An efficient quadrilateral element based on improved zigzag theory for dynamic analysis of hybrid plates with electroded piezoelectric actuators and sensors

Abstract

An efficient four-node quadrilateral element is developed using a coupled improved zigzag theory for the dynamic analysis of hybrid plates with segmented piezoelectric sensors and actuators. The theory considers a third-order zigzag approximation for inplane displacements, a layerwise quadratic approximation for the electric potential and a layerwise variation of the deflection to account for the piezoelectric transverse normal strain. The conditions on transverse shear stresses at the interfaces and at the top and bottom are satisfied exactly in the presence of electric loading. In a novel concept, the degrees of freedom (dof) corresponding to the quadratic component of the electric potential distribution are associated with the physical nodes and the electric potentials of the electroded piezoelectric surfaces are attached to separate electric nodes. The requirement of C1 continuity of interpolation functions of the deflection is circumvented by employing an improved discrete Kirchhoff constraint technique. Comparison of the present results for natural frequencies and mode shapes for a variety of bimorph, hybrid composite and sandwich plates, with three-dimensional (3D) analytical and FE solutions, and those of other available elements establishes the superiority of the present element with respect to accuracy, robustness and computational efficiency. The comparison also establishes the superiority of the zigzag theory over the smeared third-order theory having the same number of dof.