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Resonance peaks of spectral function transformed from echoes are the most important characteristics for distinguishing the different targets. So in frequency domain, response function is usually calculated with small interval in a wider frequency band to satisfy the demand of fast and high precision prediction in practical engineering. According to axis-symmetric model, we use 2 dimensional finite element method to solve the acoustic scattering problem efficiently, even when the scattering target has a large size and complex structure. This article focuses on the explanation of scattering characteristics of a special target, namely, a partially solid-filling cylinder with hemispherical cap and thin-shell. Supposing that the receiver and transmitter are in monostatic arrangement, we calculate scattering strength in far field in a frequency range of 50 Hz-10 kHz, and give pseudo-color image represented by frequency-angle to describe influences of shell, filling and the orientation of the incident wave on scattering properties. According to the numerical results, the following conclusions are given: when the transmitter is facing the hemispherical cap (the cap has a vacuum inside, and the incident angle θ is equal to 0°), the main contribution of scattered wave comes from the shell of target. When θ = 180°, the internal filling inhibits the elastic resonance of the shell, and plays an important role in the total scattering field. Because the acoustic impedance of the shell is much larger than that of the water, elastic resonance of the shell is more difficult to excite than that of the solid filling. While the material property of the solid filling is not significantly different from that of the water, so the elastic resonance of the filling fluctuates relatively fast, and the scattering function vibrates approximately with equal amplitude in a wider frequency band. When θ= 90°, the sound wave is perpendicular to the axis of the cylinder, the shell and the filling work together on scattered waves. Once the incident angle deviates from 90° and the sound wave obliquely illuminates target with respective to the axis of the cylinder, the echo of the filling material plays a predominant role in the total scattering field. The frequency-angle spectrum of the solid filling model presents the “bowl” type resonance curve. In order to validate which physical and geometrical structure must be considered in solution of scattered far field, the acoustic scattering experiments are performed in tank with a target suspending in water, which is in monostatic arrangement and satisfies the free field condition. Frequency of incident wave is in a frequency range of 10-40 kHz. For obtaining pseudo-color image of distance-angle, echoes are received and measured when the target is rotated from 0°-360°. The scattered waves are divided into mirror reflection and various components of elastic wave, and the mechanisms of these echoes are explained based on circumferential wave around the surface. Whispering gallery waves are also considered and clearly seen in the experiment. Due to the coupling interaction between the filling and elastic shell, the resonance curve of frequency-angle spectrum splays “bowl” curve outward the sides of normally direction. Experimental and numerical results are in good agreement, which is indicated by comparing the resonance peaks characteristic in spectral domain. The results of this article will be helpful in studying underwater target with more complicated structure.
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Keywords:
- 2-dimensional finite element /
- partially solid-filling cylindrical shell /
- pseudo-color image of distance-angle echoes /
- frequency-angle spectrum
[1] Flax L, Dragonette L R, Uberall H 1978 J. Acoust. Soc. Am. 63 723
[2] Hua D C, Peng L H, Yu X T 2010 Periodical of Ocean University of China 40 141 (in Chinese) [华大成, 彭临慧, 于小涛 2010 中国海洋大学学报 40 141]
[3] Shun Y, An J Y, Xu H T 2013 Acta Acoustic 38 699 (in Chinese) [孙阳, 安俊英, 徐海亭 2013 声学学报 38 699]
[4] Jin G L, Yin J F, Wen J H, Wen X S 2016 Acta Phys. Sin. 65 014305 (in Chinese) [金国梁, 尹剑飞, 温激鸿, 温熙森 2016 65 014305]
[5] Aubrey L E, Kevin L W, Daniel S P, Philip L M 2014 J. Acoust. Soc. Am. 136 109
[6] Li X K, Liu M Y, Jiang S 2015 Marine Sci. Appl. 14 208
[7] Pan A, Fan J, Zhuo L K 2012 Acta Phys. Sin. 61 214301 (in Chinese) [潘安, 范军, 卓琳凯 2012 61 214301]
[8] Pan A, Fan J, Wang B 2013 J. Acoust. Soc. Am. 134 3452
[9] Zheng G Y, Fan J, Tang W L 2009 Acta Acoustic 34 490 (in Chinese) [郑国垠, 范军, 汤渭霖 2009 声学学报 34 490]
[10] Gao H, Xu H T 2006 The Acoustic Academic Conference Xiamen, China, October 18-22, 2006 p105 (in Chinese) [高华, 徐海亭 2006 全国声学学术会议论文集, 厦门, 10月18-22日, 2006 第105页]
[11] Thompson L L 2006 J. Acoust. Soc. Am. 20 1315
[12] Ihlenburg F 1998 Finite Element Analysis of Acastc Scattering (Applied Mathmatical Science) (New York: Springer-Verlag) pp189-210
[13] Chai Y B, Li W, Gong Z, Li T Y 2016 Ocean Eng. 116 129
[14] Rajabi M, Ahmadian M T, Jamali J 2015 Compos. Struct. 128 395
[15] Zampolli M, Tesei A, Finn B J 2007 J. Acoust. Soc. Am. 122 1472
[16] Zampolli M, Alessandra T, Canepa G 2008 J. Acoust. Soc. Am. 123 4051
[17] Hu Z, Fan J, Zhang P Z, Wu Y S 2016 Acta Phys. Sin. 65 064301 (in Chinese) [胡珍, 范军, 张培珍, 吴玉双 2016 65 064301]
[18] Zhang P Z, Wang S Z, Wang R T, Chen Y F, Wang L X 2013 Acta Acoustic 39 331 (in Chinese) [张培珍, 王朔中, 王润田, 陈云飞, 王露贤 2013 声学学报 39 331]
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[1] Flax L, Dragonette L R, Uberall H 1978 J. Acoust. Soc. Am. 63 723
[2] Hua D C, Peng L H, Yu X T 2010 Periodical of Ocean University of China 40 141 (in Chinese) [华大成, 彭临慧, 于小涛 2010 中国海洋大学学报 40 141]
[3] Shun Y, An J Y, Xu H T 2013 Acta Acoustic 38 699 (in Chinese) [孙阳, 安俊英, 徐海亭 2013 声学学报 38 699]
[4] Jin G L, Yin J F, Wen J H, Wen X S 2016 Acta Phys. Sin. 65 014305 (in Chinese) [金国梁, 尹剑飞, 温激鸿, 温熙森 2016 65 014305]
[5] Aubrey L E, Kevin L W, Daniel S P, Philip L M 2014 J. Acoust. Soc. Am. 136 109
[6] Li X K, Liu M Y, Jiang S 2015 Marine Sci. Appl. 14 208
[7] Pan A, Fan J, Zhuo L K 2012 Acta Phys. Sin. 61 214301 (in Chinese) [潘安, 范军, 卓琳凯 2012 61 214301]
[8] Pan A, Fan J, Wang B 2013 J. Acoust. Soc. Am. 134 3452
[9] Zheng G Y, Fan J, Tang W L 2009 Acta Acoustic 34 490 (in Chinese) [郑国垠, 范军, 汤渭霖 2009 声学学报 34 490]
[10] Gao H, Xu H T 2006 The Acoustic Academic Conference Xiamen, China, October 18-22, 2006 p105 (in Chinese) [高华, 徐海亭 2006 全国声学学术会议论文集, 厦门, 10月18-22日, 2006 第105页]
[11] Thompson L L 2006 J. Acoust. Soc. Am. 20 1315
[12] Ihlenburg F 1998 Finite Element Analysis of Acastc Scattering (Applied Mathmatical Science) (New York: Springer-Verlag) pp189-210
[13] Chai Y B, Li W, Gong Z, Li T Y 2016 Ocean Eng. 116 129
[14] Rajabi M, Ahmadian M T, Jamali J 2015 Compos. Struct. 128 395
[15] Zampolli M, Tesei A, Finn B J 2007 J. Acoust. Soc. Am. 122 1472
[16] Zampolli M, Alessandra T, Canepa G 2008 J. Acoust. Soc. Am. 123 4051
[17] Hu Z, Fan J, Zhang P Z, Wu Y S 2016 Acta Phys. Sin. 65 064301 (in Chinese) [胡珍, 范军, 张培珍, 吴玉双 2016 65 064301]
[18] Zhang P Z, Wang S Z, Wang R T, Chen Y F, Wang L X 2013 Acta Acoustic 39 331 (in Chinese) [张培珍, 王朔中, 王润田, 陈云飞, 王露贤 2013 声学学报 39 331]
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