On the solutions of a dynamic contact problem for a thermoelastic von Kármán plate

0459254 - MÚ 2017 RIV GB eng J - Journal Article
Bock, I. - Jarušek, Jiří - Šilhavý, Miroslav
On the solutions of a dynamic contact problem for a thermoelastic von Kármán plate.
Nonlinear Analysis: Real World Applications. Roč. 32, December (2016), s. 111-135. ISSN 1468-1218. E-ISSN 1878-5719
R&D Projects: GA ČR(CZ) GAP201/12/0671
Institutional support: RVO:67985840
Keywords : thermoelastic plate * unilateral dynamic contact * rigid obstacle
Subject RIV: BA - General Mathematics
Impact factor: 1.659, year: 2016
http://www.sciencedirect.com/science/article/pii/S146812181630013X

We study a dynamic contact problem for a thermoelastic von Kármán plate vibrating against a rigid obstacle. The plate is subjected to a perpendicular force and to a heat source. The dynamics is described by a hyperbolic variational inequality for deflections. The parabolic equation for a 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. A detailed analysis of the velocity, acceleration, and reaction force of the solution is given. The singular nature of the dynamic contact makes it necessary to treat the acceleration and contact force as time-dependent measures with nonzero singular parts in the zones of contact. Accordingly, the velocity field over the plate suffers (global) jumps at a countable number of times with natural physical interpretations of the signs of the jumps.
Permanent Link: http://hdl.handle.net/11104/0259480