Functionally graded materials for impedance matching in elastic media

• We propose an iterative method for solving layered systems.
• Passbands with large bandwidths appear in systems with FGMs.
• Properties of all the bands are given and explained.

When functionally graded material layers are inserted between two impedance mismatching media, passbands with extremely large bandwidths can appear in these layered systems. An accurate and effective iterative method is developed to deal with these layered systems with extremely large layer number.