Modelling Thermoelastic Damping in Nonlinear Plates with Internal Resonance

We use a nonlinear, reduced order, coupled thermoelastic model, derived from von Karman plate equations to study the transverse resonant response of simply supported thin rectangular plates under free and forced vibrations to understand the experimentally observed behavior, specifically the change in temperature as a result of vibrations. The model is studied using Galerkin approximation, harmonic balance, and numerical continuation techniques. Multimode response for plates is considered for non-resonant excitation as well as near 1:1 resonance between the second and third linear eigenmodes of the system, with harmonic forcing close to a natural frequency. Internal resonance and associated coupled-mode dynamics are observed, with noticeable decrease in modal amplitudes and some increase in plate natural frequencies. Temperature rise in the plate is also observed as a result of the thermoelastic coupling. Various bifurcations in the system are identified and a parametric study is performed.