Fine-tuning of nonBragg bandgaps in axisymmetric ducts via arbitrary periodic walls

We investigate the nonBragg bandgap (NBBG) resulting from interference between two transverse guided wave modes in an axisymmetric duct with periodic walls. We find that the NBBG bandwidth is proportional to both the height and shape factor of the wall undulations. The shape factor is defined as the norm of the major Fourier component of the periodic wall profile. Varying the height directly tunes the bandwidth, while manipulating the wall profile results in a slight change in the shape factor, which leads to fine-tuning of the bandgap. We also find that for a fixed height, the NBBG width is related to the area under the curve for the product of the wall profile and a half-period sine or cosine function. We propose an area estimation method according to which a larger area results in a wider NBBG. A numerical example reveals that NBBG fine-tuning can be achieved by carefully varying the shape factor. The results will benefit the design of band structures, especially subtle modifications by selecting suitable wall undulations.