Abstract
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.
Highlights
FGMpiezoelectric piezoelectric beam with flexoelectricity investigated in the present paper
Gibbs free energy and the linear investigated in the present paper
Ing equation and the corresponding boundary conditions under the CCF and OCI condiSome new coupling parameters are proposed to describe the interplay between piezotions
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Su et al [11] studied the influence of the flexoelectric and piezoelectric effects on electro-mechanical coupling responses of the bilayer piezo-flexoelectric nanobeam based on the strain gradient elasticity. Chu et al [21] investigated the flexoelectric effect on the bending and vibration responses of functionally graded piezoelectric nanobeams based on a modified strain gradient theory. Xiang et al [22] studied the electro-elastic response on the bending behavior of a functionally graded elastic beam with consideration of the flexoelectric effect. They found that the vibration behavior of the nanobeam would be effectively influenced by the flexoelectricity, porosity, and graphene platelets It is not clear how the coupling of flexoelectric and piezoelectric effects acts on the electro-mechanical responses of FGM beams. The influences of the coupling between flexo-piezoelectricity and the gradient parameter on the deflection, induced electric potential, and stress distribution are presented graphically, analyzed, and discussed
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