Surface Love-type waves propagating through viscoelastic functionally graded media

This paper deals with the solution of the model equations, which describes the propagation of the surface Love-type waves in a waveguide structure consisting of a lossy isotropic inhomogeneous layer placed on a viscoelastic homogeneous substrate. The paper points to the possibility of using the triconfluent Heun differential equation to solve the model equation. The exact analytical solution within the inhomogeneous layer is expressed by the triconfluent Heun functions. The exact solutions are general in the sense that only the internal parameters of the triconfluent Heun functions can change the spatial dependencies of the material parameters in the inhomogeneous layer's thickness direction. Based on the comparison, the limits of the WKB method applicability are discussed. It is further demonstrated that substrate losses affect the dispersion characteristics only to a small extent. Using examples in which the surface layer is represented by functionally graded materials, it was shown that the distance between the modes can be influenced through those materials.