Deflection analysis of beams with extension and shear piezoelectric patches using discontinuity functions

The actuation performance of smart beams with extension and shear mode segments is investigated. The beam models are based on the first-order and higher-order shear deformation beam theories. The piezoelectric stress resultants are expressed in terms of Heaviside discontinuity functions. The state-space approach along with the Jordan canonical form is used to obtain an analytical solution for the static deflection of smart beams with arbitrary boundary conditions. Through demonstrative examples, a comparative study of a beam with extension mode actuators and the corresponding beam with a shear mode actuator is attained. The effects of actuator length and location on the deflected shape of the beam are studied. Results show that shear patches create the largest deflection if they are placed near the support, whereas extension patches create the largest deflection if they are placed at the beam center. For clamped-hinged and clamped-clamped beams, the actuation performance of the shear patches is superior to that of the extension patches.