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Anechoic coating attached to the surface of an underwater object is used for absorbing sound wave thereby reducing the reflection. The anechoic coating is often made of viscoelastic materials embedded with designed acoustic substructures, such as air cavities. The prediction of sound scattering on underwater object coated with such materials can be challenging due to the complex geometry of the anechoic coating, and it has been a research subject of interest in underwater acoustics. In this paper, we study the sound scattering on an infinite cylindrical shell coated with anechoic coating. Two types of coatings are considered: one is a layer of homogeneous isotropic material, and the other is a layer of homogeneous isotropic material with periodically embedded cylindrical air cavities. We use an equivalent method, in which the anechoic coating with air-filled cavities is regarded as a homogeneous isotropic material with equivalent material properties. The key point of the equivalent method is to ignore the internal structure of the anechoic coating, and the anechoic coating is considered as a homogeneous isotropic layer with the same complex reflection coefficient. These equivalent material properties are acquired based on the data of complex reflection coefficient obtained from either the physical experiment using water-filled impedance tube or the numerical experiment using the finite element method with COMSOL Mutiphysics software. Then a genetic algorithm is developed to inversely calculate the equivalent Young's modulus, Poisson's ratio, and damping loss factor of the coating which has the same reflection coefficient as the original coating. The results of the equivalent material properties show that 1) the three properties are all frequency dependent; 2) in general, equivalent Young's modulus increases with the increase of frequency, meanwhile the equivalent damping loss factor tends to decrease; 3) there is a wide variation in the results of equivalent Poisson's ratio. Despite that, the reflection coefficient of the equivalent homogeneous isotropic coating accords well with that of the original coating.Based on the above, the sound scattering on the infinite cylindrical shell coated with the equivalent coating is calculated by using the finite element method based on COMSOL Mutiphysics software. In order to verify the accuracy of the equivalent model, we use COMSOL Mutiphysics software to build up the full geometrical model of the coated shell to calculate the sound scattering. This can be considered as the benchmark. The results of morphic function show that the scattering calculated using equivalent material properties accords well with that obtained from the full finite element model with a mean error of about 1 dB in all frequency spectrum range.
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Keywords:
- sound scattering /
- acoustic coating /
- equivalent parameter /
- finite element method
[1] Yang H B, Li Y, Zhao H G, Wen J H, Wen X S 2014 Chin Phys. B 23 104304
[2] Zhao H G, Wen J H, Yang H B, L L M, Wen X S 2014 Appl. Acoust. 63 134303 (in Chinese) [赵宏刚, 温激鸿, 杨海滨, 吕林梅, 温熙森 2014 应用声学 63 134303]
[3] Zhao H G, Liu Y Z, Wen J H, Yu D L, Wen X S 2007 Acta Phys. Sin. 56 4700 (in Chinese) [赵宏刚, 刘耀宗, 温激鸿, 郁殿龙, 温熙森 2007 物理学报 56 4700]
[4] Gaunaurd G C, Werby M F 1990 Appl. Mech. Rev. 43 171
[5] Tang W L, Fan J 1999 Acta Acoust. 24 174 (in Chinese) [汤渭霖, 范军 1999 声学学报 24 174]
[6] Xu H L, Chen L J 2007 Acoust. Electron. Eng. 4 9 (in Chinese) [徐红兰, 陈励军 2007 声学与电子工程 4 9]
[7] Huang W, Wang Y J, Rokhlin S I 1996 J. Acoust. Soc. Am. 99 2742
[8] Zhu B L, Ren K M 1997 J. Shanghai Jiaotong Univ. 31 20 (in Chinese) [朱蓓丽, 任克明 1997 上海交通大学学报 31 20]
[9] Fan J 2001 Ph. D. Dissertation (Shanghai: Shanghai Jiaotong University) (in Chinese) [范军 2001 博士学位论文 (上海: 上海交通大学)]
[10] Brekhovskikh L M (translated by Yang X R) 1960 Waves in Layered Media (Beijing: Science Press) p5 (in Chinese) [布列霍夫斯基赫 著(杨训仁 译) 1960 分层介质中的波(北京: 科学出版社)第5页]
[11] Chen G L, Wang X F 1996 Genetic Algorithms and Application (Beijing: Posts and Telecom Press) p3 (in Chinese) [陈国良, 王熙法 1996 遗传算法及其应用(北京: 人民邮电出版社)第3页]
[12] Zhou M, Sun S D 1999 Genetic Algorithms: Theory and Application (Beijing: National Defense Industry Press) p12 (in Chinese) [周明, 孙树栋 1999 遗传算法原理及应用(北京: 国防工业出版社)第12页]
[13] Lei Y J, Zhang S W, Li X W 2005 MATLAB Genetic Algorithms Tool Box and Applications (Xi'an: University of Electronic Science and Technology of Xi'an) p57 (in Chinese) [雷英杰, 张善文,李续武 2005 MATLAB遗传算法工具箱及应用 (西安: 电子科大出版社)第57页]
[14] Zhu B L, Huang X C 2012 Key Technique of Invisible SubmarineDesign of Acoustic Coating (Shanghai: Shanghai Jiaotong University Press) p116 (in Chinese) [朱蓓丽, 黄修长 2012 潜艇隐身关键技术声学覆盖层的设计 (上海: 上海交通大学出版社)第116页]
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[1] Yang H B, Li Y, Zhao H G, Wen J H, Wen X S 2014 Chin Phys. B 23 104304
[2] Zhao H G, Wen J H, Yang H B, L L M, Wen X S 2014 Appl. Acoust. 63 134303 (in Chinese) [赵宏刚, 温激鸿, 杨海滨, 吕林梅, 温熙森 2014 应用声学 63 134303]
[3] Zhao H G, Liu Y Z, Wen J H, Yu D L, Wen X S 2007 Acta Phys. Sin. 56 4700 (in Chinese) [赵宏刚, 刘耀宗, 温激鸿, 郁殿龙, 温熙森 2007 物理学报 56 4700]
[4] Gaunaurd G C, Werby M F 1990 Appl. Mech. Rev. 43 171
[5] Tang W L, Fan J 1999 Acta Acoust. 24 174 (in Chinese) [汤渭霖, 范军 1999 声学学报 24 174]
[6] Xu H L, Chen L J 2007 Acoust. Electron. Eng. 4 9 (in Chinese) [徐红兰, 陈励军 2007 声学与电子工程 4 9]
[7] Huang W, Wang Y J, Rokhlin S I 1996 J. Acoust. Soc. Am. 99 2742
[8] Zhu B L, Ren K M 1997 J. Shanghai Jiaotong Univ. 31 20 (in Chinese) [朱蓓丽, 任克明 1997 上海交通大学学报 31 20]
[9] Fan J 2001 Ph. D. Dissertation (Shanghai: Shanghai Jiaotong University) (in Chinese) [范军 2001 博士学位论文 (上海: 上海交通大学)]
[10] Brekhovskikh L M (translated by Yang X R) 1960 Waves in Layered Media (Beijing: Science Press) p5 (in Chinese) [布列霍夫斯基赫 著(杨训仁 译) 1960 分层介质中的波(北京: 科学出版社)第5页]
[11] Chen G L, Wang X F 1996 Genetic Algorithms and Application (Beijing: Posts and Telecom Press) p3 (in Chinese) [陈国良, 王熙法 1996 遗传算法及其应用(北京: 人民邮电出版社)第3页]
[12] Zhou M, Sun S D 1999 Genetic Algorithms: Theory and Application (Beijing: National Defense Industry Press) p12 (in Chinese) [周明, 孙树栋 1999 遗传算法原理及应用(北京: 国防工业出版社)第12页]
[13] Lei Y J, Zhang S W, Li X W 2005 MATLAB Genetic Algorithms Tool Box and Applications (Xi'an: University of Electronic Science and Technology of Xi'an) p57 (in Chinese) [雷英杰, 张善文,李续武 2005 MATLAB遗传算法工具箱及应用 (西安: 电子科大出版社)第57页]
[14] Zhu B L, Huang X C 2012 Key Technique of Invisible SubmarineDesign of Acoustic Coating (Shanghai: Shanghai Jiaotong University Press) p116 (in Chinese) [朱蓓丽, 黄修长 2012 潜艇隐身关键技术声学覆盖层的设计 (上海: 上海交通大学出版社)第116页]
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