一种周向周期结构声散射快速计算方法

doi:10.12382/bgxb.2024.0291

摘要/Abstract

摘要：

针对电缆、钢索以及超表面等周向周期结构声散射特性仿真需求,提出一种基于有限元子结构的散射声场快速计算方法。通过对单周期子结构表面声载荷、位移傅里叶级数展开,并对边界载荷、位移施加与阶次有关的相位映射约束,实现各阶散射声场以及总散射声场的快速计算。对实验观察到的非镜像方向散射声场增强现象进行了机理分析。螺旋凹槽结构散射声场仿真与实验结果表明:新方法计算结果具有较高的精度,在计算精度相同的条件下较传统三维有限元方法所需内存更少、计算速度快,其加速比近似等于周向周期数。

关键词: 周向周期结构, 回声特性, 声散射, 有限元方法

Abstract:

For the simulation requirements of acoustic scattering characteristics of cyclic symmetric structures such as cable, wire rope and metasurface, a substructure method based on finite elements principle is proposed to realize the fast calculation of acoustic scattering. Through expanding the Fourier series of surface acoustic loads and displacements of a single-period substructure, and applying the phase-mapping constraints related to orders on boundary loads and displacements, the scattering acoustic field for each order and the total scattering acoustic field are rapidly calculated. The enhancement mechanism of scattering acoustic field in non-mirror direction observed in the experiment is analyzed. The simulated and experimental results of spiral groove structure indicate that the computational results obtained by the proposed method exhibit high accuracy. The proposed method requires less memory and achieves faster computation speed compared to the traditional three-dimensional finite elements method under the condition of the same computational accuracy, with an acceleration ratio being equal to the number of circumferential periods.

Key words: cyclic symmetric structures, echo characteristic, acoustic scattering, finite elements method

中图分类号:

TB56

陈于思, 张宁, 范军, 李兵, 王斌. 一种周向周期结构声散射快速计算方法[J]. 兵工学报, 2025, 46(5): 240291-.

CHEN Yusi, ZHANG Ning, FAN Jun, LI Bing, WANG Bin. A Fast Calculation Method for Acoustic Scattering of Cyclic Symmetric Structures[J]. Acta Armamentarii, 2025, 46(5): 240291-.

图/表 15

图1 周向周期结构实例

Fig.1 The instances of cyclic symmetric structure

图2 周向周期为4的螺旋凹槽壳体模型图

Fig.2 The model of spiral groove structure with four circumferential periods

表1 螺旋凹槽壳体参数

Table 1 Parameters of spiral groove structure

参数	数值/m
螺旋凹槽壳体总长d	1.29
螺旋圆柱段长d₁	1.20
圆柱外半径/半球外径r₁	0.09
螺旋凹槽半径r₂	0.015
壳体厚度w	0.04
相邻螺旋凹槽间距d₂	0.06

图3 1kHz仿真目标强度对比图

Fig.3 Comparison of monostatic target strengths at 1kHz

图4 不同角度下扫频图

Fig.4 Comparison of frequency sweepings at different incident angles

图5 时间对比图

Fig.5 Comparison of calculation times

图6 两种模型实物图

Fig.6 Experimental models

图7 实验布放示意图

Fig.7 Layout of experimental system

图8 实验目标强度角度-时域谱

Fig.8 Target strength angle-time spectra of experimental models

图9 45°时域回波图

Fig.9 Echo in time domain at 45°

图10 实验目标强度角度-频率谱

Fig.10 Target strength angle-frequency spectra of experimental models

图11 仿真与实验目标强度对比图

Fig.11 Comparison of simulated and experimental results of monostatic target strength

图12 两种模型目标强度对比图

Fig.12 Comparison of monostatic target strengths of two models

图13 干涉原理图

Fig.13 Schematic diagram of interference

表2 不同频率下干涉角度

Table 2 Interference angles at different frequencies

频率/kHz	仿真/(°)	实验/(°)	误差/(°)
	38.68	38.00	0.68
20	141.32	140.00	1.32
	218.68	219.00	-0.32
	321.31	322.00	-0.69
	24.62	24.50	0.12
	56.44	57.00	-0.56
	123.56	124.50	-0.94
30	155.38	155.00	0.38
	204.62	204.50	0.12
	236.44	236.00	0.44
	303.56	305.50	-1.94
	335.38	336.00	-0.62

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