简谐激励力作用下悬垂缆线的谐波共振

本文研究在简谐激励力作用下的悬垂缆线的谐波共振。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区域。

Harmonic Resonances of a Suspended Cable Under Harmonic Excitation

In the paper,the harmonic resonances of a suspended cable with initial sag under the harmonic excitation in vertical plane are considered.Using the Hamilton's principle,the nonlinear partial differential equations of the planar motion of the suspended cable are derived.The partial differential equation of planar motion is reduced to one ordinary differential equation via the Galerkin procedure by assuming a modal deflection shape. By applying the method of multiple scales,the superharmonic resonance and subharmonic resonance and stability of the suspended cable are studied.The approximate constant periodic solution,the averaged equations and the response curves of amplitude-frequency are obtained. This study shows that the effect of the nonlinearity is to bend the amplitude curve,form multivalued regions and lead to jump phenomena.This study also shows that the nonlinearity may produce the superharmonic resonance and subharmonic resonance.Although the frequency of the excitation is not equal to the nature frequency of system the response of the system is quite large.