Chaotic Vibrations of Rectangular FGM Plates with Thermo-mechanical Coupling

In this paper, the coupled dynamic equations of thermoelasticity together with the energy equation are derived for a simply supported rectangular FGM plate experiencing large deflections. The plate properties vary linearly in the thickness. General three dimensional stress-strain relations are taken into account and straindisplacement relations are assumed to be nonlinear. A lateral harmonic load is applied on the plate and the surfaces are exposed to free convection. Through integration over the thickness, four new thermal parameters are introduced which, together with the midplane displacements, constitute a system of seven partial differential equations. Using Galerkin formulation, these equations are changed into ordinary differential equations in time and solved utilizing Runge- Kutta method of fourth order. As the final goal, the thermal conditions and parameter values resulting in chaotic vibrations are determined and some numerical features such as Lyapunov exponent and Poincaré map are used to detect chaos

Keywords:

Chaos , thermo-elasticity , FGM