Coupling Analysis of Flexoelectric Effect on Functionally Graded Piezoelectric Cantilever Nanobeams

The flexoelectric effect has a significant influence on the electro-mechanical coupling of micro-nano devices. This paper studies the mechanical and electrical properties of functionally graded flexo-piezoelectric beams under different electrical boundary conditions. The generalized variational principle and Euler-Bernoulli beam theory are employed to deduce the governing equations and corresponding electro-mechanical boundary conditions of the beam model. The deflection and induced electric potential are given as analytical expressions for the functionally graded cantilever beam. The numerical results show that the flexoelectric effect, piezoelectric effect, and gradient distribution have considerable influences on the electro-mechanical performance of the functionally graded beams. Moreover, the nonuniform piezoelectricity and polarization direction will play a leading role in the induced electric potential at a large scale. The flexoelectric effect will dominate the induced electric potential as the beam thickness decreases. This work provides helpful guidance to resolve the application of flexoelectric and piezoelectric effects in functionally graded materials, especially on micro-nano devices.

Automated summary

The flexoelectric effect has a significant impact on the electro-mechanical coupling of micro-nano devices, particularly in functionally graded beams. This study investigates the mechanical and electrical properties of such beams under various electrical boundary conditions, highlighting the influences of flexoelectric effect, piezoelectric effect, and gradient distribution on their performance. The results show that nonuniform piezoelectricity and polarization direction play a leading role in induced electric potential, and flexoelectric effect dominates as beam thickness decreases.