Investigation of the electric response of the piezoelectric curved beam considering the direct piezoelectric and flexoelectric effects

Abstract

The performance of piezoceramic devices can be significantly affected by the size and shape of the component structures, owing to the coexistence of piezoelectricity and flexoelectricity. Here, we establish a theoretical model employing the energy variation approach and static equilibrium analysis to characterize the electrical generation mechanism of the transverse isotropic Euler curved beams by considering both piezoelectricity and flexoelectricity. Based on the energy variational approach (model I), the numerical calculation is used to estimate the impact of the shape and loading mode of the piezoelectric curved beam on the electric response. Furthermore, a comparative study using the static equilibrium analysis (model II) and numerical simulations is also conducted. The results show that when the circumferential loading is applied to the free end of the beam, the generated electric voltage of the nanobeam reaches the maximum value when the radian of nanobeam around 133.57°, and for a radial loading, the optimal radian is 0° Moreover, it is demonstrated that flexoelectricity plays a dominated role on the electricity generation as the size of the curved beam shrinks to a nanometer scale. The finding here provides alternative strategies for designing and fabricating a new generation of highly efficient piezoelectric energy harvesters.