DYNAMICS OF NONLINEAR THERMOELASTIC DOUBLE-BEAM SYSTEMS

This article describes the transverse vibrations of a symmetric elastically-coupled thermoelastic double-beam system, under even compressive axial loading. Each beam is assumed to be elastic, extensible and supported at the ends, and so hinged conditions are used for the displacements and Dirichlet ones for the temperatures. The mechanical problem is written as a nonlinear system composed of hyperbolic and parabolic partial differential equations. An existence and uniqueness result and an energy decay property are obtained. Then, fully discrete approximations are introduced based on the finite element method and the implicit Euler scheme. A discrete stability result and a priori error estimates are shown. Finally, some numerical simulations are presented to demonstrate the accuracy of the approximation and the behaviour of the solution.