Studies On Non-Linear Dynamics Of Viscoelastic Moving Belts

Moving belts used in power transmissions are an example of a class of mechanical systems commonly referred to as axially moving materials. One major problem in this system is the occurrence of large transverse belt vibrations, which result from the time-dependent crankshaft-driven belt tension. Such vibrations are termed as parametric vibrations. Dynamic properties associated with parametric vibrations are of primary concern in engineering. The dynamic properties of parametrically excited viscoelastic belts are investigated in this dissertation. The main contents are as follows.We give a review of the researches on axially moving materials system and the researches based on Galerkin approach on dynamics of viscoelastic structures.We derive and obtain the equation of motion for a span of belts by using Newton principle and the generalized Hamilton's principle.Then, we use both the method of multiple scales and the Galerkin approach to give the perturbation analysis of the governing partial differential equation. We got the averaged equations of the system in three resonant cases. Those are principal parametric resonance and 1:1 internal resonance, principal parametric resonance and 1:2 internal resonance and principal parametric resonance and 1:3 internal resonance.The theory of normal form are used to investigated the normal forms in the four dimensional nonlinear systems with cubic nonlinearities. We give the computing results of Maple programs by using the adjoint operator method.The chaotic motions of the system are investigated by using the numerical simulation. The numerical simulations results show the existence of chaotic motions.