On the solutions of a dynamic contact problem for a thermoelastic von Kármán plate |
| |
| Institution: | 1. Institute of Computer Science and Mathematics, Faculty of Electrical Engineering and Information Technology, Slovak University of Technology, Ilkovi?ova 3, 81 2 19 Bratislava 1, Slovak Republic;2. Institute of Mathematics, Academy of Sciences of the Czech Republic, ?itná 25, 1 15 67 Praha 1, Czech Republic;1. Charles University, Faculty of Mathematics and Physics, Mathematical Institute, Sokolovská 83, 186 75 Prague 8, Czech Republic;2. University of Würzburg, Institute of Mathematics, Chair of Mathematics XI, Emil-Fischer-Straße 40, 97074 Würzburg, Germany;1. School of Science, Shandong University of Technology, Zibo, 255049, PR China;2. Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 811, Taiwan |
| |
| Abstract: | 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. |
| |
| Keywords: | Thermoelastic plate Unilateral dynamic contact Rigid obstacle Penalization Measure valued accelerations and forces |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
