How much energy does a gravitational wave deposit in a metal plate?

Starting from first principles in relativistic elasticity, the authors solve exactly for the deformation of a thin rectangular plate hit by a gravitational wave — something previous detector-physics treatments handled only approximately. For a material with zero Poisson ratio the equations decouple cleanly, yielding closed-form expressions for induced displacement, absorbed energy from both short bursts and continuous waves, and even the faint gravitational wave the vibrating plate radiates back. The results directly benchmark the physics of resonant bar detectors like EXPLORER and NAUTILUS.