Vibration analysis of a trimorph plate for optimised damage mitigation

The dynamic response of a viscously damped rectangular trimorph plate subjected to a sinusoidally distributed load was investigated for simply-supported boundary conditions. The governing equation for the nonlinear deflection of the plate, which is first introduced in this paper, was derived based on the classical plate theory (CPT) and the classic allaminate theory (CLT). The governing equation was solved using the Navier method and direct numerical integration. Optimised time-domain response plots for a trimorph plate made up of aluminium (Al), polyvin ylidene fluoride (PVDF) and lead zirconate titanate (PZT) layers revealed that only three out of the six possible layer configurations are necessary for determining the best layer-stacking. In determining the best layer-stacking for the optimised dynamic response, three factors were considered namely: the stiffness, natural frequency and damping constant. Both of the Al/PVDF/PZT or Al/PZT/PVDF configurations were found to produce the best response qualities i.e. high elastic stiffness, high natural frequency and low viscous damping. Frequency-domain plots were generated to compare the nonlinear and linear responses and it was discovered that the effect of the nonlinearity predictably reduces the natural frequency of the trimorph plate. This study can be applied to the analysis of optimised damage mitigation of intelligent car bodies and safety critical structures which are subject to potentially destructive loading conditions.