Acoustical Waveguide Structures With Periodically Corrugated Boundaries

Periodic structures widely exist in the nature in the form of crystals, moreover, it can be reconstructed by artificially repeating structural unit to achieve the so-called phonon and photonic crystal materials. When sound waves propagate in these periodic structures, due to the interactions between the sound waves and the structures, some waves in a certain frequency range are localized in the waveguides, but others pass through, resulting in the similar characteristics of semiconductor band. The so-called band engineering is applied to the sound filtering, noise control, acoustic fence, and other fields, and has brought great convenience to the production and life. This thesis mainly studies the band structures in a cylindrical waveguide with periodic corrugated boundaries and proposes the special structures to realize the acoustical waveguide structures, such as the ultra-wideband reflector, single mode selector, and high-performance switch.First of all, this thesis focuses on the relationship between the band structures and the waveguide structures. Theoretical derivations describe the relationship between the band gaps and waveguide boundaries. The centre frequencies of Bragg and non-Bragg band gaps in the four waveguides with rectangular, trapezoidal, sinusoidal and triangular boundaries are very close, because this is mainly related with the wall period. While the maximum value of the band width appears in the rectangular boundary waveguide, and the band widths in trapezoid and sinusoidal boundary waveguides are extremely closed to each other, the triangular boundary waveguide has the minimum width of forbidden band. Then, the subsequent simulations with the finite element method are consistent with the theoretical results. We propose the mixed boundary method to achieve a wide band gap. We found that the mixing of different type of boundaries can only get an average width of the two original band gaps, and it’s narrower than the width of the band gap in a rectangular boundary waveguide. However, the mixing of rectangular boundary waveguides with different period length can successfully get an extremely wide gap, with the ratio of its width and center frequency almost reaching one hundred percent.Secondly, we analyzed the importance and feasibility of single-mode-selection, and predicted the frequency range in which the pure mode would be excited. The designed two acoustic waveguide show the purity of the selected single high-order transverse modes in the numerical simulations. We also perform waveguide to achieve the first-order mode, experimentally. The experimental results confirm our proposed method and realized the special control of radial sound pressures. Finally,We study the changes in the band structures of waveguides with defects. We found that the defects change both the Bragg and the non-Bragg gaps, by bringing a narrow transmission band in the Bragg gap but a frequency spike in the non-Bragg gap. The spike illustrates the non-Bragg defect mode is more suitable for high quality sound switch. Setting the defect parameters as constants, we found that the center frequencies of the defect modes move to higher frequency when increasing the waveguide period, and eventually get out of the band gap range. Increasing the wall corrugations, the center frequencies of the defect modes in the Bragg band gaps stay where they were, but their counterparts in the non-Bragg band gaps move to lower frequency. When we set the waveguide parameters unchanged, the center frequencies of Bragg and the non-Bragg defect modes move to lower frequency by enlarging the defect length. When the defect width increases, the center frequencies of the defect modes move to lower frequency at first, and then gradually move to higher frequency.In summary, we have focused on the band structures of the acoustical waveguides with periodic walls, investigated several typical structures, and found that the mode interaction theories in periodic waveguides can be used to design and implement a variety of new high-performance acoustic waveguide structures. The proposed methods not only can benefit the sound propagation control, nondestructive testing, and acoustic imaging, etc., but also can provide high-performance guided-wave structures in optical applications.