Non-linear dynamic response of a thin laminate subject to non-uniform thermal field

Non-linear dynamics behavior of a thin isotropic laminate in a simply supported boundary condition is studied for its response with both mechanical and thermal loads in effect. The thermal effects of both the in-plane and transverse non-uniform temperature variations in steady-state are considered. The equation of motion for the laminate deflection is reduced to the Duffing equation in a decoupled modal form by means of a generalized Galerkin's method. The stress field as a function of deflection and temperature variation is also obtained in a plane stress condition for its non-linear elastic behavior with von Karman strain field.For an exemplary laminated microstructure used as a printed wiring board, it is found that a high rise of the in-plane temperature increases the resonance frequency and could significantly increase the stresses of the lamina. The through thickness temperature variation has no significant effect on the deflection. Failure analysis is also made based on the composite failure criteria for a laminate to identify the critical mechanical and thermal loads.