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On the solutions of a dynamic contact problem for a thermoelastic von Kármán plate
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SYSNO ASEP 0459254 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On the solutions of a dynamic contact problem for a thermoelastic von Kármán plate Author(s) Bock, I. (SK)
Jarušek, Jiří (MU-W) RID, ORCID, SAI
Šilhavý, Miroslav (MU-W) RID, SAI, ORCIDSource Title Nonlinear Analysis: Real World Applications. - : Elsevier - ISSN 1468-1218
Roč. 32, December (2016), s. 111-135Number of pages 25 s. Language eng - English Country GB - United Kingdom Keywords thermoelastic plate ; unilateral dynamic contact ; rigid obstacle Subject RIV BA - General Mathematics R&D Projects GAP201/12/0671 GA ČR - Czech Science Foundation (CSF) Institutional support MU-W - RVO:67985840 UT WOS 000380079900008 EID SCOPUS 84966376452 DOI 10.1016/j.nonrwa.2016.04.004 Annotation 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. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2017
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