Nonlinear Vibration of the Coupled Textile / Rotor System by Finite Difference Method

Abstract

The nonlinear vibration of the coupled textile / rotor system is investigated by using the finite difference method.Both the partial differential equation for the textile transverse vibration and the ordinary differential equation for the rotor whirling vibration are derived by Hamilton's principle.When the textile is wound either on or off the rotor, the physical modes is non-conservative because the mass, inertia and unbalance magnitude of the rotor change with time, and also the length of the textile is time-dependent.A special technique of the finite difference method is developed for such a time-dependent length of the textile.The approach used here is with fixed-size grid and changing the grid number as the length varying.Finally, numerical examples are presented to demonstrate the effects of the rotating angular speed, roating angular acceleration and nonlinear terms on the transient amplitudes of the coupled system.