Smart beams with extension and thickness-shear piezoelectric actuators

Analytical models and exact solutions for beams with thickness-shear and extension piezoelectric actuators are formulated and developed. The models are based on the first-order beam theory (FOBT) and higher-order beam theory (HOBT). The beam bending problem is solved by using the state-space approach along with the Jordan canonical form. Numerical examples of beams incorporating piezoelectric actuators with various boundary conditions are presented. In these examples, the validity of the proposed models and the feasibility of using shear-mode actuators in smart beams are investigated. For the extension-mode actuators there is slight difference between the deflections of the FOBT and that of the HOBT. For the shear-mode actuators there is pronounced difference between the deflections of the FOBT and that of the HOBT. The results of the FOBT are very sensitive to the value of the shear correction factor. The results of the present work are compared with the previously reported results in the literature, where available.