Stress wave propagation when the elastic coefficients vary with depth (Q1306174)

Using Hooke's law and Newton's law, when the elastic coefficients vary as a function of depth, the author shows that analytical solutions may be readily achieved when Lamé coefficients and the density track one another with depth. A case of special interest and remarkable simplicity is that of the exponential channel, where the elastic coefficients are proportional to a function \(f(x)= e^{-\alpha x}\). This case is studied in detail, demonstrating unusual extensions to Rayleigh waves. Applications may be found in acousto-optics, microchips, high-frequency surface acoustic wave filters, and any situations where surface waves are used in an environment of high precision or at relatively large distances.