★ A reformulation of the Thomson-Haskell method is proposed. ★ The reflection coefficients of multilayer structure with arbitrary configurations are calculated based on the reformulation. ★ The reflection coefficient of multilayer structure containing fluid layer is calculated and experimentally verified. ★ This reformulation method offers an efficient and effective solution for calculating the acoustic reflection coefficients.
A reformulation of the Thomson-Haskell method is presented for calculating the reflection coefficients of multilayer structure immersing in the coupling fluid. Instead of directly multiplying the layer propagator matrix, the new method splits the layer propagator matrix and excursively determines the interface stiffness matrix starting from the bottom half-space with known stiffness. A formulation for the reflection coefficients is derived based on the obtained interface stiffness matrix of the top layer. This scheme can be applied to a single solid layers or layered structures containing both fluid and solid layers. It keeps the simplicity but naturally excludes the exponential growth term and thus can be applied at any frequency range. Its validity and feasibility were experimentally proved by the measurement of the reflection coefficients of a three layered structure of aluminum–glass–aluminum and a sandwiched layer structure of two 250 μm stainless plates filled with 100 μm deionized water based on the inversion of V(z, t) technique. The result of experiments is consistent with the theoretical calculation. The reformulation of the Thomson-Haskell method offers an efficient and effective solution for calculating the acoustic reflection coefficients of multilayer structures of any configurations.