梁索耦合结构的非线性振动

Nonlinear Vibration of Coupled Structure of Cable-stayed Beam

摘要:

在一组能描述梁索耦合结构中主缆曲率和吊索变形对系统影响的偏微分方程组基础上,通过Galerkin方法得到了系统在时域上一次截断的非线性常微分方程组.用多尺度法分析了所得的非线性常微分方程组.得到了主共振和1∶2内共振情况下以作用在梁上荷载的幅值为参数的振幅响应曲线和一次近似解析解.结果显示,一次近似解析解有良好的精度.系统发生内共振时,随激励幅值变化存在振幅突然变化的跳跃现象,而且低频共振时发生跳跃的分岔值小于高频共振时的分岔值.这说明低频共振更容易使结构发生大幅振动.该结果对工程应用有一定指导意义.

Abstract:

Based on a series of partial differential equations describing the effect of curvature of the main cables and deformation of the stay cables on the structure,the non-linear ordinary differential equations of the first order approximation on time-domain are obtained by Galerkin method and studied by multi-scale method.An analysis is made of the principal resonance and 1∶2 internal resonance.The analytical solutions of the first order approximation and the vibration amplitude response curves for the amplitude of excitation as a parameter are derived.The results indicate the first order approximate analytical solutions have a higher accuracy.In the internal resonance condition,there are jump phenomena of the vibration amplitudes of the main cables and the beam.But the low-order resonance bifurcation values of the jump phenomena are less than the high-order resonance bifurcation values,which indicates that the low-frequency resonance vibration is easier to generate substantial vibrations than the low-frequency.The study results are significant for engineering applications