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

This article focuses on developing a comprehensive three-dimensional dynamic model of flexo-electromagnetism to investigate electromagnetic (EM) wave excitation induced by flexoelectricity in dielectric plates. Extending Hamilton's principle, the study derives governing equations and boundary conditions that couple strain gradient, flexoelectric, and EM effects, specifically analyzing simple thickness vibration modes in cubic m3m crystal plates. The findings reveal that thickness-shear and thickness-twist vibration modes can effectively generate EM waves, while the thickness-stretch mode cannot excite magnetic fields or EM radiation. Numerical results demonstrate that a flexoelectric plate under thickness-shear vibration can produce significant electric and magnetic fields with radiated power exceeding typical mobile communication base station power densities, suggesting potential applications in designing nanomechanical magnetoelectric antennas for telecommunications.