Steady-state responses of a belt-drive dynamical system under dual excitations

The stable steady-state periodic responses of a belt-drive system with a one-way clutch are studied. For the first time, the dynamical system is investigated under dual excitations. The system is simultaneously excited by the firing pulsations of the engine and the harmonic motion of the foundation. Nonlinear discrete–continuous equations are derived for coupling the transverse vibration of the belt spans and the rotations of the driving and driven pulleys and the accessory pulley. The nonlinear dynamics is studied under equal and multiple relations between the frequency of the firing pulsations and the frequency of the foundation motion. Furthermore, translating belt spans are modeled as axially moving strings. A set of nonlinear piecewise ordinary differential equations is achieved by using the Galerkin truncation. Under various relations between the excitation frequencies, the time histories of the dynamical system are numerically simulated based on the time discretization method. Furthermore, the stable steady-state periodic response curves are calculated based on the frequency sweep. Moreover, the convergence of the Galerkin truncation is examined. Numerical results demonstrate that the one-way clutch reduces the resonance amplitude of the rotations of the driven pulley and the accessory pulley. On the other hand, numerical examples prove that the resonance areas of the belt spans are decreased by eliminating the torque-transmitting in the opposite direction. With the increasing amplitude of the foundation excitation, the damping effect of the one-way clutch will be reduced. Furthermore, as the amplitude of the firing pulsations of the engine increases, the jumping phenomena in steady-state response curves of the belt-drive system with or without a one-way clutch both occur.