Nonlinear Transient Behavior of a Piezothermoelastic Laminated Beam Subjected to Mechanical, Thermal and Electrical Load

Abstract

Nonlinear transient behavior of a piezothermoelastic laminate including the dynamic deformation deviated arbitrarily from the equilibrium state is analyzed. As an analytical model, we consider a laminated beam composed of the elastic structural layers and the piezoelectric layers subjected to mechanical, thermal and electrical loads as disturbances or intended control procedures. The deformation of the beam is analyzed by the classical laminate theory and the von Kárman strain. Equations of motion in terms of displacements are obtained and they are analyzed through the Galerkin method. As a result, the dynamic deflection of the beam is found to be governed by the equation for a polynomial oscillator, and the following quantities are obtained: (1) the buckling temperature due to in-plane thermal and electrical loads; (2) the static large deflection due to combined in-plane and anti-plane loads; (3) the steady vibration deviated from the static equilibrium state; (4) transient large deformation with damping effect considered due to mechanical, thermal and electrical loads. Through these results, the characteristics of the transient deformation of the beam is discussed in detail.