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Published March 2012 | public
Journal Article

Existence of Surface Waves and Band Gaps in Periodic Heterogeneous Half-spaces


We find a sufficient condition for the existence of surface (Rayleigh) waves based on the Rayleigh-Ritz variational method. When specialized to a homogeneous half-space, the sufficient condition recovers the known criterion for the existence of subsonic surface waves. A simple existence criterion in terms of material properties is obtained for periodic half-spaces of general anisotropic materials. Further, we numerically compute the dispersion relation of the surface waves for a half-space of periodic laminates of two materials and demonstrate the existence of surface wave band gaps.

Additional Information

© 2011 Springer Science+Business Media B.V. Received: 22 October 2010; Published online: 6 April 2011. The authors gratefully acknowledge the financial support of the US Office of Naval Research through the MURI grant N00014-06-1-0730 and TcSUH. The author would also like to thank the anonymous reviewer for pointing out an interesting application of Theorem 6, i.e., Corollary 7.

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