A vibrating thermoelastic plate in a contact with an obstacle

Abstract

We deal with a dynamic contact problem for a thermoelastic plate vibrating against a rigid obstacle.
Dynamics is described by a hyperbolic variational inequality for de
ections. The plate is subjected to
a perpendicular force and to a heat source. The parabolic equation for the thermal strain resultant
contains the time derivative of the de
ection. We formulate a weak solution of the system and verify its
existence using the penalization method.