A vibrating thermoelastic plate in a contact with an obstacle

Igor Bock 1  and Jiří Jarušek 2
  • 1 Institute of Computer Science and Mathematics Faculty of Electrical Engineering and Information Technology Slovak University of Technology Ilkovičova 3 SK-812-19 Bratislava 1 SLOVAKIA
  • 2 Institute of Mathematics Academy of Sciences of the Czech Republic CZ-115-67 Praha 1 CZECH REPUBLIC

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 deflections. 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 deflection. We formulate a weak solution of the system and verify its existence using the penalization method.

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