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On the solutions of a dynamic contact problem for a thermoelastic von Kármán plate.pdf
Nonlinear Analysis: Real World Applications 32 (2016) 111–135 Contents lists available at ScienceDirect
Nonlinear Analysis: Real World Applications
/locate/nonrwa
On the solutions of a dynamic contact problem for a thermoelastic von Ka′rm′an plate
I. Bocka, J. Jaruˇsekb, M. Sˇilhavy′ b,?
a Institute of Computer Science and Mathematics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Ilkoviˇcova 3, 81 2 19 Bratislava 1, Slovak Republic b Institute of Mathematics, Academy of Sciences of the Czech Republic, Zˇitn′a 25, 1 15 67 Praha 1, Czech Republic
highlights
? A contact problem for a thermoelastic von Ka′rm′an plate is studied. ? The dynamics is described by a hyperbolic variational inequality. ? The thermal strain is described by parabolic equation. ? The acceleration and contact force are represented by spatio-temporal measures. ? A detailed analysis of the velocity, acceleration, and reaction force of the solution is given.
article info
Article history: Received 9 November 2015 Received in revised form 15 April 2016 Accepted 15 April 2016 Available online 10 May 2016
Keywords: Thermoelastic plate Unilateral dynamic contact Rigid obstacle Penalization Measure valued accelerations and forces
abstract
We study a dynamic contact problem for a thermoelastic von Ka′rm′an 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
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