Coupling between electromagnetic and mechanical vibrations of thin-walled structures

Abstract

The paper addresses the issue of coupling between the electromagnetic and elastic vibrations and deals with the following three classes of problems: vibration of thin bodies in an electromagnetic field; a coupling that occurs due to perturbation of boundaries within a deformed solid; and a coupling within regions of localized stress in a composite structure with defects. It is shown that the coupling effect is negligibly small in the first case, while it becomes important in the last two classes of problems. For vibrations of thin‐walled conducting solids placed in an electromagnetic field we present a systematic new asymptotic scheme. It is observed that the magnetic field induces a ‘viscous force’, which is similar to certain problems that occur in magnetic fluids flows. When we deal with electromagnetic waves propagating through a thin‐walled periodic structure subject to regular perturbation of the boundary, an asymptotic method is applied to derive the effective boundary conditions for the perturbed inclusion within the array. We examine the effect of this perturbation on the dispersion curves for the corresponding spectral problem, and compare the asymptotic results with a finite element modelling of the perturbed structure. Finally, we show exciting results describing coupling between electromagnetic and elastic fields due to the localization associated with a defect mode in a doubly periodic structure.