甚低频十三塔天线机电耦合协同建模与分析

doi:10.12305/j.issn.1001-506X.2026.04.05

系统工程与电子技术 ›› 2026, Vol. 48 ›› Issue (4): 1145-1153.doi: 10.12305/j.issn.1001-506X.2026.04.05

• 电子技术 • 上一篇

甚低频十三塔天线机电耦合协同建模与分析

陈海涛¹^,², 刘威¹, 陈磊¹, 强惠哲³^,*(), 张树新³

1. 中国船舶集团有限公司第七二二研究所，湖北武汉 430000
2. 湖北省低频电磁通信技术重点实验室，湖北武汉 430000
3. 西安电子科技大学高性能电子装备机电集成制造全国重点实验室，陕西西安 710071

收稿日期:2025-02-24 修回日期:2025-03-25 接受日期:2026-03-10 出版日期:2025-05-20 发布日期:2025-05-20
通讯作者: 强惠哲 E-mail:qianghuiz@163.com
作者简介:陈海涛（1979—），男，研究员，博士，主要研究方向为低频电磁通信
刘　威（1980—），男，高级工程师，博士，主要研究方向为低频电磁通信
陈　磊（1976—），男，高级工程师，博士，主要研究方向为低频电磁通信
张树新（1987—），男，教授，博士，主要研究方向为柔性可展开天线/结构机电耦合、机电集成优化设计、无人机技术
基金资助:
低频电磁通信技术实验室开放基金（科技2023-07）资助课题

Co-modeling and analysis of mechanical-electric coupling of very low frequency thirteen-tower antenna

Haitao CHEN¹^,², Wei LIU¹, Lei CHEN¹, Huizhe QIANG³^,*(), Shuxin ZHANG³

1. 722 Research Institute，China State Shipbuilding Corporation，Wuhan 430000，China
2. Hubei Provincial Key Laboratory: for Low-Frequency: Electromagnetic: Communication Technology，Wuhan 430000，China
3. National Key Laboratory of Integrated Electro-mechanical Manufacturing of High-performance Electronic Equipment，Xidian University，Xi’an 710071，China

Received:2025-02-24 Revised:2025-03-25 Accepted:2026-03-10 Online:2025-05-20 Published:2025-05-20
Contact: Huizhe QIANG E-mail:qianghuiz@163.com

摘要/Abstract

摘要：

针对甚低频十三塔天线设计中电气与结构迭代耗时的问题，本文建立了一种甚低频十三塔天线机电耦合协同分析数学模型，依靠矩量法将天线结构信息离散化嵌入了电磁网格中，完成了结构模型和电气模型之间计算网格以及信息的传递与转换，实现了天线结构与电性能的协同分析。所提方法跨越了异构系统之间网格模型的单元形状不匹配的问题，在结构参数修改后，即刻生成数学结构模型，转换成矩量法电气模型并计算电性能。采用机电耦合协同建模分析方法对不同恶劣工况下天线结构变形与天线电性能进行了计算，并在相同工况下与传统建模仿真计算结果进行了对比，在计算误差不超过1%的情况下计算效率提升35%，可以为恶劣工况下甚低频十三塔天线的平衡调控提供计算工具。

关键词: 甚低频十三塔天线, 机电耦合, 协同建模, 辐射电阻, 有效高度

Abstract:

Aiming at the problem of time-consuming iterations between electrical and structural design in the very low frequency thirteen-tower antenna, a mathematical model of electromechanical coupling collaborative analysis of very low frequency thirteen-tower antenna is established. The antenna structure information is discretized and embedded into the electromagnetic grid by the method of moment. The calculation grid between the structural model and the electrical model and the transmission and conversion of information are completed, and the collaborative analysis of antenna structure and electrical performance is realized. The proposed method overcomes the problem of unit shape mismatch of grid models between heterogeneous systems. After the structural parameters are modified, the mathematical structure model is generated immediately, which is converted into the electrical model of the moment method and the electrical performance is calculated. The electromechanical coupling collaborative modeling analysis method is used to calculate the antenna structure deformation and antenna electrical performance under different harsh conditions, and compared with the traditional modeling and simulation calculation results under the same working conditions. The calculation efficiency is improved by 35 % when the calculation error is less than 1 %, which can provide a calculation tool for the balance control of the very low frequency thirteen-tower antenna under harsh conditions.

Key words: very low frequency thirteen-tower antenna, mechanical-electric coupling, collaborative modeling, radiation resistance, effective height

中图分类号:

TN 823+.12

陈海涛, 刘威, 陈磊, 强惠哲, 张树新. 甚低频十三塔天线机电耦合协同建模与分析[J]. 系统工程与电子技术, 2026, 48(4): 1145-1153.

Haitao CHEN, Wei LIU, Lei CHEN, Huizhe QIANG, Shuxin ZHANG. Co-modeling and analysis of mechanical-electric coupling of very low frequency thirteen-tower antenna[J]. Systems Engineering and Electronics, 2026, 48(4): 1145-1153.

图/表 16

图1

图2

图3

图4

图5

图6

表1

表2

图7

图8

图9

图10

表3

图11

表4

图12

参考文献 35

1	HU Y P, ZHIMA Z R, WANG T Y, et al. The typical ELF/VLF electromagnetic wave activities in the upper ionosphere recorded by the China Seismo-Electromagnetic Satellite[J]. Remote Sensing, 2024, 16 (15): 2835. doi: 10.3390/rs16152835
2	ZHAO S F, SHEN X H, ZHOU C, et al. Space-and ground-based observations of ELF/VLF electromagnetic waves and their propagation mechanisms[J]. Frontiers in Astronomy and Space Sciences, 2023, 10, 1335615.
3	YANG D H, ZHIMA Z R, WANG Q, et al. Stability validation on the VLF waveform data of the China-Seismo-Electromagnetic Satellite[J]. Science China Technological Sciences, 2022, 65 (12): 3069- 3078. doi: 10.1007/s11431-022-2059-8
4	WU C, QIU J H, QIU S, et al. A brief analysis of the latest research progress and future direction of low-frequency transmitting antenna[C]// Proc. of the 18th European Conference on Antennas and Propagation, 2024.
5	CUI W C. An overview of submersible research and development in China[J]. Journal of Marine Science and Application, 2018, 17 (4): 459- 470. doi: 10.1007/s11804-018-00062-6
6	XU X Y, XIE H, LUO Z Q, et al. Analysis of the electrical performance of multituned VLF thirteen-tower umbrella antennas[J]. International Journal of Antennas and Propagation, 2022, 2022 (1): 8590468. doi: 10.1155/2022/8590468
7	XIE H, XU X Y, WU H N, et al. Multiobjective particle swarm optimization to design the top load of a very low frequency thirteen-tower umbrella antenna[J]. International Journal of RF and Microwave Computer-Aided Engineering, 2023, 2023 (1): 1792918. doi: 10.1155/2023/1792918
8	DAGEFU F T, CHOI J H, SADLER B M, et al. A survey of small, low-frequency antennas: recent designs, practical challenges, and research directions[J]. IEEE Antennas and Propagation Magazine, 2021, 65 (1): 14- 26.
9	LIANG Y J, ZHANG Z G. Modeling of VLF valley transmitting antenna[C]// Proc. of the 3rd IEEE International Symposium on Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications, 2009: 48−50.
10	PATEL R H, DESAI A, UPADHYAYA T. A discussion on electrically small antenna property[J]. Microwave and Optical Technology Letters, 2015, 57 (10): 2386- 2388. doi: 10.1002/mop.29335
11	TRAINOTTI V, FIGUEROA G. Vertically polarized dipoles and monopoles, directivity, effective height and antenna factor[J]. IEEE Trans. on Broadcasting, 2010, 56 (3): 379- 409. doi: 10.1109/TBC.2010.2050627
12	FARTOOKZADEH M, MOHSENI ARMAKI S H, RAZAVI S M J, et al. Modification of square top loaded low-frequency antennas with investigations on catenary networks analysis[J]. Journal of Electromagnetic Waves and Applications, 2015, 29 (1): 92- 103. doi: 10.1080/09205071.2014.981643
13	JACKSON B R, MERKLEY E. Broadband body-worn antenna using a top-loaded pyramidal radiator[J]. IET Microwaves, Antennas & Propagation, 2020, 14 (4): 329- 334.
14	PADHI J, KUMAR A, REDDY G S. Top loaded wideband electrically small antenna and its quality factor analysis[C]// Proc. of the IEEE Microwaves, Antennas, and Propagation Conference, 2022: 1769−1773.
15	IGNATENKO M, SANGHAI S A, LASSER G, et al. Wide-band high-frequency antennas for military vehicles: design and testing low-profile half-loop, inverted-L, and umbrella NVIS antennas[J]. IEEE Antennas and Propagation Magazine, 2016, 58 (6): 64- 74. doi: 10.1109/MAP.2016.2609806
16	LI H F, LIU C. Calculation on characteristics of VLF umbrella inverted-cone transmitting antenna[C]// Proc. of the 6th International Conference on Ubiquitous and Future Networks , 2014: 389−391.
17	QUAN Y, XIE H, LI H K, et al. Effects of tuning mode on radiation performance of VLF umbrella transmitting antenna[J]. Journal of Physics: Conference Series, 2022, 2290 (1): 012077. doi: 10.1088/1742-6596/2290/1/012077
18	王晓蓓, 柳超. 甚低频十三塔天线的特点与分析[J]. 舰船电子工程, 2009, 29 (11): 87- 89. doi: 10.3969/j.issn.1627-9730.2009.11.024
	WANG X B, LIU C. Characteristics and analysis of a very low frequency thirteen-tower antenna[J]. Naval Electronic Engineering, 2009, 29 (11): 87- 89. doi: 10.3969/j.issn.1627-9730.2009.11.024
19	周亮, 柳超, 董颖辉, 等. 甚低频十三塔天线电气性能的研究[J]. 通信技术, 2013, 46 (9): 9- 11. doi: 10.3969/j.issn.1002-0802.2013.09.003
	ZHOU L, LIU C, DONG Y H, et al. Study on the electrical performance of the very low frequency thirteen-tower antenna[J]. Communication Technology, 2013, 46 (9): 9- 11. doi: 10.3969/j.issn.1002-0802.2013.09.003
20	鲁刚, 王付修, 陈冰, 等. 甚低频十三塔伞形天线阵的电气性能[J]. 海军工程大学学报, 2014, 26 (4): 46- 49. doi: 10.7495/j.issn.1009-3486.2014.04.011
	LU G, WANG F X, CHEN B, et al. Electrical performance of the very low frequency thirteen-tower umbrella antenna array[J]. Journal of Naval Engineering University, 2014, 26 (4): 46- 49. doi: 10.7495/j.issn.1009-3486.2014.04.011
21	严亚龙, 柳超, 董颖辉, 等. 不同工况对甚低频发射天线电性能影响的分析方法[J]. 西安交通大学学报, 2018, 52 (6): 98- 105. doi: 10.7652/xjtuxb201806015
	YAN Y L, LIU C, DONG Y H, et al. Analytical method for the influence of different operating conditions on the electrical performance of very low frequency transmitting antennas[J]. Journal of Xi’an Jiaotong University, 2018, 52 (6): 98- 105. doi: 10.7652/xjtuxb201806015
22	KOZIEL S, PIETRENKO-DABROWSKA A. Knowledge-based performance-driven modeling of antenna structures[J]. Knowledge-Based Systems, 2022, 237, 107698. doi: 10.1016/j.knosys.2021.107698
23	CHU Z R, DENG Z Q, QI X Z, et al. Modeling and analysis of a large deployable antenna structure[J]. Acta Astronautica, 2014, 95, 51- 60. doi: 10.1016/j.actaastro.2013.10.015
24	HUANG Y. Antennas: from theory to practice[M]. Hoboken: John Wiley & Sons Limited, 2021.
25	ZHU L P, MA W Y, ZHANG R. Modeling and performance analysis for movable antenna enabled wireless communications[J]. IEEE Trans. on Wireless Communications, 2024, 23 (6): 6234- 6250.
26	LU H Q, ZENG Y. Communicating with extremely large-scale array/surface: unified modeling and performance analysis[J]. IEEE Trans. on Wireless Communications, 2021, 21 (6): 4039- 4053.
27	AMOSOV A G. Special software application for antenna modelling in mechanical engineering[C]// Proc. of the Journal of Physics: Conference Series, 2021.
28	段宝岩. 电子装备机电耦合理论、方法及其应用[M]. 北京: 科学出版社, 2011.
	DUAN B Y. Electromechanical coupling theory, methods, and applications of electronic equipment[M]. Beijing: Science Press, 2011.
29	SOBISCH L, KAISER T, FURLAN T, et al. A user material approach for the solution of multi-field problems in Abaqus: theoretical foundations, gradient-enhanced damage mechanics and thermo-mechanical coupling[J]. Finite Elements in Analysis and Design, 2024, 232, 104105. doi: 10.1016/j.finel.2023.104105
30	OHALETE N, ADERIBIGBE A, ANI E, et al. Challenges and innovations in electro-mechanical system integration: a review[J]. Acta Electronica Malaysia, 2024. DOI: 10.26480/aem.01.2024.11.20.
31	GOHNERT M, BRADLEY R. Reinforced concrete beam design using catenary theory[J]. International Journal of Civil Engineering, 2023, 21 (5): 751- 762. doi: 10.1007/s40999-022-00799-w
32	COSTA R S, LAVALL A C C, DA SILVA R G L, et al. Cable structures: an exact geometric analysis using catenary curve and considering the material nonlinearity and temperature effect[J]. Engineering Structures, 2022, 253, 113738. doi: 10.1016/j.engstruct.2021.113738
33	ASHOURI H, HSU K L, SOROOSHIAN S, et al. PERSIANN-CDR: daily precipitation climate data record from multisatellite observations for hydrological and climate studies[J]. Bulletin of the American Meteorological Society, 2015, 96 (1): 69- 83. doi: 10.1175/BAMS-D-13-00068.1
34	ELSHERBENI Z A, NAYERI P, REDDY J C. Antenna analysis and design using FEKO electromagnetic simulation software[M]. London: The Institution of Engineering and Technology, 2014.
35	WATT A D. VLF radio engineering: international series of monographs in electromagnetic waves[M]. Oxford: Elsevier, 2013.

参数名称	数值
密度/（kg/m³）	8 960
弹性模量/GPa	117
泊松比	0.34
导线直径/m	0.0254
导线横截面积/ m²	0.00 050 671
重力加速度/（cm/s²）	980
垂度	0.047
频率范围/kHz	15~40

工况名称	风速/（m/s）	覆冰厚度/mm	温度/℃
工况1（自重）	0	0	20
工况2（八级大风）	18	0	10
工况3（覆冰+八级大风）	18	10	−5

工况名称	辐射电阻
工况1（自重）	0.4991
工况2（八级大风）	0.6501
工况3（覆冰+八级大风）	0.5409

方法	辐射电阻/Ω	有效高度h_e/m	所用时间/h
传统建模	0.2534	190.0211	7
协同建模	0.2511	189.1455	4.5
效率对比/%	0.91	0.46	35.7

[1]	汪江鹏, 杨萍, 汪民乐, 闫少强. 基于协同和网络效应的作战体系效能评估方法[J]. 系统工程与电子技术, 2025, 47(11): 3754-3764.
[2]	项斌斌, 王从思, 王伟, 连培园, 张树新, 保宏. 基于机电耦合的反射面天线副面位置调整方法[J]. 系统工程与电子技术, 2018, 40(3): 489-497.
[3]	连培园，王　伟，保　宏，许万业. 基于机电耦合理论的智能反射面天线形状最优控制[J]. 系统工程与电子技术, 2014, 36(3): 417-421.
[4]	王从思，李兆，康明魁，徐慧娟，王伟，普涛，宋正梅，李江江. 偏置反射面天线的机电耦合建模与分析[J]. 系统工程与电子技术, 2014, 36(2): 214-219.
[5]	王伟，宋立伟，李鹏，马洪波. 从远场方向图反推天线面板调整量[J]. Journal of Systems Engineering and Electronics, 2011, 33(9): 1959-1962.
[6]	兰佩锋, 仇原鹰, 邵晓东. 一种反射面天线机电耦合分析的新方法[J]. Journal of Systems Engineering and Electronics, 2009, 31(2): 296-299.
[7]	李鹏, 张志华, 王伟, 郑飞. 基于不同网格形式的反射面天线方向图分析[J]. Journal of Systems Engineering and Electronics, 2009, 31(2): 347-351.

甚低频十三塔天线机电耦合协同建模与分析

Co-modeling and analysis of mechanical-electric coupling of very low frequency thirteen-tower antenna

RichHTML

PDF (PC)

可视化

摘要/Abstract

引用本文

使用本文

图/表 16

参考文献 35

相关文章 7

编辑推荐

Metrics

本文评价