An analogical study of wave equations, physical quantities, conservation and reciprocity equations between electromagnetic and elastic waves

doi:10.1088/1674-1056/ad7724

中国物理B ›› 2024, Vol. 33 ›› Issue (11): 114301-114301.doi: 10.1088/1674-1056/ad7724

An analogical study of wave equations, physical quantities, conservation and reciprocity equations between electromagnetic and elastic waves

Yuchen Zang(臧雨宸)†

School of Physics and Technology, Nanjing Normal University, Nanjing 210023, China

收稿日期:2024-06-28 修回日期:2024-08-16 接受日期:2024-09-04 出版日期:2024-11-15 发布日期:2024-11-15
基金资助:
This work was funded by the National Natural Science Foundation of China (Grant No. 12404507), the Natural Science Research of Jiangsu Higher Education Institutions of China (Grant No. 24KJB140013), and the Scientific Startup Foundation of Nanjing Normal University (Grant No. 184080H201B49).

An analogical study of wave equations, physical quantities, conservation and reciprocity equations between electromagnetic and elastic waves

Yuchen Zang(臧雨宸)†

School of Physics and Technology, Nanjing Normal University, Nanjing 210023, China

Received:2024-06-28 Revised:2024-08-16 Accepted:2024-09-04 Online:2024-11-15 Published:2024-11-15
Contact: Yuchen Zang E-mail:zangyuchen@nnu.edu.cn
Supported by:
This work was funded by the National Natural Science Foundation of China (Grant No. 12404507), the Natural Science Research of Jiangsu Higher Education Institutions of China (Grant No. 24KJB140013), and the Scientific Startup Foundation of Nanjing Normal University (Grant No. 184080H201B49).

摘要/Abstract

摘要： This paper presents an analogical study between electromagnetic and elastic wave fields, with a one-to-one correspondence principle established regarding the basic wave equations, the physical quantities and the differential operations. Using the electromagnetic-to-elastic substitution, the analogous relations of the conservation laws of energy and momentum are investigated between these two physical fields. Moreover, the energy-based and momentum-based reciprocity theorems for an elastic wave are also derived in the time-harmonic state, which describe the interaction between two elastic wave systems from the perspectives of energy and momentum, respectively. The theoretical results obtained in this analysis can not only improve our understanding of the similarities of these two linear systems, but also find potential applications in relevant fields such as medical imaging, non-destructive evaluation, acoustic microscopy, seismology and exploratory geophysics.

关键词: analogical study, electromagnetic waves, elastic waves, wave equations, physical quantities, conservation laws, reciprocity theorems

Abstract: This paper presents an analogical study between electromagnetic and elastic wave fields, with a one-to-one correspondence principle established regarding the basic wave equations, the physical quantities and the differential operations. Using the electromagnetic-to-elastic substitution, the analogous relations of the conservation laws of energy and momentum are investigated between these two physical fields. Moreover, the energy-based and momentum-based reciprocity theorems for an elastic wave are also derived in the time-harmonic state, which describe the interaction between two elastic wave systems from the perspectives of energy and momentum, respectively. The theoretical results obtained in this analysis can not only improve our understanding of the similarities of these two linear systems, but also find potential applications in relevant fields such as medical imaging, non-destructive evaluation, acoustic microscopy, seismology and exploratory geophysics.

Key words: analogical study, electromagnetic waves, elastic waves, wave equations, physical quantities, conservation laws, reciprocity theorems

中图分类号: (Analogies)

43.20.Wd

41.20.Jb (Electromagnetic wave propagation; radiowave propagation) 46.40.-f (Vibrations and mechanical waves)

Yuchen Zang(臧雨宸). An analogical study of wave equations, physical quantities, conservation and reciprocity equations between electromagnetic and elastic waves[J]. 中国物理B, 2024, 33(11): 114301-114301.

Yuchen Zang(臧雨宸). An analogical study of wave equations, physical quantities, conservation and reciprocity equations between electromagnetic and elastic waves[J]. Chin. Phys. B, 2024, 33(11): 114301-114301.

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An analogical study of wave equations, physical quantities, conservation and reciprocity equations between electromagnetic and elastic waves

An analogical study of wave equations, physical quantities, conservation and reciprocity equations between electromagnetic and elastic waves

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