Numerical analysis of wave propagating in a periodic layered structure

Controlling sound fields is a key technology for noise removal, acoustic lenses, energy harvesting, etc. This study investigated the control of sound field by a periodic layered structure. At first, we formulated the wave propagation in a periodic layered structure and proved that the wave fields constructed by the periodic boundary conditions are limited to plane wave modes with discretely different propagation directions. Numerical calculations clarified that the desired plane wave mode can be obtained in the transmitted wave through an intermediate thin-plate stacked region in a periodic layered structure, in which Lamb waves travel in each plate at different phase velocities and create phase difference at the exit of the intermediate thin-plate region. Further numerical investigations revealed that tuning frequency and the length of the thin-plate region provides wave field more dominantly with a single wanted plane wave mode.