Distortion of a Harmonic Elastic Wave Reflected From a Dry Friction Support

This study is motivated by the need to understand the elastodynamic response of belts in frictional contact with pulleys. To this end, a simplified model for belt/pulley contact is used to investigate the dynamic response of a belt subject to a train of harmonic tension waves. Through a nondimensionalization, a single dimensionless parameter Ω is identified which governs the dynamic response. A numerical solution is developed and exercised over a wide range of values of Ω An approximate closed-form solution is derived assuming the belt stretches quasi-statically, and is shown to yield accurate results for small values of Ω Reported results include the distortion of an initially harmonic tension wave, the energy reflected from the frictional support, and the distance harmonic waves penetrate into the support. The results suggest that the quasi-static stretching assumption may be further utilized as a modeling simplification for belt drives characterized by values of Ω $<1/3$⁠.