Vibration control of conical shell with multi-flexoelectric actuation

The converse flexoelectric effect can be applied to control thin-shell structures. In this paper, the vibration control of a conical shell with multiple flexoelectric actuators is studied. In order to investigate the actuation performance of the flexoelectric patch, this study analyzes the electric field gradient, modal forces, and displacement of a conical shell driven by the flexoelectric patch and their relationships with the design parameters. In the physical model, the AFM probe is positioned on the upper surface of the flexoelectric patch to create a high-intensity non-uniform electric field within the flexoelectric actuator. In turn, generates internal stress in the flexoelectric actuator patch through the converse flexoelectric effect. The case study shows that the high-intensity non-uniform electric field generated by the AFM probe has nearly zero contribution to the electric field in areas far from the contact point. As a result, the stress generated by the converse flexoelectric effect primarily concentrates near the AFM probe, with the size and shape of the flexoelectric patches having minimal influence on the actuation. Based on the assumption of small deformation and linear displacement, considering the vibration control of multiple flexoelectric actuators on the truncated conical shell, the lateral displacement results controlled by multiple flexoelectric actuators can be calculated by the superposition principle. When multiple flexoelectric actuators work together, the same flexoelectric actuator in different positions may induce opposite lateral displacements at a specific point on the surface of the truncated conical shell. This can result in the cancellation of vibrational displacements produced by the flexoelectric actuators. Approximate optimal distribution positions for the multi-channel flexoelectric actuators were determined through experimental simulations. In this study, the superior vibration suppression capabilities of multi-channel flexoelectric actuators are highlighted through a comparative analysis with single-channel configurations, demonstrating their effectiveness in controlling complex vibration modes in conical shell structures.