Acoustic radiation from a cylinder in shallow water by finite element-parabolic equation method

Zhi-Wen Qian; De-Jiang Shang; Qi-Hang Sun; Yuan-An He; Jing-Sheng Zhai

doi:10.7498/aps.68.20181452

Acta Physica Sinica, Volume. 68, Issue 2, 024301-1(2019)

Acoustic radiation from a cylinder in shallow water by finite element-parabolic equation method

Zhi-Wen Qian¹, De-Jiang Shang^2、*, Qi-Hang Sun², Yuan-An He³, and Jing-Sheng Zhai^1、*

Author Affiliations

¹School of Marine Science and Technology, Tianjin University, Tianjin 300072, China

²College of Underwater Acoustics Engineering, Harbin Engineering University, Harbin 150001, China

³Systems Engineering Research Institute, Beijing 100036, China

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Figures & Tables(16)

Fig. 1. Principle of FEM-PE in shallow water.浅海波导下结构声辐射FEM-PE计算原理图

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Fig. 2. Schematic diagram of IFDM used Crank-Nicolson.Crank-Nicolson有限差分法示意图

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Fig. 3. Acoustic propagation model of point source in shallow water.浅海波导下点源声传播模型

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Fig. 4. Verification of point source used FEM-PE: (a) f = 30 Hz; (b) f = 300 Hz. 点源的FEM-PE理论验证　(a) f = 30 Hz; (b) f = 300 Hz

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Fig. 5. FEM model diagram of elastic spherical shell in shallow water.浅海下弹性球壳声辐射有限元模型示意图

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Fig. 6. Verification of elastic sphere used FEM-PE: (a) f = 30 Hz; (b) f = 300 Hz. 弹性球壳的FEM-PE理论验证　(a) f = 30 Hz; (b) f = 300 Hz

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Fig. 7. Contrast between method of FEM-PE and CWSM at 60 Hz.60 Hz频率下FEM-PE与CWSM计算结果对比

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Fig. 8. Model of cylindrical sound radiation used FEM-PE in shallow water.浅海波导下圆柱壳声辐射FEM-PE预报模型

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Fig. 9. Curves of coupled modal frequency changed with diving depth: (a) Modal (4, 1); (b) modal (4, 2); (c) modal (6, 1); (d) modal (6, 2); (e) modal (6, 3); (f) modal (6, 4).耦合模态随潜深的变化曲线　(a) (4, 1); (b) (4, 2); (c) (6, 1); (d) (6, 2); (e) (6, 3); (f) (6, 4)

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Fig. 10. Colour maps of structural sound propagation at different frequencies: (a) f = 50 Hz; (b) f = 100 Hz; (c) f = 150 Hz; (d) f = 200 Hz. 不同频率下结构声场传播伪彩图　(a) f = 50 Hz; (b) f = 100 Hz; (c) f=150 Hz; (d) f = 200 Hz

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Fig. 11. Acoustic propagation contrast between structure and point souce at different frequencies: (a) f = 50 Hz; (b) f = 100 Hz; (c) f = 150 Hz; (d) f = 200 Hz. 不同频率下结构辐射声场与点源声场对比　(a) f = 50 Hz; (b) f = 100 Hz; (c)f = 150 Hz; (d) f = 200 Hz

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Fig. 12. Analysis of structural sound propagation at different frequencies: (a) f = 50 Hz; (b) f = 100 Hz; (c) f = 150 Hz; (d) f = 200 Hz. 不同频率下结构辐射场传播特性分析　(a) f = 50 Hz; (b) f = 100 Hz; (c) f = 150 Hz; (d) f = 200 Hz

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Table 1.
Convergence analysis of the method.
方法收敛性分析

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Table 1.
Convergence analysis of the method.
方法收敛性分析

FEM	\begin{document}$\scriptstyle {d_{\rm FEM}}$\end{document}	\begin{document}$\scriptstyle \lambda $\end{document}	\begin{document}$\frac{\lambda }{2}$\end{document}	\begin{document}$\frac{\lambda }{4}$\end{document}	\begin{document}$\frac{\lambda }{6}$\end{document}	\begin{document}$\frac{\lambda }{8}$\end{document}	\begin{document}$\frac{\lambda }{{10}}$\end{document}	\begin{document}$\frac{\lambda }{6}$\end{document}
PE	\begin{document}$\scriptstyle {d_z}$\end{document}	\begin{document}$\frac{\lambda }{8}$\end{document}						\begin{document}$\scriptstyle \lambda $\end{document}	\begin{document}$\frac{\lambda }{2}$\end{document}	\begin{document}$\frac{\lambda }{4}$\end{document}	\begin{document}$\frac{\lambda }{8}$\end{document}	\begin{document}$\frac{\lambda }{{16}}$\end{document}
PE	\begin{document}$\scriptstyle {d_r}=2{d_z}$\end{document}	\begin{document}$\frac{\lambda }{4}$\end{document}						\begin{document}$\scriptstyle 2\lambda $\end{document}	\begin{document}$\scriptstyle \lambda $\end{document}	\begin{document}$\frac{\lambda }{2}$\end{document}	\begin{document}$\frac{\lambda }{4}$\end{document}	\begin{document}$\frac{\lambda }{8}$\end{document}
\begin{document}$\scriptstyle \varpi $\end{document}/％		11.6	6.8	4.2	3.3	3.4	3.5	13.8	11.2	7.8	3.3	3.5
DOF/ \begin{document}$\scriptstyle \times {10^4}$\end{document}		2.2	3.4	7.2	13.1	20.9	40.9	11.5	11.6	11.9	13.1	17. 7
RAM/GB		1.9	2.0	1.9	2.0	2.2	2.5	2.0	2.0	2.0	2.0	2.1
t/s		2.3	4.5	7.5	12.4	17.3	21.9	11.5	11.6	11. 7	12.4	14.1

Table 2.
The contrast test of runtime between FEM-PE and CWSM (unit: min).
运行时间对比测试 (单位: min)

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Table 2.
The contrast test of runtime between FEM-PE and CWSM (unit: min).
运行时间对比测试 (单位: min)

l/km		\begin{document}$\scriptstyle \lambda-5$\end{document}				\begin{document}$\scriptstyle \lambda-1$\end{document}	\begin{document}$\scriptstyle \lambda-10$\end{document}	\begin{document}$\scriptstyle \lambda-50$\end{document}	\begin{document}$\scriptstyle \lambda-100$\end{document}
f/Hz		30	60	90	100	60
注: \begin{document}$\textstyle {\eta _{\rm CWSM/FEM{\text{-}}PE}}$\end{document}为两种方法时间比值, FEM-PE网格为 \begin{document}$\scriptstyle {d_{\rm FEM}}=\lambda /6$\end{document}, \begin{document}$\scriptstyle {d_z}=\lambda /8$\end{document}及 \begin{document}$\scriptstyle {d_r}=\lambda /4$\end{document}.
t	CWSM	24.62	40.47	62.00	68.78	27.97	98.98	189.57	276.68
	FEM-PE	2.20	4.18	7.21	9.45	2.17	5.98	11.60	18.76
	\begin{document}$\textstyle {\eta _{\rm CWSM/FEM {\text{-}} PE}}$\end{document}	11 : 1	10 : 1	9 : 1	8 : 1	14 : 1	17 : 1	16 : 1	14 : 1

Table 3.
Comparison of coupled modal frequency in different fluid environments (unit: Hz).
不同流体环境下圆柱壳耦合模态频率(单位: Hz)

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Table 3.
Comparison of coupled modal frequency in different fluid environments (unit: Hz).
不同流体环境下圆柱壳耦合模态频率(单位: Hz)

Environment	(4, 1)	(4, 2)	(6, 1)	(6, 2)	(6, 3)	(6, 4)
Free field	7.72	27.18	9.75	18. 19	35.12	57.63
Half-space	7.83	27.53	9.87	18.41	35.62	58.18
Pekeris	7.80	27.42	9.80	18.26	35.26	57.71

Table 4.
Normal mode frequencies in Pekeris waveguide.
Pekeris波导中各阶简正波频率
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Table 4.
Normal mode frequencies in Pekeris waveguide.
Pekeris波导中各阶简正波频率
n 1 2 3 4 5 6
f/Hz 35.52 106.56 177.60 248.65 319.69 390.73

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Zhi-Wen Qian, De-Jiang Shang, Qi-Hang Sun, Yuan-An He, Jing-Sheng Zhai. Acoustic radiation from a cylinder in shallow water by finite element-parabolic equation method[J]. Acta Physica Sinica, 2019, 68(2): 024301-1

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Paper Information

Category: Research Articles

Received: Jul. 30, 2018

Accepted: --

Published Online: Sep. 29, 2019

The Author Email: Zhai Jing-Sheng (zhiwenqian@tju.edu.cn)

DOI:10.7498/aps.68.20181452

Topics

Nuclear physics

Particles and fields

Particle and nuclear astrophysics and cosmology

Table 1. Convergence analysis of the method.方法收敛性分析

Table 1. Convergence analysis of the method.方法收敛性分析

Table 2. The contrast test of runtime between FEM-PE and CWSM (unit: min).运行时间对比测试 (单位: min)

Table 2. The contrast test of runtime between FEM-PE and CWSM (unit: min).运行时间对比测试 (单位: min)

Table 3. Comparison of coupled modal frequency in different fluid environments (unit: Hz).不同流体环境下圆柱壳耦合模态频率(单位: Hz)

Table 3. Comparison of coupled modal frequency in different fluid environments (unit: Hz).不同流体环境下圆柱壳耦合模态频率(单位: Hz)

Table 4. Normal mode frequencies in Pekeris waveguide.Pekeris波导中各阶简正波频率

Table 4. Normal mode frequencies in Pekeris waveguide.Pekeris波导中各阶简正波频率

Table 1.
Convergence analysis of the method.
方法收敛性分析

Table 1.
Convergence analysis of the method.
方法收敛性分析

Table 2.
The contrast test of runtime between FEM-PE and CWSM (unit: min).
运行时间对比测试 (单位: min)

Table 2.
The contrast test of runtime between FEM-PE and CWSM (unit: min).
运行时间对比测试 (单位: min)

Table 3.
Comparison of coupled modal frequency in different fluid environments (unit: Hz).
不同流体环境下圆柱壳耦合模态频率(单位: Hz)

Table 3.
Comparison of coupled modal frequency in different fluid environments (unit: Hz).
不同流体环境下圆柱壳耦合模态频率(单位: Hz)

Table 4.
Normal mode frequencies in Pekeris waveguide.
Pekeris波导中各阶简正波频率

Table 4.
Normal mode frequencies in Pekeris waveguide.
Pekeris波导中各阶简正波频率