Two-to-One Internal Resonance in Serpentine Belt Drive Systems

The coupled nonlinear equations of motion of serpentine belt drive systems are solved using the direct multiple scales method. The entire hybrid system, which includes continuous belt spans, discrete pulleys, and tensioner arm, is divided into two subsystems. The case of a two-to-one internal resonance with primary external resonance is considered. No assumptions regarding the spatial dependence of the motion are made. Solutions for the amplitude of non-trivial limit cycles are obtained. It is shown that quadratic nonlinearity terms in the equations affect the behavior of the system significantly and direct multiple scales method yields better results for the system than the ordinary discretization multiple scales method. The effects of excitation frequencies, excitation amplitudes and the internal detuning parameter on dynamic responses are investigated.