Abstract
We derive explicit asymptotic formulations for surface, interfacial and edge waves in elastic solids. The effects of mixed boundary conditions and layered structure are incorporated. A hyperbolic-elliptic duality of surface and interfacial waves is emphasized along with a parabolic-elliptic duality of the edge bending wave on a thin elastic plate. The validity of the model for the Rayleigh wave is illustrated by several moving load problems.
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Bibliography
J.D. Achenbach, Wave propagation in elastic solids, North-Holland, Amsterdam, 1973.
J.D. Achenbach, Explicit solutions for carrier waves supporting surface waves and plate waves, Wave Motion 28 (1998) 89–97.
P. Chadwick, Surface and interfacial waves of arbitrary form in isotropic elastic media, J. Elast. 6 (1976) 73–80.
J. Cole and J. Huth, Stresses produced in a half plane by moving loads, J. Appl. Mech. 25 (1958) 433–436.
R. Courant and D. Hilbert, Methods of Mathematical Physics, Vol. 2, John Wiley & Sons, New York, 1989.
H.H. Dai, J. Kaplunov, D.A. Prikazchikov, A long-wave model for the surface elastic wave in a coated half-space, Proc. Roy. Soc. A. 466 (2010) 3097–3116.
M. Destrade, Surface acoustic waves in rotating orthorhombic crystals, Proc. Roy. Soc. A. 460 (2004) 653–665.
M. Destrade, Seismic Rayleigh waves on an exponentially graded, orthotropic half-space, Proc. Roy. Soc. A. 463 (2007) 495–502.
M.A. Dowaikh, R.W. Ogden. On surface waves and deformations in a pre-stressed incompressible elastic solid. IMA Jl Appl Math. 44 (1990) 261–284.
M.A. Dowaikh, R.W. Ogden. On surface waves and deformations in a compressible elastic half-space. SAACM, 1 (1991) 27–45.
B. Erbaş, J. Kaplunov and D.A. Prikazchikov, The Rayleigh wave field in mixed problems for a half-plane, IMA Jl Appl. Math. (2012) doi:10.1093/imamat/hxs010.
F.G. Friedlander, On the total reflection of plane waves, Quart. J. Mech. Appl. Math. 1 (1948) 376–384.
Y.B. Fu, Existence and uniqueness of edge waves in a generally anisotropic elastic plate, Q. J. Mech. Appl. Math. 56 (2003) 605–616.
Y.B. Fu, An explicit expression for the surface-impedance matrix of a generally anisotropic incompressible elastic material in a state of plane strain, Int. J. Non-linear Mech. 40 (2005) 229–239.
H.G. Georgiadis, G. Lykotrafitis, A method based on the Radon transform for three-dimensional elastodynamic problems of moving loads. J. Elast. 65 (2001) 87–129.
V. G. Gogoladze, Rayleigh waves on the interface between a compressible fluid medium and a solid elastic half-space. Trudy Seism. Inst. Acad. Nauk. USSR 127 (1948) 27–32.
R.V. Goldstein, Rayleigh waves and resonance phenomena in elastic bodies, J. Appl. Math. Mech. (PMM) 29(3) (1965) 516–525.
T.C. Kennedy and G. Herrmann, Moving load on a fluid-solid interface: supersonic regime, J. Appl. Mech. 40 (1973a) 137–142.
T.C. Kennedy and G. Herrmann, Moving load on a fluid-solid interface: subsonic and intersonic regimes, J. Appl. Mech. 40 (1973b) 885–890.
J. Kaplunov, Transient dynamics of an elastic half-plane subject to a moving load, Preprint No.277, Institute for Problems in Mechanics, Moscow, 1986 (in Russian).
J. Kaplunov, E.L. Kossovich, R.R. Moukhomodiarov and O.V. Sorokina, Explicit models for bending and interfacial in thin elastic plates, Izvestia SGU, Math. Mech. Inf., 13(1), (2013) 56–63.
J. Kaplunov, E. Nolde and D.A. Prikazchikov, A revisit to the moving load problem using an asymptotic model for the Rayleigh wave,Wave Motion 71 (2010) 440–451.
J. Kaplunov, D.A. Prikazchikov, B. Erbaş and O. S¸ahin. On a 3D moving load problem for an elastic half space, Wave Motion (2013) (doi: 10.1016/j.wavemoti.2012.12.008)
J. Kaplunov, A. Zakharov and D.A. Prikazchikov, Explicit models for elastic and piezoelastic surface waves, IMA J. Appl. Math. 71 (2006) 768–782.
A.P. Kiselev and D.F. Parker, Omni-directional Rayleigh, Stoneley and Schölte waves with general time dependence, Proc. Roy. Soc. A. 466 (2010) 2241–2258.
A.P. Kiselev, G.A. Rogerson, Laterally dependent surface waves in an elastic medium with a general depth dependence. Wave Motion 46(8) (2009), 539–547.
Yu.K. Konenkov, A Rayleigh-type bending wave, Sov. Phys. Acoust. 6, (1960) 122–123.
J.B. Lawrie, J. Kaplunov, Edge waves and resonance on elastic structures: an overview. Math. Mech. Solids 17(1), (2012) 4–16 (doi:10.1177/1081286511412281).
Lord J.W.S. Rayleigh, On waves propagated along the plane surface of an elastic solid, Proc. R. Soc. Lond. 17 (1885) 4–11.
A.N. Norris, Bending edge waves, J. Sound Vib. 174 (1994) 571–573 .
A.N. Norris, V.V. Krylov, and I.D. Abrahams. Bending edge waves and comments on ”A new bending wave solution for the classical plate equation”. J. Acoust. Soc. Am. 107, (2000) 1781–1784 .
D.F. Parker and A.P. Kiselev, Rayleigh waves having generalised lateral dependence, Quart. J. Mech. Appl. Math. 62 (2009) 19–30.
D.F. Parker, Evanescent Schölte waves of arbitrary profile and direction, Europ. J. Appl. Math. 23 (2012) 267–287. (doi:10.1017/S0956792511000362).
A.V. Pichugin, G.A. Rogerson, Extensional edge waves in pre-stressed incompressible plates, Math. Mech. Solids 17, (2012) 27–42.
D.A. Prikazchikov, Development of the asymptotic models for surface and interfacial waves, Vestnik NGU, 4(4) (2011) 1713–1715 (in Russian).
D.A. Prikazchikov, Rayleigh waves of arbitrary profile in anisotropic media, Mech. Rec. Comm, (2013, to appear). (doi:10.1016/j.mechrescom.2013.03.009).
J.G. Schölte, The range of existence of Rayleigh and Stoneley waves, Roy. Astron. Soc. Lond. Month. Not. Geophys. Suppl. 5(3) (1947) 120–126.
J.G. Schölte, On true and pseudo Rayleigh waves, Proc. Konink. Ned. Akad. Wetensch. 52 (1949) 652–653.
A.L. Shuvalov, A.G. Every, On the long-wave onset of dispersion of the surface-wave velocity in coated solids. Wave Motion 45(6) (2008) 857–863.
R. Stoneley, Elastic waves at the surface of separation of two solids, Proc. Roy. Soc. A 106 (1924) 416–428.
A.G. Sveshnikov, A.N. Tikhonov, The Theory of Functions of a Complex Variable. Moscow: Mir Publishers, 1978.
H.F. Tiersten, Elastic surface waves guided by thin films, J. Appl. Phys. 40(2) (1969) 770–789.
D.D. Zakharov, Analysis of the acoustical edge bending mode in a plate using refined asymptotics. J. Acoust. Soc. Am. 116(2) (2004) 872–878.
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Kaplunov, J., Prikazchikov, D.A. (2013). Explicit Models for Surface, Interfacial and Edge Waves. In: Craster, R.V., Kaplunov, J. (eds) Dynamic Localization Phenomena in Elasticity, Acoustics and Electromagnetism. CISM International Centre for Mechanical Sciences, vol 547. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1619-7_3
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DOI: https://doi.org/10.1007/978-3-7091-1619-7_3
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