Dynamic analysis of viscoelastic serpentine belt drive systems

grantor: University of TorontoThis thesis is devoted to accurately modeling and analyzing the dynamic behavior of damped serpentine belt drive systems. A viscoelastic moving material model is proposed to describe the transverse vibration of belt spans and a hybrid (continuous/discrete components) viscoelastic system is proposed to represent the dynamics of the entire serpentine belt drive. The direct multiple scales method is applied to the nonlinear vibration analysis of free, forced and parametric vibration of viscoelastic moving belts. Nonlinear natural frequencies and near-modal nonlinear response of free vibration of viscoelastic moving belts are obtained in closed-form. The amplitude of near- and exact-resonant response is predicted for viscoelastic moving belts excited by the eccentricity of pulleys. Closed-form solutions of response amplitudes, existence conditions, and stability conditions of limit cycles are derived for parametrically excited viscoelastic moving belts. Block-by-block numerical integration method together with a Galerkin discretization using travelling eigenfunctions is proposed to calculate the transient response of moving belts with general viscoelasticity. An explicit exact characteristic equation of eigenvalues for undamped hybrid serpentine belt drives is derived, which could provide insight into effects of design parameters on the frequency spectrum of the system. A complex modal analysis method is developed for linear vibration analysis of non-self-adjoint hybrid serpentine belt drive systems for the first time. The adjoint eigenfunction can be conveniently determined from the proposed auxiliary system. Nonlinear vibrations of viscoelastic and elastic hybrid serpentine belt drive systems are analyzed using the discretization multiple scales method for the first time. This provides a basic understanding of parametric excitation threshold levels and the existence of multiple limit cycles. The direct multiple scales method is developed for the nonlinear analysis of elastic hybrid serpentine belt drive systems. Comparisons between the direct multiple scale method and the discretization multiple scales help better understand the relationship between the two approaches.Ph.D