悬垂缆线的非线性振动

Nonlinear Oscillations of a Suspended Cable

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 。

In this paper,the nonlinear oscillations of a suspended cable with an initial sag undegoing a harmonic excitation in a vertical plan are analyzed. Using Hamiltons principle,the nonlinear partial differential equation of the planar motion of the cable is derived.The partial differential equation is reduced to an ordinary differential equation via the Galerkin procedure by assuming a modal deflection shape.By applying the method of multiple scales,this paper studies its primary resonance,superharmonic resonance,subharmonic resonance and stability.The approximate constant periodic solution,averaged equations,the curves of the amplitude of frequency response function are obtained.This study shows that the effect of the nonlinearity is to bend the amplitude frequency response curve,form multivalued regions and lead to jump phenomena.This study also shows that the nonlinearity may produce primary resonance,superharmonic resonance and subharmonic resonance.