A closed-form solution to propagation of guided waves in a layered half-space under a time-harmonic load: An application of elastodynamic reciprocity.

This article is concerned with the application of reciprocity in computing guided wave motions generated by a time-harmonic load in a layer of uniform thickness joined to a half-space. Explicit expressions for free Rayleigh waves and Love waves propagating in the layered half-space are introduced. Exact solutions of Rayleigh waves and Love waves are derived from reciprocity relations between an actual state - guided waves generated by a time-harmonic line load and a virtual state - an appropriately chosen free wave traveling in the structure.

An improved approximation of Bergmann's form for the Rayleigh wave velocity.

In the present paper an improved approximation for the Rayleigh wave velocity in isotropic elastic solids is obtained using the method of least squares. It is of Bergmann's form, i.e.

Explanation for Malischewsky's approximate expression for the Rayleigh wave velocity.

An approach for obtaining approximations of the Rayleigh wave velocity created by the principle of least squares is introduced. In view of this approach, Malischewsky's approximation of the Rayleigh wave velocity for Poisson ratios v in the set of [-1, 0.5] proposed quite recently is explained.

On Rayleigh waves in incompressible orthotropic elastic solids.

In this paper the secular equation for the Rayleigh wave speed in an incompressible orthotropic elastic solid is obtained in a form that does not admit spurious solutions. It is then shown that inequalities on the material constants that ensure positive definiteness of the strain-energy function guarantee existence and uniqueness of the Rayleigh wave speed. Finally, an explicit formula for the Rayleigh wave speed is obtained.