Preprint / Version 2

On Complex Vibration Intensity and Vortices

##article.authors##

  • Takuya Yabu Mitsubishi Motors Corpolation

DOI:

https://doi.org/10.31224/6992

Keywords:

complex vibration intensity, complex acoustic intensity, vibration active intensity, vibration reactive intensity, vibration intensity, acoustic active intensity, acoustic reactive intensity, acoustic intensity, structure design, structural design, vector analysis, divergence, rotation, upwelling point, sucking point, coupling of vibration and acoustics, elimination of complex vibration intensity, elimination of complex acoustic intensity, elimination of vibration active intensity, elimination of vibration reactive intensity, elimination of acoustic active intensity, elimination of acoustic reactive intensity

Abstract

The mathematical properties of complex vibration intensity, which is an extension of vibration intensity to complex numbers, were clarified from the constitutive equations of elastic bodies and acoustics in order to obtain knowledge that allows structural design to take vibration intensity into account in the preliminary stage of structural analysis. The mathematical properties obtained were applied to a dynamic absorber, and the properties of the dynamic absorber as revealed by the complex vibration intensity were explained. Furthermore, the coupling of vibration and acoustics was discussed using the relationship between complex vibration intensity and complex acoustic intensity. Furthermore, we discussed the significance of eliminating complex vibration intensity and complex acoustic intensity using external forces and external sound sources. Finally, the mathematical properties of complex vibration intensity were applied to structural design, and the findings that can be applied to structural design were presented.

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Posted

2026-05-04 — Updated on 2026-05-06

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Copyright (c) 2026 Takuya Yabu

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This work is licensed under a Creative Commons Attribution 4.0 International License.

Version justification

Sections 5.2, 5.4, 5.6.1.2, 5.6.2.2, and Chapter 6 describe the elimination of complex vibration intensity and complex acoustic intensity using external forces and external sound sources. A new chapter, Chapter 7, has been added to explain its significance. The abstract, introduction, and conclusion have been revised accordingly. Errors in the metadata have also been corrected and additions have been made. We sincerely apologize for any inconvenience this may cause during the review process. Thank you for your cooperation.