One-to-one auto-parametric resonance in serpentine belt drive systems

The coupled non-linear 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. A one-to-one internal resonance combined with a primary external resonance is investigated. Solutions for the amplitude of non-trivial limit cycles are obtained. A stability analysis is performed on the steady state solutions. The quadratic non-linearity terms in the equations of motion are found to affect the belt drive systems significantly. It is shown that the 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.