Dynamic Localization Phenomena in Elasticity, Acoustics and Electromagnetism
Suggested readings
L. Brillouin, Wave propagation in periodic systems, Dover, 1953.
R.V. Craster, J. Kaplunov and A. Pichugin, High frequency homogenization for periodic media, Proc R Soc Lond A, 466, 2341–2362, 2010.
Horgan C.O., Knowles J K, 1983, Recent developments concerning Saint-Venant principle, Advances in Applied Mechanics, 23, 179–269.
Karp B., Durban D., 2011, Saint Venant’s principle in dynamics of structures, Applied Mechanics Reviews, pending, 72 p ms., 150 refs.
S. Anantha Ramakrishna, Tomasz M. Grzegorczyk, Physics and Applications of Negative Refractive Index Materials,CRC Press, 2008.
S. Maier, Plasmonics – Fundamentals and Applications, Springer Verlag, 2007.
P. Chadwick, Surface and interfacial waves of arbitrary form in isotropic elastic media. – Elasticity 6 (1976), 73–80.
A.N. Norris, V.V. Krylov, and I.D. Abrahams, Flexural edge waves and comments on ‘A new bending wave solution for the classical plate equation’. – JASA 107 (2000), 1781–1785.
J. Kaplunov, A. Zakharov, and D. Prikazchikov, Explicit models for elastic and piezoelastic surface waves. – IMA J. Appl. Math. 71 (2006), 768–782.
Linton, C.M. & McIver, P. Embedded trapped modes in water waves and acoustics. Wave Motion, 45, 16–29 (2007).
V. Pagneux, Revisiting the edge resonance for Lamb waves in a semiinfinite plate.
Journal of the Acoustical Society of America, 120(2), 649–656 (2006)
V. Pagneux, Complex resonance and localized vibrations at the edge of a semi-infinite elastic cylinder, Mathematics and Mechanics of Solids 1081286511412439, first published on July 7, 2011 as doi:10.1177/1081286511412439.
V. Zernov and J.Kaplunov, Three dimensional edge-waves in plates. Proceedings of the Royal Society of London, A464, 301–318 (2008).
D.J. Steigmann and R.W. Ogden, 2007, Surface waves supported by thin-film/substrate interactions. IMA J. Appl. Math. 72, 730–47.
D.J. Steigmann, 2009, On the formulation of balance laws for electromagnetic continua. Math. Mech. Solids 14, 390–402.
D.J. Steigmann, 2009, Linear theory for the bending and extension of a thin, residually stressed, fiber-reinforced lamina. Int. J. Engng. Sci. 47, 1367–78.
D.J. Steigmann, 2010, Elastic waves interacting with a thin, pre-stressed, fiber-reinforced surface film. Int. J. Engng. Sci. 48, 1604–09.
M. Barham, D.J. Steigmann and D. White, Magnetoelasticity of highly deformable thin films: theory and simulation. Int. J. Non-linear Mech. (doi: 10.1016/j.ijnonlinmec.2011.05.004).