Elastic waves interacting with a thin, prestressed, fiber-reinforced surface film. (English) Zbl 1231.74189
Summary: Elastic surface waves propagating at the interface between an isotropic substrate and a thin, transversely isotropic film are analyzed. The transverse isotropy is conferred by fibers lying parallel to the interface. A rigorous leading-order model of the thin-film/substrate interface is derived from the equations of three-dimensional elasticity for prestressed, transversely isotropic films having non- uniform properties. This is used to study Love waves.
References:
| [1] | Steigmann, D. J.; Ogden, R. W., Surface waves supported by thin-film/substrate interactions, IMA J. Appl. Math., 72, 730-747 (2007) · Zbl 1128.74021 |
| [2] | Achenbach, J. D., Wave Propagation in Elastic Solids (1973), North-Holland: North-Holland Amsterdam · Zbl 0268.73005 |
| [3] | Murdoch, I., The propagation of surface waves in bodies with material boundaries, J. Mech. Phys. Solids, 24, 137-146 (1976) · Zbl 0342.73017 |
| [4] | Pichugin, A. V.; Rogerson, G. A., An asymptotic membrane-like theory for long-wave motion in a pre-stressed elastic plate, Proc. Roy. Soc. Lond., A458, 1447-1468 (2002) · Zbl 1056.74033 |
| [5] | Shuvalov, A. L.; Every, A. G., On the long-wave onset of dispersion of the surface-wave velocity in coated solids, Wave Motion, 45, 857-863 (2008) · Zbl 1231.76284 |
| [6] | Ting, T. C.T., Steady waves in an anisotropic elastic layer attached to a half-space or between two half-spaces: a generalization of Love waves and Stoneley waves, Math. Mech. Solids, 14, 52-71 (2009) · Zbl 1257.74089 |
| [7] | Knops, R. J.; Payne, L. E., Uniqueness Theorems in Linear Elasticity, Springer Tracts in Natural Philosophy, 19 (1971) · Zbl 0224.73016 |
| [8] | Spencer, A. J.M., Constitutive theory for strongly anisotropic solids, (Spencer, A. J.M., Continuum Theory of the Mechanics of Fibre-Reinforced Composites. Continuum Theory of the Mechanics of Fibre-Reinforced Composites, CISM Courses and Lectures, vol. 282 (1984), Springer: Springer Wien), 1-32 · Zbl 0588.73117 |
| [9] | Steigmann, D. J., Linear theory for the bending and extension of a thin, residually stressed, fiber-reinforced lamina, Int. J. Eng. Sci., 47, 1367-1378 (2009) · Zbl 1213.74210 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
