Coupling between electromagnetic and mechanical vibrations of thin‐walled structures

• Published in: Quarterly journal of mechanics and applied mathematics Vol. 57; no. 3; pp. 407 - 428
• Main Authors: Guenneau, S., MOVCHAN, A. B., POULTON, C. G., NICOLET, A.
• Format: Journal Article
• Language: English
• Published: Oxford Oxford University Press 01.08.2004; Oxford Publishing Limited (England)
• Subjects: Applied classical electromagnetism; Electromagnetic wave propagation, radiowave propagation; Electromagnetism; electron and ion optics; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Mathematical methods in physics; Numerical approximation and analysis; Numerical simulation, solution of equations; Physics; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Stress analysis; Dispersion (wave); Electromagnetism; Electromagnetic; Fault location; Thin body; Finite element method; Vibrations; Electromagnetic waves; Modelling; Asymptotic approximation; Coupling; Defect structure; Thin wall; Periodic structures
• ISSN: 0033-5614; 1464-3855
• DOI: 10.1093/qjmam/57.3.407

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.