DYNAMIC STABILITY OF A MOVING STRING UNDERGOING 3-DIMENSIONAL VIBRATION

This paper studies the dynamic stability of a moving string in three-dimensional vibration. The partial differential equations of motion are derived by using Hamilton's principle and are simplified as ordinary differential equations by the Galerkin method. The initial tension is assumed as a small periodic perturbation superimposed upon a steady-state value, and the parametric instability occurs in this system. Furthermore, owing to the existence of a Coriolis term, the system equation is transformed by a special modal analysis procedure into independent sets of first-order simultaneous differential equations. Herein the multiple-scale method is used to obtain approximate solutions and the boundaries of stable-unstable regions of this system. Finally, the effects of transport speed, the wave propagation speed and the initial tension of string on the change in the boundaries of the unstable regions are investigated numerically.