Coupling between electromagnetic and mechanical vibrations of thin-walled structures

Quarterly Journal of Mechanics and Applied Mathematics

Volumn 57, Issue 3, 2004, Pages 407-428

  Guenneau, S ^a   Movchan, A B ^b   Poulton, C G ^c   Nicolet, A ^d  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b UNIVERSITY OF LIVERPOOL   (United Kingdom)

^c UNIVERSITY OF KARLSRUHE   (Germany)

^d AIX MARSEILLE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMPOSITE STRUCTURES; CONDUCTIVE MATERIALS; ELASTICITY; ELECTROMAGNETIC FIELD EFFECTS; ELECTROMAGNETIC WAVE PROPAGATION; FINITE ELEMENT METHOD; MAGNETIC FIELDS; MAGNETIC FLUIDS; MATHEMATICAL MODELS; MAXWELL EQUATIONS; PERTURBATION TECHNIQUES;

ELASTIC VIBRATIONS; ELECTROMAGNETIC VIBRATIONS; PHOTOELASTIC EFFECTS; TRANSVERSE ELECTROMAGNETIC;

VIBRATIONS (MECHANICAL);

EID: 4444301032     PISSN: 00335614     EISSN: None     Source Type: Journal    
DOI: 10.1093/qjmam/57.3.407     Document Type: Article

References (30)

1. L. Brillouin, La Théorie des Quanta et l'Atome de Bohr (Presses Universitaires de France, Paris 1923).
2. P. Debye, Methods to Determine the Electrical and Geometrical Structure of Molecules, Nobel Lectures, Chemistry 1922-1941 (Elsevier, Amsterdam 1941) 383-401.
3. P. St J. Russell, E. Marin, A. Diez, S. Guenneau and A. B. Movchan, Sonic band-gaps in PCF preforms: enhancing the interaction of sound and light, Optics Express 11 (2003) 2555-2560.
4. J. Sapriel, Acousto-Optics (Wiley, New York 1979).
5. C. Kittel, Introduction to Solid State Physics, 7th edn (Wiley, New York 1996).
6. D. F. Nelson, Electric, Optic and Acoustic Interactions in Dielectrics (Wiley, New York 1979).
7. E. I. Gordon, A review of acousto-optical deflection and modulation devices, Proc. IEEE 54 (1967) 1391-1400.
8. R. Adler, Interaction between light and sound, IEEE Spectrum 4 (1967) 42-48.
9. J. P. Wolfe, Imaging Phonons. Acoustic Wave Propagation in Solids (Cambridge University Press, Cambridge 1998).
10. T. A. Birks, P. J. Roberts, P. St J. Russell, D. M. Atkin and T. J. Shepherd, Full 2-D photonic bandgaps in silica/air structures, Electronic Letters 31 (1995) 1941-1942.
11. J. C. Knight, J. Broeng, T. A. Birks and P. St J. Russell, Photonic band gap guidance in optical fibers, Science 282 (1998) 1476-1478.
12. C. G. Poulton, S. Guenneau, A. B. Movchan and A. Nicolet, Transverse propagating waves in perturbed periodic structures, Asymptotics, Singularities and Homogenisation in Problems in Mechanics (ed. A. B. Movchan; Kluwer, Dordrecht 2003) 147-158.
13. G. A. Maugin, Continuum Mechanics of Electromagnetic Solids (North-Holland, Amsterdam 1988).
14. L. D. Landau, E. M. Lifshitz and L. P. Pitaevskii, Electrodynamics of Continuous Media (Butterworth-Heinemann, New York 1984).
15. U. Müller and L. Bühler, Magnetofluiddynamics in Channels and Containers (Springer, Berlin 2001).
16. S. Briguglio, G. Vlad, F. Zonca and G. Fogaccia, Nonlinear saturation of shear Alfven modes and self-consistent energetic ion transport in burning plasmas with advanced tokamak equilibria, Phys. Lett. A 302 (2002) 308-312.
17. K. M. Leung and Y. F. Liu, Full vector wave calculation of photonic band structures in face-centred cubic dielectric media, Phys. Rev. Lett. 65 (1990) 2646-2649.
18. N. A. Nicorovici, R. C. McPhedran and B. Ke-Da, Propagation of electromagnetic waves in periodic lattices of spheres. Green's function and lattice sums, Phys. Rev. E 51 (1995) 690-702.
19. J. B. Pendry, Calculating photonic band structure, J. Phys. Condensed Matter 8 (1996) 1085-1108.
20. S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I, Comm. Pure Appl. Math. 12 (1959) 623-727.
21. S. Agmon, A. Douglis and L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, II, ibid. 17 (1964) 35-92.
22. N. A. Nicorovici, R. C. McPhedran and L. C. Botten, Photonic band gaps for arrays of perfectly conducting cylinders, Phys. Rev. E 52 (1995) 1135-1145.
23. C. G. Poulton, A. B. Movchan, R. C. McPhedran, N. A. Nicorovici and Y. A. Antipov, Eigenvalue problems for doubly periodic elastic structures and phononic band gaps, Proc. R. Soc. A 456 (2000) 2543-2559.
24. H. Brezis, Analyse Fonctionnelle (Masson, Paris 1983).
25. Ph. Langlet, A.-C. Hladky-Hennion and J.-N. Decarpigny, Analysis of the propagation of plane acoustic waves in passive periodic materials using the finite element method, J. Acoust. Soc. Amer. 98 (1995) 2792-2800.
26. A. Nicolet, S. Guenneau, C. Geuzaine and F. Zolla, Modeling of electromagnetic waves in periodic media with finite elements, J. Comp. Appl. Math. 168 (2004) 321-329.
27. B. Meys, Ph.D. Thesis. Université de Liège (1999).
28. L. N. Trefethen and D. Bau III, Numerical Linear Algebra (SIAM, Philadelphia 1997).
29. P. Dular, C. Geuzaine, F. Henrotte and W. Legros, A general environment for the treatment of discrete problems and its application to the finite element method, IEEE Trans. on Magnetics 34 (1998) 3395-3398.
30. A. Yariv and P. Yeh, Optical Waves in Crystals: Propagation and Control of Laser Radiation (Wiley, New York 1984).