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

0459254 - MÚ 2017 RIV GB eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR(CZ) GAP201/12/0671
Institucionální podpora: RVO:67985840
Klíčová slova: thermoelastic plate * unilateral dynamic contact * rigid obstacle
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 1.659, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0259480