The transverse vibrations of viscoelastic axiallymoving flexible elements

Abstract

In this article bending oscillations of moving belt drive, which is described by differential equations are investigated. They contain mixed derivative in time and space coordinates. The nonlinearity of the material mechanical properties is concidered. It was described by Kelvin - Voigt viscoelastic model. Taking into account the finite length of flexible element is made assumptions about the influence of nonlinear force on laws of change over time amplitude and frequency of the bending vibrations. Therefore, the differential equation considered to be weakly nonlinear. The solution of differential equation and method of Krylov-Bogolyubov-Mitropolsky are presented as asymptotic series. Ordinary differential equations for the amplitude and phase of bending vibrations are obtained. It is investigated the influence of the velocity of longitudinal movement, Young's modulus and dynamic viscosity of the material on the amplitude and the frequency of vibration.