Acoustic bandgap formation in a periodic structure with multilayer unit cells

Using the transfer matrix method and Floquet's theorem we have derived the dispersion relation for acoustic wave propagation in a periodic layered structure in which each unit cell contains several sub-layers of different materials. Structures with unit cells containing two, four and six sublayers of different thickness and two types of materials were used as examples for our study. It was found that narrow passbands and broad stopbands could be obtained when the unit cell has more than two sublayers. The calculated results were verified experimentally using glass-water structures containing only one to three cells. Good agreement was obtained between the experimental results and the transfer matrix calculations. Desired bandgap structures can be produced in less than three cells, revealing application potential for the bandgap materials in vibration control devices and acoustic filters.