Resonances of three transverse standing-wave modes in a waveguide with periodic wall undulations

• We investigate the interactions of three transverse modes in a periodic waveguide.
• Three mode resonances result in the splitting of the traditional forbidden band.
• We find the transparency of the forbidden band to a single high-order mode.
• The transmission losses of two ducts illustrate the transparencies in the gaps.
• The radial distributions and their fittings show the purity of the generated modes.

Interactions of three transverse modes are investigated in a waveguide with periodic walls. Resonances of two guided wave modes always result in forbidden bands for wave propagations when the wavenumber matching conditions are satisfied. As a third mode is involved due to the selected wall corrugations, we find that a single high-order mode can penetrate through the forbidden band based on the complex interactions. A method for generating a single high-order transverse mode is proposed by manipulating the multimode interactions. The numerical simulations on acoustic waveguides, showing the extreme suppression of the unwanted modes in the Bragg and non-Bragg gaps, demonstrate the validity and the efficiency of the proposed method.