Nonlinear bending and vibration analysis of a variable-width piezoelectric nanoplate with flexoelectric effects

The nonlinear bending and vibration behaviors of a variable-width piezoelectric nanoplate considering flexoelectric effect are investigated in this paper. The nonlinear Mindlin plate theory and finite element method are applied to derive the governing equations of variable-width piezoelectric nanoplate with flexoelectricity. The influences of geometric nonlinearity, flexoelectricity, and varying width on the bending deflection and natural frequency of the piezoelectric nanoplate with flexoelectricity under four kinds of boundary conditions are explored in detail. The numerical results show that the flexoelectric effect can strongly influence the maximum deflection, the morphology of deformation, and the natural frequency of the variable-width piezoelectric nanoplate. The consideration of geometric nonlinearity becomes necessary for nanoplate exhibiting strong flexoelectricity or subject to significant voltage loads. The boundary conditions not only affect the morphology of deformation but also influence the variation trend of natural frequency with the variable-width ratio of the piezoelectric nanoplate. While the variation trend of maximum deflection is jointly affected by the boundary conditions and flexoelectricity. The closer the shape of the piezoelectric nanoplate is to a triangle, the greater the combined effect of boundary conditions and flexoelectricity on the variation trend of maximum deflection. The results of this study can contribute to the optimization of piezoelectric nanostructures, and they are helpful in enhancing our comprehension of the mechanical behavior of piezoelectric nanostructures.