Shear-wave resonances in a fluid–solid–solid layered structure

• Properties of inhomogeneous layer modeled with exponentials.
• Exact solutions found using hypergeometric functions.
• Accurate asymptotic approximations developed.

An inhomogeneous solid layer is bounded on one side by a fluid half-space and on the other by a homogeneous solid half-space. An acoustic wave in the fluid is incident on the layer. Experiments suggest that some kind of shear-wave resonance of the layer exists. Here, the layer is modeled with exponential variations of the material properties (Epstein model). Solutions in terms of hypergeometric functions are found. Genuine resonances are found but only when the layer is not bonded to the solid half-space; these are analogous to Jones frequencies in fluid–solid interaction problems. When the solid half-space is present, the resonances become complex: they are scattering frequencies. Simple but accurate asymptotic approximations are found using known estimates for hypergeometric functions with large parameters.