梁索耦合结构的非线性振动

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....

Nonlinear Vibration of Coupled Structure of Cable-stayed Beam

Abstract: Using a system of partial differential equations, the affect of curvature of the main cables and deformation of the stay cables on the structure is expressed by the partial differential equations, the non-linear ordinary differential equations of the first order approximation on time-domain is obtained by Galerkin method. The ordinary differential equations are studied by multi-scale method. The external resonance and internal resonance is analyzed in this paper. The analytical solutions of the first order approximation and the vibration amplitude response curves with the amplitude of excitation as a parameter are derived. The results indicate the first order approximate analytical solution has 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. This indicates that the low-frequency resonance vibration is easier to generate substantial vibrations than the low-frequency. These results have some guiding significance in engineering applications