Analysis of Wave Propagation in Flexoelectric Beam Using Mixed Finite Element Method

A dynamic model of flexoelectric Timoshenko beams is established to investigate wave propagation characteristics. The dispersion curves of bending and shear waves are numerically obtained using the mixed finite element method (FEM). Compared with pure elastic beams, the flexoelectric effect increases the effective stiffness of the beam, leading to higher frequencies of bending and shear waves. This frequency increase becomes more pronounced at higher wavenumbers. Additionally, the study reveals a significant size-dependent characteristic of the flexoelectric effect, which is more pronounced at the nanoscale and diminishes with increasing beam thickness.