Vol. 4, No. 4, 2009

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Existence of one-component Rayleigh waves, Stoneley waves, Love waves, slip waves and one-component waves in a plate or layered plate

Thomas C. T. Ting

Vol. 4 (2009), No. 4, 631–647

It is known that one-component surface (Rayleigh) waves exist in an anisotropic elastic half-space. Since the solution shows that the displacement normal to the free surface vanishes everywhere, a one-component surface wave is also a one-component slip wave in the half-space if the boundary of the half-space is a slippery surface. We show that no other one-component slip waves exist for the half-space. As to steady waves in a bimaterial that consists of two dissimilar anisotropic elastic materials, one-component slip waves can be constructed from two one-component surface waves. There are no other one-component slip waves for a bimaterial. By imposing the continuity of the displacement at the interface on the one-component slip wave, a one-component Stoneley wave is obtained. Although one-component waves for the half-space can also propagate in a homogeneous plate, we present new one-component waves in a plate for which the Stroh eigenvalue p is real. By superposition of the one-component waves in the layer and in the half-space, one-component Love waves can be constructed. Finally, we show that one-component waves can propagate in a layered plate.

anisotropic, steady waves, slip waves, one-component waves, Rayleigh waves, Stoneley waves, plate, layered plate, dispersion equations
Received: 22 November 2007
Accepted: 15 April 2008
Published: 7 August 2009
Thomas C. T. Ting
Division of Mechanics and Computation
Stanford University
Durand 262
Stanford, CA 94305
United States