Harmonic wave propagation in flexoelectric microbeams

This paper presents a theoretical analysis of time-harmonic flexural wave propagation in a flexoelectric beam. By adopting the Euler–Bernoulli beam theory integrated with electromechanical coupling induced by strain gradients, the governing equations for the flexoelectric beam were derived. These equations were analytically solved to establish the dispersion relationship, from which the angular frequency, phase velocity, and group velocity were formulated. The analysis reveals that the flexoelectric coefficient, microinertia, and size-effect parameters significantly influence the wave propagation characteristics. Specifically, it is demonstrated that an increase in the wavenumber leads to a proportional rise in the excitation frequency and enhances the flexoelectric coupling effect. This interaction results in a distinct alteration of the propagation pattern, characterized by localized energy concentration within the beam structure. These findings provide a quantitative basis for designing systems with controllable dynamic responses, such as micro/nanoscale sensors and electromechanical actuators, and offer critical insights into the wave phenomena of advanced MEMS/NEMS structures.