Free and forced nonlinear vibration of a transporting belt with pulley support ends

This paper focuses on the free and forced nonlinear vibration of a viscoelastic transporting belt supported by pulleys for the first time. The transporting belt boundary conditions are usually specified as simply supported or fixed. Therefore, the static equilibrium of the belt is supposed to remain straight. However, the belt wraps around two pulleys in most practical mechanical systems. The round support of the pulleys causes nonhomogeneous terms in the boundary condition. A nonlinear dynamic model is established to describe the transverse vibration of the transporting belt. The static equilibrium configuration caused by the nonhomogeneous boundary conditions is determined by developing a numerical iteration scheme. By means of coordinate transformation, the influence of nonhomogeneous boundary conditions is eliminated. Then, the natural frequencies of transverse vibration of the belt around the equilibrium configuration are obtained by adopting the differential quadrature method. Furthermore, the inertia excitation of the belt system is taken from the periodic motion of the foundation. In dynamic mechanical systems, this kind of fluctuation induced by the engine is very common. By applying the differential quadrature method and the Runge-Kutta time discretization, the time histories of the forced vibration are numerically calculated. Resonance areas of the belt are studied by using the frequency sweep. Moreover, parametric studies are carried out to understand the influences of the system parameters. It is concluded that pulley support ends cause nonhomogeneous boundaries and the static equilibrium configuration, and consequences are exacerbated by transmission speed.