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Research on sound scattering from a finite quasi-periodic bulkhead cylindrical shell is conducted. The small deviation of bulkhead array exists. Firsts some applications are given to investigate the problem of backscattering from a periodic bulkhead cylindrical shell in order to verify the theory. Then the angle-frequency spectrum of the backscattering from quasi-periodic bulkhead cylindrical shell is calculated, and the angle-frequency spectrum shows that the quasi-periodic array of bulkhead results in the diffusion of Bloch-Floquet wave and background field. However, the resonance of bulkheads is covered by background field. Finally, the influences of the array random variable of bulkheads, the number of bulkheads and the spacing between bulkheads are discussed. The calculations show that the diffusion of Bragg waves is more evident with array random variable increasing; the power of Bragg waves is concentrated with the number of bulkheads increasing; with the spacing between bulkheads becoming broad, the number of Bragg waves increases and the diffusion of high modes Bragg waves becomes more serious. Based on the geometric characteristics of Bragg waves, the approximate calculation formula of the Bragg wave position on the angle-frequency spectrum is presented. The formula can forecast the position of Bragg wave on the angle-frequency spectrum exactly and the diffusion of Bragg waves roughly when the bulkheads array quasi-periodic.
[1] M Tran-Van-Nhieu 2001 J. Acoust. Soc. Am. 110 2858
[2] R Liétard, D Décultot, G Maze, M Tran-Van-Nhieu 2005 J. Acoust. Soc. Am. 118 2142
[3] Douglas M P 1991 J. Acoust. Soc. Am. 91 771
[4] Douglas M P 1991 J. Acoust. Soc. Am. 91 1897
[5] Douglas M P 1994 J. Acoust. Soc. Am. 97 1409
[6] Anderson P W 1957 Phys. Rev 109 1492
[7] Tran-Van-Nhieu M 2002 J. Acoust. Soc. Am. 112 403
[8] Guo Y P 1992 J. Acoust. Soc. Am. 91 926
[9] Guo Y P 1993 J. Acoust. Soc. Am. 93 1936
[10] Pan A, Fan J, Zhuo L K 2012 Acta Phys. Sin. (in Chinese) [潘安, 范军, 卓琳凯 2012 物理学报]
[11] Miguel C J, Feit D 1986 Sound, Structure and their interaction 2nd ed (MIT Press, Cambridge, MA)
[12] Guo Y P 1994 J. Acoust. Soc. Am. 95 2550
[13] Abramowitz M, Stegun I A 1970 Handbook of mathematical functions with formulas graphs and mathematical tables (Dover, New York)
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[1] M Tran-Van-Nhieu 2001 J. Acoust. Soc. Am. 110 2858
[2] R Liétard, D Décultot, G Maze, M Tran-Van-Nhieu 2005 J. Acoust. Soc. Am. 118 2142
[3] Douglas M P 1991 J. Acoust. Soc. Am. 91 771
[4] Douglas M P 1991 J. Acoust. Soc. Am. 91 1897
[5] Douglas M P 1994 J. Acoust. Soc. Am. 97 1409
[6] Anderson P W 1957 Phys. Rev 109 1492
[7] Tran-Van-Nhieu M 2002 J. Acoust. Soc. Am. 112 403
[8] Guo Y P 1992 J. Acoust. Soc. Am. 91 926
[9] Guo Y P 1993 J. Acoust. Soc. Am. 93 1936
[10] Pan A, Fan J, Zhuo L K 2012 Acta Phys. Sin. (in Chinese) [潘安, 范军, 卓琳凯 2012 物理学报]
[11] Miguel C J, Feit D 1986 Sound, Structure and their interaction 2nd ed (MIT Press, Cambridge, MA)
[12] Guo Y P 1994 J. Acoust. Soc. Am. 95 2550
[13] Abramowitz M, Stegun I A 1970 Handbook of mathematical functions with formulas graphs and mathematical tables (Dover, New York)
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