On the mechanics of curved flexoelectric microbeams

Based on the flexoelectric theory incorporating strain gradient and polarization gradient, a flexoelectric curved microbeam model is established. The governing equations, boundary conditions and initial conditions are derived by Hamilton's principle. Both the static bending and natural vibration problems are solved. The direct and converse flexoelectric responses are numerically analyzed. In the direct flexoelectric response, more collected charges are expected in the beam with larger original curvature for simply supported boundary, but the opposite is true for clamped boundary. In the converse flexoelectric response, the voltage-induced bending exists even in a clamped curved beam while it is not the case for a clamped straight beam and larger original curvature always implies larger deflection for both boundary conditions. In addition, the strain gradient elastic effect is found to reduce both the flexoelectric responses especially when the thickness is comparable to the length scale parameter associated with strain gradient.