On the enhanced attractive load capacity of resonant flexural squeeze-film levitators

This paper uses numerical and asymptotic methods to investigate the fluid dynamics underlying the anomalously large attractive forces that were recently observed in squeeze-film levitation systems driven by resonant vibrations of a flexible oscillator. Namely, in a recent experimental study, a thin plastic disk driven near one of its natural frequencies attractively levitated, for the first time, an object weighing several hundred grams. This behavior is in stark contrast with that of rigid-body systems, which produce attractive forces thousands of times weaker and only within a limited range of operating conditions. Flexural systems driven by standing-wave deformations of the oscillator are addressed in this paper in a unifying matched-asymptotic analysis that accounts for effects of fluid viscosity, inertia, and compressibility, as well as pressure variations beyond the outer boundary of the squeeze film. While the weak attractive forces produced by rigid-body systems are known to depend critically on the existence of a net pressure drop across this peripheral region, the present analysis reveals that the augmented attractive load capacity of resonant flexural systems is associated instead with spikes of underpressure near the nodes of the standing wave. Furthermore, the wavenumber, which represents the number of nodes in the waveform, is found to correlate strongly with the attractive load capacity as well as the range of frequencies and oscillator surface areas for which attractive forces can be produced.