NONLINEAR DYNAMIC STABILITY OF A MOVING STRING BY HAMILTONIAN-FORMULATION

In this paper, the stability behavior of an axially moving string is e xamined in the presence of parametric and combination resonances. The Galerkin discretization utilizing stationary string eigenfunctions is used to transform the partial differential equation governing transver se response into a set of coupled ordinary differential equations. Ham iltonian formulation and averaging method are used to yield a set of a utonomous equations. The conditions of parametric and summed resonance s are obtained over specific ranges between the natural and exciting f requencies. Explicit results of the stability boundaries for the first and secondary principal parametric and the first summation resonances and the bifurcation paths of the nontrivial amplitudes are obtained. (C) 1998 Elsevier Science Ltd. All rights reserved.