A novel method to fully suppress single and bi-modal excitations due to the support vibration by means of piezoelectric actuators

Vibration attenuation and control is a typical topic in mechanical, civil and aeronautical engineering. In recent years, there has been extensive research on smart materials and among all of them, the piezoelectrics seem to be the most attractive for passive and active vibration damping applications. Furthermore if multiple modes are concurrently excited, as in case of turbomachinery blades, active damping systems may remarkably increase their life-cycle and outweigh the shortcomings of implementing such systems. However the damping efficiency of the piezoelectric actuators is strictly bound to their driving voltage, size and location on the structure. In this work, a cantilever piezoelectric bimorph beam under base motion is considered and the analytical expression of the electric potential that nullifies the elastic tip displacement of the beam is derived in case of single and bi-modal excitations. The model allows to identify for every bi-modal excitations a set of solutions, each of them represented by three parameters: voltage amplitude, left and right corner positions of the piezoelectric actuators pair. As a result, designers can choose the best solution for their specific application demands. For example, if the supply voltage must to be kept as low as possible, then wider actuators should be used and vice versa. It was also found out that the control parameters do not depend on the spectral distribution between the two excited modes. Hence, even if the spectral distribution between the two coupled modes changes over time, it is not necessary to adjust either the voltage or the position of the actuator pair. The analytical predictions were compared with the results of FEM multi-physics simulations for several base motion excitations and a fair agreement was observed.