Modal signal analysis of conical shells with flexoelectric sensors

Flexoelectricity is known as the electromechanical coupling effect between the strain gradient and the polarization. In this study, a flexoelectric sensor is laminated on conical shells to monitor the natural modal signal distributions. The sensing mechanism of a generic flexoelectric sensor patch is presented first. Then, the spatially distributed microscopic sensing signal with respect to coordinates is evaluated in detail to reveal the modal signal distributions. Due to the gradient effect, the bending strain component is the only contribution to the total sensing signal. The total signal consists of two components resulting from the circumferential and longitudinal bending strain components. Analytical results show that the flexoelectric sensing signal induced by the longitudinal bending strain is the dominant contribution to the total signal for lower order modes; the contribution of the circumferential bending strain components increases while increasing the circumferential mode number. In lower modes, the optimal location of flexoelectric sensor is at the minor end and shifts to the middle for shallow shells. In higher modes, the optimal location is at the middle of the shell, but first shifts to the major end and then shifts to the minor end while increasing the semi-apex angle.