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Higher order mode wave propagation in duct

Higher order mode wave propagation in duct. Yan Li 机械系统与振动国家重点实验室 上海交通大学， 200240 ，上海. Outline. Research background Higher order mode In a rectangular duct In a circular duct In expansion chamber Conclustion. Research Background. Sound transmission characteristics of duct system

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Higher order mode wave propagation in duct

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  1. Higher order mode wave propagation in duct Yan Li 机械系统与振动国家重点实验室 上海交通大学，200240，上海

  2. Outline • Research background • Higher order mode • In a rectangular duct • In a circular duct • In expansion chamber • Conclustion

  3. Research Background • Sound transmission characteristics of duct system • Building, automotive and aeronautic noise control • Bends, constrictions, expansions & side branches • Many study at low frequency • Inaccurate estimates at first cut-on frequency • Higher order mode wave propagation

  4. Outline • Research background • Higher order mode wave propagation • In a rectangular duct • In a circular duct • In expansion chamber

  5. Higher order mode in a rectangular duct Boundary condition at the wall of the duct requires: b z a x Transmission wave number for (m, n) mode: Cutoff frequencies:

  6. Higher order mode in a rectangular duct the number of pressure nodal lines in the x direction the number of pressure nodal lines in the y direction Fig. 1. Nodal lines for transverse pressure distribution in a rectangular duct up to m=3, n=3 higher order mode

  7. Higher order mode in a circular duct y z R x Fig. 2. Bessel function of the first kind for order m=0,1,2. Boundary condition met when slopes goes to zero at wall of circular duct

  8. Higher order mode in a circular duct Fig. 3. Nodal lines for transverse pressure distribution in circular duct up to m=3, n=3 higher node with preferred notation for m, n

  9. Higher order mode in a circular duct • Cutoff frequency • First asymmetric mode m=1,n=0 • First circularly symmetric/radial mode m=0, n=1

  10. Effects in expansion chamber Fig. 4. Schematic of illustrations of instantaneous axial pressure distribution for higher mode propagation, tunneling and leakage of one mode

  11. Effects in expansion chamber Fig. 5. Insertion loss measurements on expansion chamber using broad band noise excitation on impedance tube with anechoic termination (c=345m/s)

  12. Outline • Research background • Higher order mode • In a rectangular duct • In a circular duct • In expansion chamber • Conclustion

  13. Thanks ！

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