Transient dynamics of elastic hele-shaw cell due to external forces

Abstract eng:
We study the transient dynamics of a viscous liquid contained in a narrow gap between a rigid surface and a parallel elastic plate. The elastic plate is deformed due to an externally applied time-varying pressure-field. We model the flow-field via the lubrication approximation and the plate deformation by the Kirchhoff-Love plate theory. We obtain a self-similarity solution for the case of an external point impulse acting on the elastic plate. We examine a distributed external pressure, spatially uniform and linearly increasing with time, acting on the elastic plate over a finite region and during a finite time period, similar to the viscous-elastic interaction time-scale. The interaction between elasticity and viscosity is shown to reduce by order of magnitude the pressure within the Hele-Shaw cell compared with the externally applied pressure, thus suggesting such configurations may be used for impact mitigation.

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