Formulas for the H/V ratio of Rayleigh waves in incompressible pre-stressed half-spaces

Abstract

In this paper, the propagation of a Rayleigh wave in an incompressible pre-stressed elastic half-space is considered. The main aim is to derive exact formulas for the H/V ratio, the ratio of the amplitude of the horizontal displacement to the amplitude of the vertical displacement of the Rayleigh wave. First, the H/V ratio equations are obtained using the secular equation and the relation between the H/V ratio and the Rayleigh wave velocity. Then, the exact formulas for the H/V ratio have been derived for a general strain-energy function by analytically solving the H/V ratio equations. These formulas are then specified to several particular strain-energy functions. Since the obtained formulas are exact and totally explicit, they will be a good tool for nondestructively evaluating pre-stresses of structures before and during loading.