Active tuning of vibration and wave propagation in elastic beams with periodically placed piezoelectric actuator/sensor pairs

Abstract

A novel strategy is proposed to actively tune the vibration and wave propagation properties in elastic beams. By periodically placing the piezoelectric actuator/sensor pairs along the beam axis, an active periodic beam structure which exhibits special vibration and wave propagation properties such as the frequency pass-bands and stop-bands (or band-gaps) is developed. Hamilton's principle is applied to establish the equations of motion of the sub-beam elements i.e. the unit-cells, bonded by the piezoelectric patches. A negative proportional feedback control strategy is employed to design the controllers which can provide a positive active stiffness to the beam for a positive feedback control gain, which can increase the stability of the structural system. By means of the added positive active stiffness, the periodicity or the band-gap property of the beam with periodically placed piezoelectric patches can be actively tuned. From the investigation, it is shown that better band-gap characteristics can be achieved by using the negative proportional feedback control. The band-gaps can be obviously broadened by properly increasing the control gain, and they can also be greatly enlarged by appropriately designing the structural sizes of the controllers. The control voltages applied on the piezoelectric actuators are in reasonable and controllable ranges, especially, they are very low in the band-gaps. Thus, the vibration and wave propagation behaviors of the elastic beam can be actively controlled by the periodically placed piezoelectric patches.