基于延拓方法的悬索非线性振动分析

NONLINEAR OSCILLATIONS OF SUSPENDED CABLES USING THE CONTINUATION METHOD

研究了受谐波激励作用下悬索的非线性响应.基于索的拟静态假设,同时考虑悬索的几何非线性,首先利用Hamilton变分原理得到了悬索面内运动的非线性方程.然后把悬索的位移展开成固有模态的级数和.并利用Galerkin方法得到一个有限维的动力系统.再利用打靶法和延拓方法研究了悬索的周期运动.同时利用数值积分研究了超谐波共振区的一些非周期运动.最后讨论了激励幅值对悬索周期运动的影响.

The dynamic response of a suspended cable subjected to a harmonic excitation was investigated. Based on the assumption of quasi - static stretching due to the fact that the transverse wave speed is much lower than the longitudinal wave speed, the nonlinear governing in - plane equation of the suspended cable was derived by means of Hamilton principle, which took into account the geometric nonlinearity of the suspended cable. And the displacement of the suspended cable was expanded in a series of the natural modes of the suspended cable. Then, the Galerkin method was used to obtain a finite - dimensional dynamical system. The periodic motions of the suspended cable were examined by means of the shooting method and the continuation method ,while the non -periodic motions were studied through direct simulations. A comparison with the direct numerical results was performed. At last, the effects of the amplitude of the harmonic excitation on the periodic motion of the suspended cable were investigated.