斜拉桥双索与桥面耦合的非线性参数振动特性分析

Performance Study of the Nonlinear Parametric Vibration of Coupled Bridge Decks and Two Cables

考虑斜拉索几何非线性的影响,以及桥面运动而引起的拉索内力变化,基于牛顿定律,推导了斜拉桥双索与桥面耦合的非线性振动方程.运用Galerkin方法将非线性偏微分方程转化为关于时间的二阶常微分方程.利用多尺度法对系统进行摄动分析,发现系统存在许多参数共振形式,并针对其中一种参数共振,数值分析了双索在振动过程中的相互影响.结果表明:只变动其中一根索的参数,另一根索的运动特性会受到较大影响.这说明索-索的间接耦合作用不容忽视.

The non-linear equations of parametric vibration, in which the variation of internal force as well as the geometric no-linearity was considered, were derived, and then, a set of partial differential equations were diverted into a set of ordinary differential equations by applying Galerkin method. And the method of multiple scales was applied to the differential equation to analyze the parametric resonance of stayedcable. Numerical sim- ulation was done to study the interaction between two cables. The numerical calculation results have shown that, by changing the parameter of one cable only, the vibration performance of the other cable will be affected noticeably, indicating that the indirect coupled phenomenon between two cables can not be neglected.