# Dynamic Interaction of a Layer and a Half-Space

*by*Jan D. Achenbach,

Howard I. Epstein,

**Serial Information**:

*Journal of the Engineering Mechanics Division*, 1967, Vol. 93, Issue 5, Pg. 27-42

**Document Type:**Journal Paper

**Abstract:**

The equations of the theory of linear elasticity are used to compute dispersion curves for free time-harmonic waves propagating in a layer and a supporting half-space of different material properties. Both welded and smooth contacts are considered, and the layer may be acoustically softer or stiffer than the half-space. An infinite number of modes exists if the velocity of shear waves in the layer is less than the velocity of shear waves in the half-space. Generally, only one mode exists in the opposite case. The phase velocities of the two lowest modes approach, with decreasing wave length, the velocities of Rayleigh waves in the layer and the velocity of Stoneley waves, if the latter waves are possible. The phase velocities of all higher modes, if these modes exist, approach the velocity of shear waves in the layer. The conditions for existence of Stoneley waves are established.

**Subject Headings:**Wave velocity | Shear waves | Rayleigh waves | Material properties | Shear stress | Half space | Rocks | Wave equations

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