Dynamics of multilayered thermoviscoelastic plates

This paper deal with laminated thin-walled structures. The laminated structures considered herein consist of three layers. The following assumptions are assumed. The thickness of inner layer is considerably greater the others. The kinematic relations for the inner layer are examined in the form of Mindlin–Reissner shell theory, for the outer layers are in the form of membrane theory. The deformations of the whole layered structure are defined by the polyline hypothesis. The material of outer layers is supposed to be thermoelastic isotropic, whereas inner one is isotropic thermoviscoelastic. A variational principle for 3-layered thermoviscoelastic thin-walled structures is obtained. The variational technique is utilized to derive the equations of motion and heat conduction as well as appropriate boundary and initial conditions. In the case of plane mean surface the solutions of this equations are obtained in the terms of scalar potentials. The numerical example for the simply supported elliptic plate is shown.