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

doi:10.1088/1674-1056/ad7724

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.

Keywords: analogical study electromagnetic waves elastic waves wave equations physical quantities conservation laws reciprocity theorems

Received: 28 June 2024
Revised: 16 August 2024
Accepted manuscript online: 04 September 2024

PACS:	43.20.Wd	(Analogies)
	41.20.Jb	(Electromagnetic wave propagation; radiowave propagation)
	46.40.-f	(Vibrations and mechanical waves)

Fund: 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).

Corresponding Authors: Yuchen Zang
E-mail: zangyuchen@nnu.edu.cn

Cite this article:

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

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

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