Stoneley waves with spring contact and evaluation of the quality of imperfect bonds

In this paper, the propagation of Stoneley waves along the interface between two orthotropic elastic half-spaces is investigated. The half-spaces are compressible or incompressible and they are in spring contact with each other. The main aim of the paper is to derive secular equations and formulas for the ratios of displacement components at the interface and to show that Stoneley waves are a good tool for evaluating the quality of imperfect bonds modeled as spring contacts. First, the secular equation and the formulas for the displacement-component ratios for the compressible case (two half-spaces are compressible) are derived. Then, those for the incompressible cases (one or both half-spaces are incompressible) are obtained by using the incompressible limit method. The obtained secular equations reveal that, while Stoneley waves are non-dispersive for the welded contact and the sliding contact, they are dispersive for the spring contact. Employing the obtained secular equations and formulas for the displacement-component ratios, two particular examples are carried out for determining the spring constants from the measured values of the displacement-component ratios and the wave velocity. It is shown that the ratios of displacement components at two sides of the interface are the best choice for evaluating the quality of imperfect bonds.