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Backscattering enhancement associated with subsonic Rayleigh wave resonance of a polymethlmethacrylate (PMMA) cylinder is observed at low frequencies in water, which suggests that the PMMA cylinders may have essential applications in the low-frequency standard scatterer design. A slightly deformed surface structure with regular corrugation is presented to manipulate the low-frequency backscattering resonance frequency of PMMA cylinder passively. Using the perturbation method, the approximate resonance frequency shift is derived for an infinite slightly deformed cylinder with regular corrugations. Based on the phase matching of Rayleigh waves, the mechanism of low-frequency resonance frequency shift is revealed. Studies show that compared with a bare cylinder, a small boundary deformation can cause the propagation path of Rayleigh waves to change, namely, the Rayleigh waves propagate along the slightly deformed surface with regular corrugations. The modified propagation path can cause the propagation phase to change, which brings about the low-frequency backscattering resonance frequency shift of a PMMA cylinder. Furthermore, how the resonance frequency shifts with the deformation coefficient and period of the corrugation is discussed in detail. The backscattering resonance frequency of the regular corrugated cylinder shifts to low frequency with the increase of ξ under the condition of the deformation coefficient ξ > 0, but shifts to high frequency with the decrease of ξ at ξ < 0, and the resonance frequency shift increases with the increase of absolute value of deformation coefficient. When corrugation period m < 10, the phase variation with m is too small, so the corrugation period has little effect on the resonance frequency shift. Finally, acoustic scattering experiment of the regular corrugated cylinder is conducted in the tank. The resonance frequency shift is obviously observed in the experiment, which is in good agreement with the theoretical prediction. Hence, the characteristics of backscattering enhancement associated with subsonic Rayleigh wave and the resonance frequency shifts make the PMMA deformed cylinder have potential applications such as in standard scatter design and identification using “AcoustiCode”.
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Keywords:
- regular corrugation /
- cylinder /
- subsonic Rayleigh wave /
- resonance scattering
[1] Ge L, Song Q H, Redding B, Eberspacher A, Wiersig J, Cao H 2013 Phys. Rev. A. 88 043801
Google Scholar
[2] Ge L, Song Q H, Redding B, Cao H 2013 H Phys. Rev. A. 87 023833.1
Google Scholar
[3] Fawcett J A 2016 IEEE J. Ocean. Eng. 41 682
Google Scholar
[4] Zhang L G, Sun N H, Marston P L 1992 J. Acoust. Soc. Am. 91 1862
Google Scholar
[5] Fawcett J A 2001 J. Acoust. Soc. Am. 109 1312
Google Scholar
[6] Guel-Tapia J A, Villa-Villa F, Mendoza-Suarez A, Perez-Aguilar H 2016 Archives of Acoustics 41 461
Google Scholar
[7] Hartmann B, Jarzynski B 1974 J. Acoust. Soc. Am. 56 1469
Google Scholar
[8] Hefner B T, Marston P L 2000 J. Acoust. Soc. Am. 107 1930
Google Scholar
[9] Satish A, Trivett D, Sabra K G 2020 J. Acoust. Soc. Am. 147 EL517
Google Scholar
[10] Srivastava P, Nichols B, Sabra K G 2017 J. Acoust. Soc. Am. 142 EL573
Google Scholar
[11] Doolittle R D, Überall H, Uginčius P 1968 J. Acoust. Soc. Am. 43 1
Google Scholar
[12] Dubertrand R, Bogomolny E, Djellali N, Lebental M, Schmit C 2008 Phys. Rev. A. 77 013804.1
Google Scholar
[13] Donald B, Gaunaurd G C 1983 J. Acoust. Soc. Am. 73 1448
Google Scholar
[14] 龙云亮, 文希理, 谢处方 1994 数值计算与计算机应用 2 88
Google Scholar
You Y L, Wen X L, Xie C F 1994 Journal on Numerical Methods and Computer Applications 2 88
Google Scholar
[15] 汤渭霖 1995 声学学报 06 456
Google Scholar
Tang W L 1995 ACTA. ACUSTICA. 06 456
Google Scholar
[16] Marston P L, Sun N H 1995 J. Acoust. Soc. Am. 97 777
Google Scholar
[17] 周彦玲, 范军, 王斌 2019 物理学报 68 214301
Google Scholar
Zhou Y L, Fan J, Wang B 2019 Acta Phys. Sin. 68 214301
Google Scholar
[18] 汤渭霖, 范军, 马忠诚 著 2018 水中目标声散射 (北京: 科学出版社) 第99—104页
Tang W L, Fan J, Ma Z C 2018 Acoustic Scattering of Underwater Targets (Beijing: Science Press) pp99–104 (in Chinese)
[19] 彭茜蕤, 周彦玲, 范军 2018 声学技术 37 528
Peng X R, Zhou Y L, Fan J 2018 Technical Acoustics 37 528
[20] 程建春 著 2019 声学原理 (北京: 科学出版社) 第615—619页
Cheng J C 2019 Acoustical Principle (Beijing: Science Press) pp615–619 (in Chinese)
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图 1 无限长微弱形变规则波纹表面圆柱体
Figure 1. Infinite regular-corrugated cylinder.
图 2 基于微扰法无限长规则波纹圆柱形态函数幅频特性 (a)反向散射; (b)局部放大
Figure 2. Form function of the infinite regular-corrugated cylinder based on the perturbation method: (a) Backscattering; (b) local enlargement.
图 3 PMMA圆柱中Rayleigh波相速度频散曲线(黑色线), 曲线
$2{\text{π}}a{f_0}/M$ (蓝色点划线)和曲线$Sf/M$ (红色虚线)Figure 3. Dispersion curve of subsonic Rayleigh waves (black line), curve
$2{\text{π}}a{f_0}/M$ (blue dashed-dotted line) and curve$Sf/M$ (red dotted line).
图 4 亚音速Rayleigh波传播路径 (a)光滑圆柱; (b)规则波纹圆柱
Figure 4. Ray diagram for subsonic Rayleigh waves propagating around: (a) Bare cylinder; (b) regular-corrugated cylinder.
图 5 不同方法获取共振频率误差
Figure 5. The relative error of resonance frequencies obtained by different methods.
图 6 (a)频率-波纹微扰系数谱; (b)频率-波纹周期谱
Figure 6. (a) Frequency-height spectra; (b) frequency-period spectra.
图 7 不同波纹周期对应相位变化量
Figure 7. Phase varying with corrugated period.
图 8 实验模型
Figure 8. Experimental objects.
图 9 实验布放
Figure 9. Diagram of experimental system setup.
图 10 光滑圆柱和规则波纹表面圆柱反向散射形态函数实验结果
Figure 10. Backscattering form function of regular-corrugated cylinders in the experiment.
图 12 规则波纹圆柱频率-角度谱 (a) ξ = 0; (b) ξ = –3%; (c) ξ = –10%
Figure 12. Frequency-angle spectra: (a) ξ = 0; (b) ξ = –3%; (c) ξ = –10%.
表 1 计算所用材料参数
Table 1. Material parameters used in the calculations.
材料 密度/(kg·m–3) 纵波波速/(m·s–1) 剪切波波速/(m·s–1) PMMA 1190 2690 1340 水 1000 1500 — 
DownLoad: CSV
表 2 无限长PMMA圆柱和规则波纹圆柱共振频率
Table 2. Resonance frequency of PMMA bare and corrugated cylinder
l ${f_0}$/Hz $f_0^{\prime}$/Hz ${f_\xi }$ /Hz $f_\xi^{\prime}$/Hz 1 6419 6420 6259 6240 2 9953 9955 9704 9700 3 13383 13385 13048 13050 4 16790 16790 16370 16375
DownLoad: CSV
表 3 实验模型共振峰频率
Table 3. Resonance frequencies of experimental objects.
l ${f_0}$/Hz ${f_{\xi_ 1} }$/Hz $f_{\xi_1} ^{\prime}$ /Hz ${f_{\xi_ 2} }$/Hz $f_{\xi_ 2}^{\prime}$/Hz 1 6649 6748.7 6852 6981.4 6966 2 8643 8772.6 9098 9075.1 9294 3 12410 12596.0 12996 13031.0 13192
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[1] Ge L, Song Q H, Redding B, Eberspacher A, Wiersig J, Cao H 2013 Phys. Rev. A. 88 043801
Google Scholar
[2] Ge L, Song Q H, Redding B, Cao H 2013 H Phys. Rev. A. 87 023833.1
Google Scholar
[3] Fawcett J A 2016 IEEE J. Ocean. Eng. 41 682
Google Scholar
[4] Zhang L G, Sun N H, Marston P L 1992 J. Acoust. Soc. Am. 91 1862
Google Scholar
[5] Fawcett J A 2001 J. Acoust. Soc. Am. 109 1312
Google Scholar
[6] Guel-Tapia J A, Villa-Villa F, Mendoza-Suarez A, Perez-Aguilar H 2016 Archives of Acoustics 41 461
Google Scholar
[7] Hartmann B, Jarzynski B 1974 J. Acoust. Soc. Am. 56 1469
Google Scholar
[8] Hefner B T, Marston P L 2000 J. Acoust. Soc. Am. 107 1930
Google Scholar
[9] Satish A, Trivett D, Sabra K G 2020 J. Acoust. Soc. Am. 147 EL517
Google Scholar
[10] Srivastava P, Nichols B, Sabra K G 2017 J. Acoust. Soc. Am. 142 EL573
Google Scholar
[11] Doolittle R D, Überall H, Uginčius P 1968 J. Acoust. Soc. Am. 43 1
Google Scholar
[12] Dubertrand R, Bogomolny E, Djellali N, Lebental M, Schmit C 2008 Phys. Rev. A. 77 013804.1
Google Scholar
[13] Donald B, Gaunaurd G C 1983 J. Acoust. Soc. Am. 73 1448
Google Scholar
[14] 龙云亮, 文希理, 谢处方 1994 数值计算与计算机应用 2 88
Google Scholar
You Y L, Wen X L, Xie C F 1994 Journal on Numerical Methods and Computer Applications 2 88
Google Scholar
[15] 汤渭霖 1995 声学学报 06 456
Google Scholar
Tang W L 1995 ACTA. ACUSTICA. 06 456
Google Scholar
[16] Marston P L, Sun N H 1995 J. Acoust. Soc. Am. 97 777
Google Scholar
[17] 周彦玲, 范军, 王斌 2019 物理学报 68 214301
Google Scholar
Zhou Y L, Fan J, Wang B 2019 Acta Phys. Sin. 68 214301
Google Scholar
[18] 汤渭霖, 范军, 马忠诚 著 2018 水中目标声散射 (北京: 科学出版社) 第99—104页
Tang W L, Fan J, Ma Z C 2018 Acoustic Scattering of Underwater Targets (Beijing: Science Press) pp99–104 (in Chinese)
[19] 彭茜蕤, 周彦玲, 范军 2018 声学技术 37 528
Peng X R, Zhou Y L, Fan J 2018 Technical Acoustics 37 528
[20] 程建春 著 2019 声学原理 (北京: 科学出版社) 第615—619页
Cheng J C 2019 Acoustical Principle (Beijing: Science Press) pp615–619 (in Chinese)
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