Optimal Voltage Distribution on PZT Actuator Pairs for Vibration Damping in Beams with Different Boundary Conditions

In recent decades, many studies have been conducted on the use of smart materials in order to dampen and control vibrations. Lead zirconate titanate piezoceramics (PZT) are very attractive for such applications due to their ability of delivering high energy strain in the structure. A pair of piezoelectric actuators can actively dampen the resonances of the structure, but the damping effectiveness strongly relies on its location. Damping effectiveness can be substantially increased if the structure is fully covered with PZT actuator pairs and the voltage distribution on each pair is optimized. In this way, each actuator pair contributes to the vibration attenuation and only the driving voltage's sign, distributed on each actuator pair, needs to be identified for each resonance. This approach is here applied to the case of Euler-Bernoulli beams with constant cross-section and the optimal voltage distribution is investigated for several boundary conditions. The theoretical model results were corroborated with finite element simulations, which were carried out considering beams covered by ten PZT actuator pairs. The numerical results agree remarkably well with the theoretical predictions for each examined case (i.e., free-free, pinned-pinned, and fixed-fixed).