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Helmholtz resonators are commonly used as underwater acoustic transducers to transmit low-frequency, great power acoustic waves at fluid cavity resonant frequency. Therefore, it is an important problem in the study of how to calculate accurately the fluid cavity resonant frequency of Helmholtz resonator, especially when the Helmholtz resonator is used in underwater acoustic environment where Helmholtz transducers cannot be designed using the classical air acoustic Helmholtz resonator theory. The elasticity of the cavity wall has to be considered because it has a strong influence on the fluid cavity resonant frequency at low frequency band. In this paper, the method of calculating accurately fluid cavity resonant frequency is researched for low-frequency Helmholtz underwater transducers. A Helmholtz resonator is a slender cylindrical shell, the boundary condition of its two ends is free: one side is a radiating port, and the other side is considered as a rigid baffle. Firstly, the fluid cavity resonant frequency of the rigid wall Helmholtz resonator is given, then the radial mechanical impedance of the slender cylindrical shell is derived based on the wave equations. Elasticity of the cavity wall is introduced into the acoustic impedance of fluid cavity in the form of additional impedance. Based on the low-frequency lumped parameter model of the slender cylindrical shell, additional acoustic impedance expression of elastic cavity wall is derived, complete equivalent circuit diagram of elastic Helmholtz underwater transducers is developed, taking into account the elasticity of the cavity wall. Based on the equivalent circuit, the accurate fluid cavity resonant frequency formula has been derived; the formula shows that both the structure size and material characteristics of the cavity wall have influence on the fluid cavity resonant frequency. The thinner the cavity wall, the lower the fluild cavity resonant frequency; and the smaller the Young's modulus of the material, the lower the fluild cavity resonant frequency. To verify the accuracy of the present theory, several slender cylindrical shell models with different wall thickness, materials, and wall length are investigated by both elastic theory method and finite element method (using ANSYS software). These results reveal that the elastic theory results are in excellent agreement with the finite element simulation results. That means, compared to traditional rigid wall theory results, the results from elastic theory in this paper is much closer to the real situation. This conclusion can provide a theoretical support for the accurate design of low-frequency elastic Helmholtz underwater acoustic transducers.
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Keywords:
- elastic helmholtz resonant cavity /
- underwater acoustic transducer /
- fluid cavity resonant frequency /
- acoustic impedance
[1] Marsset T, Marsset B, Ker S, Thomas Y, Le Gall Y 2010 Deep Sea Res. Part I 57 628
[2] Mosca F, Matte G, Shimura T 2013 J. Acoust. Soc. Am. 133 EL61
[3] Morozov A K, Webb D C 2003 Ocean Eng. 28 174
[4] Ker S, Marsset B, Garziglia S, Le Gonidec Y, Gibert D, Voisset M, Adamy J 2010 Geophys. J. Int. 182 1524
[5] Butler J L, Butler A L 1999 J. Acoust. Soc. Am. 105 1119
[6] Morozov A K, Webb D C 2007 J. Acoust. Soc. Am. 122 777
[7] Rossby T, Ellis J, Webb D C 1993 J. Atmos. Oceanic Technol. 10 397
[8] Norris A N, Wickham G 1993 J. Acoust. Soc. Am. 93 617
[9] He S P, Tang W L, Liu T, Fan J 2003 J. Ship. Mech. 7 97 (in Chinese) [何世平, 汤渭霖, 刘涛, 范军 2003 船舶力学 7 97]
[10] Liu T, Fan J, Tang W L 2002 Acta Acustica 27 62 (in Chinese) [刘涛, 范军, 汤渭霖 2002 声学学报 27 62]
[11] Tang W L, Fan J 2004 Acta Acustica 29 385 (in Chinese) [汤渭霖, 范军 2004 声学学报 29 385]
[12] Wang Z F, Hu Y M 2008 Acta Acustica 33 184 (in Chinese) [王泽锋, 胡永明 2008 声学学报 33 184]
[13] Wang Z F, Hu Y M, Meng Z, Ni M 2008 Acta Phys. Sin. 57 7022 (in Chinese) [王泽锋, 胡永明, 孟洲, 倪明 2008 57 7022]
[14] Wang Z F, Hu Y M, Xiong S D, Luo H, Meng Z, Ni M 2009 Acta Phys. Sin. 58 2507 (in Chinese) [王泽锋, 胡永明, 熊水东, 罗洪, 孟洲, 倪明 2009 58 2507]
[15] Zhou C G, Liu B L, Li X D, Tian J 2007 Acta Acoustic 32 426 (in Chinese) [周城光, 刘碧龙, 李晓东, 田静 2007 声学学报 32 426]
[16] Sherman C H, Butler J L 2007 Transducers and arrays for underwater sound (New York: Springer) p92
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[1] Marsset T, Marsset B, Ker S, Thomas Y, Le Gall Y 2010 Deep Sea Res. Part I 57 628
[2] Mosca F, Matte G, Shimura T 2013 J. Acoust. Soc. Am. 133 EL61
[3] Morozov A K, Webb D C 2003 Ocean Eng. 28 174
[4] Ker S, Marsset B, Garziglia S, Le Gonidec Y, Gibert D, Voisset M, Adamy J 2010 Geophys. J. Int. 182 1524
[5] Butler J L, Butler A L 1999 J. Acoust. Soc. Am. 105 1119
[6] Morozov A K, Webb D C 2007 J. Acoust. Soc. Am. 122 777
[7] Rossby T, Ellis J, Webb D C 1993 J. Atmos. Oceanic Technol. 10 397
[8] Norris A N, Wickham G 1993 J. Acoust. Soc. Am. 93 617
[9] He S P, Tang W L, Liu T, Fan J 2003 J. Ship. Mech. 7 97 (in Chinese) [何世平, 汤渭霖, 刘涛, 范军 2003 船舶力学 7 97]
[10] Liu T, Fan J, Tang W L 2002 Acta Acustica 27 62 (in Chinese) [刘涛, 范军, 汤渭霖 2002 声学学报 27 62]
[11] Tang W L, Fan J 2004 Acta Acustica 29 385 (in Chinese) [汤渭霖, 范军 2004 声学学报 29 385]
[12] Wang Z F, Hu Y M 2008 Acta Acustica 33 184 (in Chinese) [王泽锋, 胡永明 2008 声学学报 33 184]
[13] Wang Z F, Hu Y M, Meng Z, Ni M 2008 Acta Phys. Sin. 57 7022 (in Chinese) [王泽锋, 胡永明, 孟洲, 倪明 2008 57 7022]
[14] Wang Z F, Hu Y M, Xiong S D, Luo H, Meng Z, Ni M 2009 Acta Phys. Sin. 58 2507 (in Chinese) [王泽锋, 胡永明, 熊水东, 罗洪, 孟洲, 倪明 2009 58 2507]
[15] Zhou C G, Liu B L, Li X D, Tian J 2007 Acta Acoustic 32 426 (in Chinese) [周城光, 刘碧龙, 李晓东, 田静 2007 声学学报 32 426]
[16] Sherman C H, Butler J L 2007 Transducers and arrays for underwater sound (New York: Springer) p92
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