Vol. 5, No. 1, 2010

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Elastic SH wave propagation in a layered anisotropic plate with periodic interface cracks: exact versus spring boundary conditions

Anders Boström and Oleg V. Kvasha

Vol. 5 (2010), No. 1, 67–78

The propagating antiplane (SH) modes in a symmetrically three-layered, anisotropic, thick plate with a periodic array of interface cracks are investigated. The exact dispersion relation can be derived with the help of a hypersingular integral equation approach and Floquet’s theorem. The interface cracks can be a model for interface damage, but a much simpler model is a recently developed spring boundary condition. This boundary condition is used both for the thick plate and in the derivation of plate equations with the help of power series expansions in the thickness coordinate. For low frequencies (cracks small compared to the wavelength) the three models are shown to give the same results and this is a confirmation that the spring boundary condition is a valid approximation at low frequencies.

elastic waves, periodic cracks, anisotropy, spring boundary conditions, plate equations
Received: 12 March 2009
Revised: 10 July 2009
Accepted: 13 July 2009
Published: 19 April 2010
Anders Boström
Department of Applied Mechanics
Chalmers University of Technology
SE-412 96 Göteborg
Oleg V. Kvasha
Institute for Mathematics, Mechanics and Informatics
Kuban State University
Krasnodar 350080