界风速表达式，建立拉索受风力作用的非线性运动微分方程,基于索纵向运动相对较小而导出关于索横向运动的偏微分振动方程,运用Galerkin法将该方程转化为常微分方程组,用以描述索的多模态自激振动；应用非线性振动的平均法,求解得到该系统的自激振动分析解,确定索张弛振荡及存在性条件,分析计算索前二阶模态张弛振荡的临界风速,并通过数值模拟验证.提出风激拉索多模态张弛振荡及临界风速的分析方法,研究结果表明,拉索张弛振荡的临界风速随结构模态阻尼而提高,并受振动模态、风速变化和风力系数等影响.

Self-excited oscillation analysis of a taut cable under wind loading

The fluid-flow-induced cable vibration is an active research subject in structural engineering and has practical importance for structural improvement and vibration control.To study the characteristics of the self-excited oscillation of an inclined taut cable with multi-vibration modes under wind loading and to obtain the analytical expression of the critical wind velocity,the nonlinear differential equations of motion were derived for the wind-induced vibration of the cable.Then the partial differential equation for the transverse cable vibration was obtained based on the assumption of longitudinal cable vibration comparatively small.By using the Galerkin approach,this partial differential equation was converted into ordinary differential equations which describe the self-excited oscillation of the cable as multi-modes system.The analytical solutions,in particular,limit cycle solutions to the system in self-excited oscillation were obtained further by using the averaging method for nonlinear vibration.The wind-induced strong cable oscillation and its existence conditions were analytically determined finally.The critical wind velocities for first two modes of the cable system in self-oscillation were analyzed and verified by numerical results.Thus the analytical method for the wind-induced self-excited oscillation of taut cables with multi-modes and the critical wind velocity is developed.It is concluded that the critical wind velocity of the cable self-oscillation increases with structural mode damping and is affected by other factors such as vibration modes,transverse wind velocity varied with time and space,drag and lift coefficients.