Non-linear dynamic behaviour of a piezothermoelastic laminate

Abstract

Non-linear dynamic behaviour of a piezothermoelastic laminate including the dynamic deflection deviated arbitrarily from the equilibrium state is analysed. As an analytical model, we consider a rectangular laminate composed of fiber-reinforced laminae and piezoelectric layers subjected to mechanical, thermal, and electrical loads. Non-linear large deformation of the laminate is analysed based on the von Kármán strains and the first-order shear deformation theory. Equations of motion of the laminate are analysed using the Galerkin method. As a result, it is found that the dynamic deflection of the laminate is governed by the equation for a polynomial oscillator, and the following quantities are obtained: (1) the buckling temperature due to in-plane thermal load; (2) the static large deflection due to combined in-plane and anti-plane loads; (3) the natural frequency of the oscillation in the vicinity of the static equilibrium state; (4) the dynamic large deflection deviated arbitrarily from the state. Moreover, numerical examples are shown to investigate the methods to rise the buckling temperature and to linearize thermal deflection and the natural frequency by applying the electrical voltage to the piezoelectric actuators. As a result, it is found that appropriate application of the electrical voltage serves as structural stabilization of the laminate.