TY - JOUR
T1 - A long-wave model for the surface elastic wave in a coated half-space
AU - Dai, H. H.
AU - Kaplunov, J.
AU - Prikazchikov, D. A.
PY - 2010/10/8
Y1 - 2010/10/8
N2 - The paper deals with the three-dimensional problem in linear isotropic elasticity for a coated half-space. The coating is modelled via the effective boundary conditions on the surface of the substrate initially established on the basis of an ad hoc approach and justified in the paper at a long-wave limit. An explicit model is derived for the surface wave using the perturbation technique, along with the theory of harmonic functions and Radon transform. The model consists of three-dimensional 'quasi-static' elliptic equations over the interior subject to the boundary conditions on the surface which involve relations expressing wave potentials through each other as well as a two-dimensional hyperbolic equation singularly perturbed by a pseudo-differential (or integro-differential) operator. The latter equation governs dispersive surface wave propagation, whereas the elliptic equations describe spatial decay of displacements and stresses. As an illustration, the dynamic response is calculated for impulse and moving surface loads. The explicit analytical solutions obtained for these cases may be used for the non-destructive testing of the thickness of the coating and the elastic moduli of the substrate. © 2010 The Royal Society.
AB - The paper deals with the three-dimensional problem in linear isotropic elasticity for a coated half-space. The coating is modelled via the effective boundary conditions on the surface of the substrate initially established on the basis of an ad hoc approach and justified in the paper at a long-wave limit. An explicit model is derived for the surface wave using the perturbation technique, along with the theory of harmonic functions and Radon transform. The model consists of three-dimensional 'quasi-static' elliptic equations over the interior subject to the boundary conditions on the surface which involve relations expressing wave potentials through each other as well as a two-dimensional hyperbolic equation singularly perturbed by a pseudo-differential (or integro-differential) operator. The latter equation governs dispersive surface wave propagation, whereas the elliptic equations describe spatial decay of displacements and stresses. As an illustration, the dynamic response is calculated for impulse and moving surface loads. The explicit analytical solutions obtained for these cases may be used for the non-destructive testing of the thickness of the coating and the elastic moduli of the substrate. © 2010 The Royal Society.
KW - Asymptotic model
KW - Coating
KW - Radon transform
KW - Singular perturbation
KW - Surface wave
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U2 - 10.1098/rspa.2010.0125
DO - 10.1098/rspa.2010.0125
M3 - RGC 21 - Publication in refereed journal
VL - 466
SP - 3097
EP - 3116
JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
SN - 0080-4630
IS - 2122
ER -