Unified efficient layerwise theory for smart beams with segmented extension/shear mode, piezoelectric actuators and sensors

Abstract

A unified coupled efficient layerwise theory is presented for the dynamics of smart laminated beams with surface-mounted and embedded piezoelectric actuators and sensors with arbitrary poling directions, acting in extension or shear mode. The theory considers a global third-order variation across the thickness combined with a layerwise linear variation for the axial displacement, expressed in terms of only three primary variables, and accounts for the transverse normal strain due to the electric field in the approximation for the transverse displacement. The electric potential is approximated as piecewise quadratic across sublayers. A finite element is developed which has two physical nodes with mechanical and some electric potential degrees of freedom (DOF), and an electric node for the electric potentials of the electroded surfaces of the piezoelectric patches. The electric nodes eliminate the need for imposition of equality constraints of the electric DOF on the equipotential electroded surfaces of the segmented piezoelectric elements and result in significant reduction in the number of electric DOF. The electric DOF associated with the physical nodes allow for the inplane electric field that is induced via a direct piezoelectric effect. The accuracy of the formulation is established by comparing the results with those available in literature and the 2D piezoelasticity solutions for extension and shear mode actuators, sensors and adaptive beams. The effect of segmentation of the electroded surface on the deflection, sensory potential and natural frequencies is illustrated for both extension and shear mode cases. The influence of the location of extension and shear mode actuators and sensors on the response is investigated for a hybrid mode composite beam. The effect of actuator thickness on the actuation authority is studied.