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研究了在曲线平面内受到简谐激励力作用下的悬垂缆线的非线性振动。用 Hamilton原理导出悬垂缆线面内运动的非线性偏微分方程。通过假设悬垂缆线的挠度曲线 ,运用 Galerkin方法将偏微分方程转化为常微分方程。用多尺度法研究悬垂缆线的主共振、超谐波共振和次谐波共振 ,得到了系统的定常周期解 ,平均方程和幅频曲线。研究了非线性对幅频曲线的影响和定常运动的稳定性。研究表明 ,由于非线性 ,系统不仅有激励频率接近固有频率的主共振 ,而且还会出现激励频率接近固有频率整数倍或分数倍的次谐波共振和超谐波共振
The nonlinear vibration of suspension cable under harmonic excitation force is studied in the plane of the curve. Nonlinear Partial Differential Equation Derived from the In - Plane Movement of Suspension Cables Derived by Hamilton Principle. By assuming the deflection curves of the suspended cables, the Galerkin method is used to convert partial differential equations into ordinary differential equations. The multi-scale method is used to study the main resonance, superharmonic resonance and subharmonic resonance of the suspension cables. The periodic solution, average equation and amplitude-frequency curve of the system are obtained. The influence of nonlinearity on amplitude-frequency curve and the stability of steady motion are studied. The research shows that due to the nonlinearity, the system not only has the main resonance whose excitation frequency is close to the natural frequency, but also the subharmonic resonance and the superharmonic resonance whose excitation frequency is close to the integer multiple or fractional multiple of the natural frequency