The flexoelectric effect in solid dielectric is another form of electrol-mechanical coupling, which is different from piezoelectric effect. Flexoelectricity usually refers to the ability of a dielectric body to polarize under non-uniform deformation, which is a electrol-mechanical coupling phenomenon between the electric field and the strain gradient. The flexoelectric smart structure can realize the sensing, vibration control and stability control of the structure, so the flexoelectric smart structure has a broad application prospect in engineering applications.

In this paper, the vibration control of a conical shell with multiple flexoelectric actuators is studied, and the optimal position distribution of the flexoelectric actuators is predicted by using the neural network model. In the physical model, the AFM probe is placed on the upper surface of the flexoelectric patch to induce a high intensity non-uniform electric field on the flexoelectric actuator, thus generating the internal stress of the flexoelectric actuator patch according to the reverse flexoelectric effect. The case studys show that the high intensity non-uniform electric field generated by the AFM probe has almost zero contribution to the electric field in the area far from the contact point, so the stress generated by the converse flexoelectric effect is mainly concentrated near the AFM probe, and the size and shape of the torsion plate have very limited 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 torsional electric actuators can be calculated by the superposition principle. When multiple flexoelectric actuators work together, when the same flexoelectric actuator is in different positions, it may produce opposite lateral displacement at a point on the surface of the truncated conical shell, this situation will make the vibration displacement of the flexoelectric actuator cancel each other. The approximate optimal distribution positions of the multi-channel flexoelectirc actuators were obtained through experimental simulation.

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