A variational principle in flexo-electromagnetism with an application to electromagnetic wave generation from flexoelectric plates

Electromagnetic (EM) waves are the primary information carriers for modern communication devices, enabling the rapid transmission and reception of data. The excitation of EM waves through electromechanical couplings, such as the piezoelectric effect in non-centrosymmetric materials, was systematically studied by Mindlin. In contrast, this paper investigates the excitation of EM waves induced by flexoelectricity in dielectric plates, a mechanism applicable to all materials. By incorporating strain gradient, flexoelectric, and EM effects, we extend Hamilton’s principle to derive the governing equations and corresponding boundary/continuity conditions for flexo-electromagnetism. Using this newly developed theoretical framework, we analyze the vibration and EM radiation behavior of an infinite flexoelectric plate in simple thickness modes. Unlike piezoelectric mechanisms, our study reveals that EM waves can be effectively excited by thickness-shear (associated with u₁) and thickness-twist (associated with u₂) modes, while the thickness-stretch (associated with u₃) mode fails to generate EM radiation. Numerical results demonstrate that a flexoelectric plate with thickness-shear modes can excite significant electric and magnetic fields, with observable radiation power. For example, under a strain of 10^-5 in a plate of 40 µm thickness, the radiated power reaches approximately 41 W/m², above the power density of mobile communication base stations in China (<40 W/m²). This provides the telecommunication industry with novel insights into the design of nanomechanical magnetoelectric antennas.