Continuous modeling and minimal dimension reduction for thermomechanically coupled nonlinear vibrations of laminated plates

A unified formulation of thermomechanically coupled laminated plates with von Karman nonlinearities, undergoing finite amplitude vibrations, is presented. It integrates mechanical and thermal aspects, by addressing them in parallel via the introduction of generalized 2D variables and equations. The general formulation virtually embeds a multitude of possible models, resulting from different assumptions about the plate mechanical and thermal configurations. The obtained continuous model is then subjected to a minimal dimension reduction via Galerkin procedure. Further simplified models variably accounting for the presence of also thermal conditions are identified. Their suitability to reliably describe some main effects of thermomechanical phenomena in variable system and excitation conditions is comparatively discussed.