Distributed flexoelectric modal signals on circular cylindrical shells

Flexoelectricity exhibits both direct effect and converse effect. For direct flexoelectric effect, mechanical strain gradients induce a homogeneous electric polarization in dielectrics. Thus, the induced electric field between the electrodes can be measured. Compared with the piezoelectric sensors, the main advantage of the flexoelectric sensors is that they are not sensitive to the in-plane strains. This paper presents segmented flexoelectric sensors laminated on circular cylindrical shells, and investigates the electromechanical strain-gradient/signal-generation characteristics and distributed modal flexoelectric signals on the cylindrical shells. The dynamic equations of the proposed flexoelectric sensor are derived based on the direct flexoelectric effect and thin shell assumptions. The model of modal signal is derived to investigate the sensing characteristics. In case studies, the effects of design parameters, i.e. size and thickness of the sensors and geometry of the shells, are evaluated and compared. Numerical results indicate that the contribution of longitudinal bending strain gradient is dominant in the total signals of most evaluated modes, except that in modes 1 and 2, where the contribution of the circumferential bending strain gradient is slightly higher. The amplitudes of the modal signals decrease with the shell radius, but increase with the sensor thickness.