An efficient coupled theory for multilayered beams with embedded piezoelectric sensory and active layers

Abstract

An efficient coupled electromechanical model is developed for multilayered composite beams with embedded or surface bonded piezoelectric laminae subjected to static electromechanical excitation. The model combines third order zigzag approximations for the displacement field with a layerwise representation of the electric field. Interfacial continuity of the inplane displacement and the transverse shear stress and traction free conditions on the top and bottom surfaces are ensured under general electromechanical loading situation. The model allows for a non-uniform variation of transverse displacement in the piezoelectric layers caused by the electric field induced normal transverse strain. The theory has the same number of primary variables as first order theory and hence the computational cost is independent of the number of layers in the laminate. The governing equations of stress and charge equilibrium and the variationally consistent boundary conditions are derived from the principle of virtual work. To illustrate the accuracy, applicability and robustness of the theory, an analytical solution is obtained for hybrid beams with simply supported ends. Present results for simply supported hybrid beams with sensory and actuated piezoelectric layers are compared with the exact three dimensional solution and uncoupled first order theory solution. The present results show significant improvement over the first order solution and compare very well with the exact solution for both thin and thick piezoelectric laminated beams. Capability of the developed theory to model sensory, active and combined response of smart composite beams with general laminate configurations has been demonstrated through additional numerical examples. Feasibility of controlling deflection by applying appropriate actuation potential has been illustrated.