  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 force acting on the elastic plate. The pressure and
deformation field during and after the application of the external force are
derived and presented by closed form expressions. We examine a uniform external
pressure 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.
