The vibration of a spring damped vibrator under a long cylindrical squeeze film force

Squeeze film effects between two concentric cylinders are common and important in many mechanical systems. The models for cylindrical squeeze film force and vibrating system with squeeze film effects have not been well understood. In this paper, we model a cylindrical squeeze film force starting from the simplification of the full Navier–Stokes equations and then get an expression for the squeeze film force. We study the influence of a harmonic exciting force on a spring damped vibrator with squeeze film effect by establishing a non-linear mathematical model, and we investigate the behavior of the system numerically. As a forced vibrating system, the fundamental frequency of the response is consistent with the exciting frequency; the response of the resultant non-linear system shows obvious superharmonic phenomenon; the number of the superharmonic peaks increase with Reynolds number, and the superharmonic components mainly come from the non-linearity of the flow convection.