Finite-element analysis of the frequency response of a metallic cantilever coupled with piezoelectric transducer

This paper is devoted to modeling the dynamic response of an electromechanical system consisting of a piezoelectric transducer glued on part of the upper surface of a metallic cantilever. The piezo works both as vibration sensor and as actuator, and the system is the basis of many vibration-control devices of current interest. A three-dimensional (3D) finite-element method (FEM) model that reproduces the physical system is proposed, and its advantages with respect to an analytical approach and to one-dimensional (1D) and two-dimensional (2D) FEM models are discussed. In sensor mode, the frequency response in terms of the voltage at the electrodes is drawn; while in actuator mode, the frequency response of acceleration and displacement at the free end of the cantilever is calculated. The 3D model has been verified through the comparison with the results from the experiment carried out at the University of L´Aquila, Italy. Furthermore, experimental inaccessible quantities such as stresses at the piezo-cantilever interface are computed in both modes as a preliminary step in the study of delamination phenomena and their impact on the performance of the system in vibration-control applications.