Active Actuating of a Simply Supported Beam with the Flexoelectric Effect

Piezoelectric materials with the electro-mechanical coupling effect have been widely utilized in sensors, dampers, actuators, and so on. Engineering structures with piezoelectric actuators and sensors have provided great improvement in terms of vibration and noise reduction. The flexoelectric effect-which describes the coupling effect between the polarization gradient and strain, and between the strain gradient and electric polarization in solids-has a fourth-rank order tensor electro-mechanical coupling coefficient, and in principle makes the flexoelectricity existing in all insulating materials and promises an even wider application potential in vibration and noise control. In the presented work, a flexoelectric actuator was designed to actuate a simply supported beam. The electric field gradient was generated by an atomic force microscopy probe. Flexoelectric control force and moment components could be induced within the flexoelectric control layer. As flexoelectricity is size-dependent, the key parameters that could affect the actuating effect were examined in case studies. Analytical results showed that the induced flexoelectric control moment was strongly concentrated at the probe location. The controllable transverse displacement of the simply supported beam was calculated with the modal expansion method. It was found that the controllable transverse displacement was dependent on the probe location as well.