Efficient layerwise finite element model for dynamic analysis of laminated piezoelectric beams

An one-dimensional beam finite element with electric degrees of freedom is presented for the dynamic analysis of hybrid piezoelectric beams, using the coupled efficient layerwise (zigzag) theory developed recently by the authors. The beam element has two nodes with four mechanical and a variable number of electric potential degrees of freedom at each node. In the thickness direction, the electric field is approximated as piecewise linear across an arbitrary number of sub-layers in the piezoelectric layers. Cubic Hermite interpolation is used for the deflection and electric potentials at the sub-layers and linear interpolation is used for the axial displacement and the shear rotation. The formulation is validated by comparing the results with the available analytical solution of the zigzag theory for hybrid composite and sandwich beams with simply-supported ends. The finite element model is free of shear locking. The present zigzag finite element results for natural frequencies, mode shapes and forced vibration response of cantilever and clamped–clamped beams are compared with the two-dimensional finite element results using ABAQUS to establish the accuracy of the zigzag theory for dynamic response under these boundary conditions.