Precise deflection analysis of beams with piezoelectric patches

Abstract

Precise deflection models of beams with n pairs of piezoelectric patches are developed analytically. To formulate the models, the first-order and higher-order beam theories are used. The analytical solutions are obtained with the aid of the state-space approach and Jordan canonical form. A case study is presented to evaluate the performance of the authors previously reported models. Through a demonstrative example, a comparative study of the first-order and higher-order beams with two piezoelectric pairs is attained. It is shown that the first-order beam lacks that ability to accurately predict the beam behavior in the region of the patches when compared with the results of the higher-order beam. Further applications of the solutions are presented by investigating the effects of patch lengths and locations on the deflected shape of beams with two piezoelectric pairs. For clamped–hinged and clamped–clamped (C–C) beams, the deflected shape switches from negative to positive when the piezoelectric pairs are moved toward the supports. The results of C–C beams show that increasing the patch lengths does not necessarily increase the deflection. The presented solutions can be used in the design process to obtain detailed deformation information of beams with various boundary conditions. Moreover, the presented analysis can be readily used to perform precise shape control of beams with n pairs of piezoelectric patches.