Analytical modeling and optimal resistance estimation in vibration control of beams with resistively shunted piezoelectrics

Transverse beam vibrations can be controlled by bonding resistively shunted piezoelectrics to the beam's surface. The piezoelectrics convert a part of the system's mechanical energy into electrical energy, which is dissipated by the shunted resistance. An analytical model is presented in this paper to represent the resistively shunted piezoelectric beam. A single expression for the system response, encompassing both the mechanical and electrical aspects, is derived. The aptness of the presented model in describing the system is evident from the discussions of the shortcomings of the two most employed models found in literature. In deriving the optimal resistor from the magnitude plot of the FRF, the previous works ignore the inherent damping of the structure in their analytical models. In this paper, the optimal resistance is derived from the analytical model which includes the inherent damping of the structure. A modification was done to the presented analytical model to include the design of the metallic electrodes covering the piezoceramics. Experimental results from literature were used to validate the presented model, and it was found that the presented analytical model offered closer predictions than the model given in the literature. Furthermore, results from the experiments conducted on a cantilever piezoelectric beam were used to validate the modified analytical model.