Formulas for the H/V ratio (ellipticity) of Rayleigh waves in orthotropic elastic half-spaces

ABSTRACT

This paper concerns the propagation of Rayleigh waves in compressible and incompressible orthotropic elastic half-spaces. The main aim of the paper is to derive formulas for the H/V ratio (ellipticity) of Rayleigh waves. First, the expression of the H/V ratio in terms of the Rayleigh wave velocity for compressible orthotropic elastic half-spaces is derived using the surface impedance matrix. From this expression and the secular equation of Rayleigh waves, the equation for the H/V ratio is obtained. It is a cubic equation. Employing the theory of cubic equations, the formula for the H/V ratio for compressible orthotropic elastic half-spaces has been derived. The H/V ratio formula for incompressible orthotropic elastic half-spaces has been obtained using the incompressible limit method. Since the H/V ratio of Rayleigh waves is a good tool for nondestructively evaluating mechanical properties of structures before and during loading, the obtained formulas will be very significant in practical applications.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) [grant number 107.02-2017.07].