  We report (semi-)analytical solutions of a problem involving a
visco-hyperelastic solid material layer sandwiched between two fluid layers, in
turn confined by two long planar walls that undergo oscillatory motion. The
resulting system dynamics are rationalized, based on fluid viscosity and solid
elasticity, via wave and boundary-layer theory. This allows for physical
interpretation of elasto-hydrodynamic coupling, potentially connecting to a
broad set of biophysical phenomena and applications, from synovial joint
mechanics to elastometry. Further, obtained solutions are demonstrated to be
rigorous benchmarks for testing coupled incompressible fluid--hyperelastic
solid and multiphase numerical solvers, towards which we highlight challenging
parameter sets. Finally, we provide an interactive, online sandbox to build
physical intuition, and open-source our code-base.
