斜拉桥拉索模态耦合非线性共振响应特性

考虑拉索垂度及几何非线性的影响,导出了斜拉索的面内外耦合非线性振动方程。通过Galerkin方法,将偏微分方程化为常微分方程,用多尺度法对耦合方程求解,得出了面内外一阶模态耦合振动特性。对典型斜拉桥拉索进行了计算,结果表明:拉索可能产生1:1内共振,共振频率区间及振动幅值与索的垂度大小有关;索内阻尼对共振特性也有较大的影响;由于非线性的影响,响应幅值与初始条件有关。

NONLINEAR INTERNAL RESONANCE CHARACTERISTICS OF MODAL INTERACTION FOR STAY CABLES OF CABLE-STAYED BRIDGES

In this paper, taking the sagging effect and geometrical non-linearity into consideration, the nonlinear equations of stay cables for coupling in-plane and out-of-plane vibrations are derived. By the Galerkin method, the partial differential equations are transformed into ordinary differential equations, which are solved with multi-scale method. The nonlinear modal interaction characteristics of cables of cable-stayed bridges are obtained. Some typical cables of cable-stayed bridges are investigated. The results demonstrate that 1:1 internal resonance may occur and both the resonance frequency range and the response amplitude are related with the initial sag of cable. And cable damping affects the internal resonance significantly. Also, the response amplitude is changed with the initial conditions due to the nonlinear effects of the cables.