Global dynamics of the cable under combined parametrical and external excitations

Abstract

The chaotic dynamics and global bifurcations of the suspended elastic cable under combined parametric and external excitations are investigated. The non-linear equations of motion of the elastic cable to small vibration of one support are derived. The averaged equations are obtained by using the method of multiple scales. Based on the averaged equations, the theory of normal form and Maple program are used to obtain the explicit expressions of normal form associated with a double zero and a pair of pure imaginary eigenvalues. On the basis of the normal form, global bifurcation analysis of the parametrically and externally excited suspended elastic cable is given by a global perturbation method developed by Kovacic and Wiggins. The chaotic motion of the elastic cable is also found by numerical simulation.