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

Typical rigid-body squeeze-film levitation systems produce repulsive forces of up to several kilograms, and under a limited range of operating conditions, attractive forces of less than a gram. In a 2021 experimental study, researchers demonstrated attractive levitation of several hundred grams using an oscillator that displayed pronounced elastic standing-wave deformations. In this presentation, we employ the method of matched asymptotic expansions to model the viscoacoustic fluid flow in such flexural squeeze-film systems. Our analysis reveals that, while the weak attractive forces produced by rigid-body systems occur as a result of a sufficient drop in mean pressure near the outer periphery of the film, the much stronger attraction generated by resonant flexural systems owes instead to local extrema of mean underpressure near the nodes of the standing wave. Both the attractive load capacity and the range of operating conditions under which attractive forces can be generated are found to correlate strongly with the associated wavenumber. The results of our study offer fundamental insights that may guide the development of future non-contact levitation devices and their implementation in relevant applications such as mobile soft robots and surface-mount technologies.