| There are many studies on vibrations of moving belts originated from automotive belt drives. These studies, however, mainly consider nonlinear effect of the transversal vibration of the belt under transversal excitation without considering the coupling effect between the transversal and longitudinal vibrations under longitudinal excitation.The nonlinear system is solved using the Analog Equation Method. The two coupled nonlinear hyperbolic differential equations of the system are reduced to two uncoupled linear equations pertaining to the longitudinal and transverse deformation of a substitute beam with unit longitudinal and bending stiffness, respectively. The reduced equations are under a fictitious time dependent load distributions with the same boundary and initial conditions. The fictitious forces are established numerically from the integral expression of the oscillator solution with the requirement that the equations of motion be satisfied at discrete time intervals.It is found that the transversal vibration appears as a stable and predictable beating phenomenon due to an internal resonance from the periodic energy transfer between the longitudinal excitation and the transversal vibration, which manifests itself as a standing wave.The theoretical results are in good agreement with the experimental results obtained from the transversal wave amplitude envelope. Using the theoretical model, further simulations are conducted to predict the vibration amplitude and its time variation for different belt tensions, stiffness, excitation displacements, excitation forces amplitudes and frequencies. The amplitude of the transversal vibration shows strong dependency on the initial transversal displacement at the excitation point.In this thesis, a nonlinear model is built for a tensioned belt periodically excited longitudinally at one end with a known amplitude and frequency and with the other end clamped. This model allows for coupling between periodic longitudinal excitation and transversal vibration. |
