On the translating damping caused by a thin viscous fluid layer between a translating string and a translating rigid surface

Abstract

A vibrating, translating string is coupled to a translating rigid surface through a fluid film at the interface. The coupling is modelled as a translating, distributed damping and investigated through the waves propagating in the fluid-string coupled system. An approximate method, similar to the method of slowly varying parameters, gives explicit predictions of the stability boundary in parameter space and of responses of the possibly unstable modes near the stability boundary. The translating damping destabilizes waves propagating in the direction of damping propagation when the mean film speed relative to the string exceeds the wave speed in the string without fluid coupling. Through the same excitation mechanism, the maximum stable speed of a shell rotating on a stationary shaft is shown to be twice the critical rotation speed of the shell in the absence of the fluid coupling.