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

Journals >Acta Physica Sinica >Volume 68 >Issue 2 >Page 024301-1 > Article

Acta Physica Sinica
Vol. 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

show less

DOI: 10.7498/aps.68.20181452 Cite this Article

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 Copy Citation Text

show less

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

Download full size | View in the Article

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

Download full size | View in the Article

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

Download full size | View in the Article

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

Download full size | View in the Article

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

Download full size | View in the Article

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

Download full size | View in the Article

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

Download full size | View in the Article

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

Download full size | View in the Article

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)

Download full size | View in the Article

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

Download full size | View in the Article

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

Download full size | View in the Article

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

Download full size | View in the Article

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 1.

Convergence analysis of the method.

方法收敛性分析

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 2.

The contrast test of runtime between FEM-PE and CWSM (unit: min).

运行时间对比测试 (单位: min)

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