Parametric analysis of the vibration control of sandwich beams through shear-based piezoelectric actuation

This paper presents a comparative numerical analysis of shear and extension actuation mechanisms for the bending vibrations control of sandwich beams. The extension actuation mechanism denotes the use of through-thickness poled piezoelectric actuators bonded on the surfaces of the structure such that, when submitted to a through-thickness applied electric potential, these actuators produce axial stresses or strains. The shear actuation mechanism, in the contrary, is obtained through an embedded longitudinally poled piezoelectric actuator that, subjected to the same electric potential, produces shear stresses or strains. Theoretical and finite element models of a sandwich beam, capable of dealing with both mechanisms, are presented. The models are based on Bernoulli-Euler assumptions for the surface layers and Timoshenko ones for the core. An optimal state feedback control Law is used to maximize the damping of the first four natural modes of the sandwich beam. The influence of important parameters variation, such as: actuator thickness and structure/actuator modulus ratio, on the performance of the control system is analyzed under limited input voltage and induced beam tip transverse deflection. Results suggest that shear actuators can be more effective than extension ones for the control of bending vibrations.