Fy. Huang et Cd. Mote, ON THE TRANSLATING DAMPING CAUSED BY A THIN VISCOUS-FLUID LAYER BETWEEN A TRANSLATING STRING AND A TRANSLATING RIGID SURFACE, Journal of sound and vibration, 181(2), 1995, pp. 251-260
A vibrating, translating string is coupled to a translating rigid surf
ace 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 p
redictions of the stability boundary in parameter space and of respons
es of the possibly unstable modes near the stability boundary. The tra
nslating damping destabilizes waves propagating in the direction of da
mping propagation when the mean film speed relative to the string exce
eds the wave speed in the string without fluid coupling. Through the s
ame excitation mechanism, the maximum stable speed of a shell rotating
on a stationary shaft is shown to be twice the critical rotation spee
d of the shell in the absence of the fluid coupling.