Flexoelectric vibration control of parabolic shells

The presented work focuses on the spatially distributed actuation behavior of flexoelectric actuators on a parabolic cylindrical shell panel with simply supported boundary conditions. A flexoelectric actuator with significant electric field gradients could generate actuation forces and control moments to drive or control system oscillations. For an engineering structure with initial excitations, flexoelectric actuators could be employed to achieve vibration control with designed electric inputs. The dynamic equations of the parabolic cylindrical panel laminated with an arbitrary flexoelectric actuator are defined first. The transverse displacement excited by an external mechanical loading and flexoelectric actuators is calculated. Actuation effects and vibration control efficiency contributed by various design parameters including flexoelectric patch thickness and atomic force microscopy (AFM) probe radius are studied. As the purpose of this study is to accelerate the vibration attenuation, the open-loop control usually causes insufficient control or over-actuation effects. Using displacement feedback, velocity feedback, and acceleration feedback, the effectiveness of these three closed-loop control methods is analyzed and evaluated by the modal response. Analyses suggest that the velocity feedback could effectively attenuate oscillations with the lowest voltage input than in the other two cases. Specifically, the system damping ratio can be adjusted with velocity feedback. Lower voltage input could benefit system design and release stress concentrations caused by high electric field gradients. This research provides a basis for vibration control based on flexoelectric parabolic shell structures and provides an optimal choice for the design of flexoelectric drive closed-loop control for parabolic shell structures.