On the long-wave explicit model for the surface wave on a coated half-space
Julius Kaplunov (Keele University), Danila Prikazchikov (Keele University, UK)
SES Medal Symposium in honor of D.J. Steigmann
Mon 4:20 - 5:40
MacMillan 115
The paper is concerned with analysis of near-surface dynamics of a coated elastic half-space. The presence of a coating adds interesting features to the mathematical formulation and is also rather important for engineering applications, see e.g. [1]. The developed approach relies on the hyperbolic-elliptic model for an elastic half-space [2], aiming to extract the contribution of the Rayleigh wave to the overall dynamic response. Within the model the surface wave propagation is described by an explicit hyperbolic equation, while the decay into the interior is governed by a pseudo-static elliptic equation. The methodology in [2] can be extended to a coated half-space [3]. The effective boundary conditions at the substrate-coating interface are derived using the long-wave asymptotic integration. Hence, it is shown that the effect of the coating leads to a singular perturbation of the hyperbolic equation on the surface in the form of a a pseudo-differential operator. The established model allows to treat transient non-homogeneous boundary value problems and also drastically simplifies a more traditional analysis of the associated dispersion relation. As an example, the surface wave fields induced by impulse and moving loads are considered. The obtained results may also be extended to coatings with more advanced material properties, including the effect of anisotropy, viscosity, and pre-stress, e.g. see [4,5]. References [1] D.J. Steigmann, R.W. Ogden, IMA J. Appl. Math. 72 (2007) 730-747. [2] J. Kaplunov, A. Zakharov and D.A. Prikazchikov, IMA J. Appl. Math. 71 (2006) 768-782. [3] H.-H. Dai, J. Kaplunov, and D.A. Prikazchikov, Proc. Roy. Soc. A. 466 (2010) 3097-3116. [4] D.J. Steigmann, Int. J. Eng. Sci. 48 (2010) 1604-1609. [5] D. J. Steigmann, Int. J. Non-Linear Mech., 39 (2004) 1193-1216.