Journal of Applied Science and Engineering

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Jia-Min Shen1, Yue-Chao Liu2This email address is being protected from spambots. You need JavaScript enabled to view it., Gui-Dong Xu1, Chen-Guang Xu1, Bai-Qiang Xu1, and Sai Zhang1This email address is being protected from spambots. You need JavaScript enabled to view it.

1Department of Physics, Jiangsu University, Zhenjiang 212013, China

2Dept Math & Phys, Hebei Key Lab Phys & Energy Technol, North China Electric Power University, Baoding 071003, China


Received: December 18, 2023
Accepted: January 29, 2024
Publication Date: March 8, 2024

 Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

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Time reversal (TR) serves as a crucial method for addressing sound source localization challenges in intricate structures. Previous studies have indicated that introducing a random scattering layer between the source and the receiving array significantly enhances the effectiveness of TR focusing. Nevertheless, the situation of a source situated within the scattering layer have not been deeply studied. In this work, the acoustic field characteristics and the effects of TR focusing for the source located in periodic phononic crystals, weakly disordered phononic crystals, and random scattering structures are investigated. To begin, employing acoustic reciprocity theory, a two-dimensional theoretical method and model are established for these structures. Subsequently, finite element simulations are executed to study the characteristics of the forward-propagating acoustic field. Building upon this foundation, the TR focusing characteristics of the source within these structures are analyzed, revealing that strong disorder is crucial for achieving high-resolution focusing. Moreover, the influence of the number of array elements on TR focusing characteristics is explored. The results indicate that random scattering structures can achieve high-resolution focusing using a single array element, which cannot be achieved in homogeneous media, periodic phononic crystals, or weakly disordered phononic crystals. This phenomenon is attributed to the degree of correlation between scattering field transmission paths. Our study demonstrates that the source within the structure can attain effective localization through TR, expanding the practical applications of TR and carrying substantial research implications for fields such as acoustic detection and source localization in complex structures.

Keywords: Periodic phononic crystals; Weakly disordered phononic crystals; Random scattering; Time reversal; Source focusing

  1. [1] B. E. Anderson, L. Pieczonka, M. C. Remillieux, T. J. Ulrich, and P.-Y. Le Bas, (2017) “Stress corrosion crack depth investigation using the time reversed elastic nonlinearity diagnostic" The Journal of the Acoustical Society of America 141(1): EL76–EL81. DOI: 10.1121/1.4974760.
  2. [2] C. Preston, A. M. Alvarez, M. Allard, A. Barragan, and R. S. Witte, (2023) “Acoustoelectric TimeReversal for Ultrasound Phase-Aberration Correction" IEEE Transactions on Sonics and Ultrasonics 70: 854–864. DOI: 10.1109/TUFFC.2023.3292595.
  3. [3] Y. Song, C. Su, Q. Li, and W. Lin, (2021) “A study on the phase correction method in transcranial ultrasound planewave imaging" Applied Acoustics 40: 1–10. DOI: 10.11684/j.issn.1000-310X.2021.01.001.
  4. [4] S. Hidalgo-Caballero, S. Kottigegollahalli Sreenivas, V. Bacot, S. Wildeman, M. Harazi, X. Jia, A. Tourin, M. Fink, A. Cassinelli, M. Labousse, and E. Fort, (2023) “Damping-driven time reversal for waves" Physical Review Letters 130: 087201. DOI: 10.1103/PhysRevLett.130.087201.
  5. [5] G. Byun and J. Kim, (2015) “Improved multiple focusing with adaptive time-reversal mirror in the ocean" Journal of the Acoustical Society of America 138: 1948–1948. DOI: https: //
  6. [6] X. Sun, Q. Yan, and G. XiangYing, (2021) “Characteristic Research of Low Frequency Band Gaps and Structural Improvement in Single-Sided Column Local Resonance Phononic Crystals" Journal of Synthetic Crystals 50: 1378–1385. DOI: 10.16553/j.cnki.issn1000-985x.20210623.002.
  7. [7] Z. Yuan and J. Cheng. “The propagation of acoustic wave in 2D weak disordered phononic crystals”. In: Proc. of 2005 Youth Academic Conference of the Chinese Society of Acoustics. 2005, 60–62.
  8. [8] A. Derode, A. Tourin, and M. Fink, (2001) “Random multiple scattering of ultrasound. I. Coherent and ballistic waves" Physical Review E 64: 036605. DOI: 10.1103/ PhysRevE.64.036605.
  9. [9] M. Rupin, F. Lemoult, G. Lerosey, and P. Roux, (2014) “Experimental Demonstration of Ordered and Disordered Multiresonant Metamaterials for Lamb Waves" Physical Review Letters 112: 234301–234301. DOI: 10.1103/PhysRevLett.112.234301.
  10. [10] A. Tourin, F. Van Der Biest, and M. Fink, (2006) “Time Reversal of Ultrasound through a Phononic Crystal" Physical Review Letters 96: 104301. DOI: 10.1103/ PhysRevLett.96.104301.
  11. [11] V. S. Gomez, I. Spiousas, and M. C. Eguia, (2021) “Time reversal focusing in the audible range using a tunable sonic crystal" The Journal of the Acoustical Society of America 149: 4024–4035. DOI: 10.1121/10.0005196.
  12. [12] Y. Wang, J. Li, Y. Fu, R. Bao, W. Chen, and Y. Wang, (2021) “Tunable guided waves in a soft phononic crystal with a line defect" APL Materials 9: 051124. DOI: 10.1063/5.0049574.
  13. [13] A. Derode, A. Tourin, and M. Fink, (2000) “Limits of time-reversal focusing through multiple scattering: Longrange correlation" The Journal of the Acoustical Society of America 107: 2987–2998. DOI: 10.1121/1.429328.
  14. [14] G. Zhou, G. Li, and J. Cheng, (2009) “A new method for detecting underwater acoustic signals under the background of marine environmental noise" Acoustics and Electronic Engineering: 21–23+27. DOI: CNKI:SUN: SXDG.0.2009-02-007.
  15. [15] S. Yang, X. Liu, H. Wang, C. Liu, Y. Chen, and H. Zhou, (2023) “Simulation study of K-wave based transcranial ultrasound focusing simulation" Technical Acoustics 42: 39–45. DOI: 10.16300/j.cnki.1000-3630.2023.01.007.
  16. [16] X. Gao. “Research on Acoustic Monitoring and Localization of Boiler Tube Leakage Based on Multi-Sensors Three-Dimensional Arrays". (mathesis). North China Electric Power University, 2014.
  17. [17] J. Li, H. Zhu, H. Zhao, and S. Guo, (2009) “Study of time reversal highly resolved localization by decomposition of the time reversal operator" Acta Acustica 34: 60–66. DOI: 10.15949/j.cnki.0371-0025.2009.01.006.
  18. [18] D. Chen. “Study on the Application of Aeolian Tones Radiated from Jet Flow past Tubes in Boiler Tube Leak Detection". (mathesis). North China Electric Power University, 2015.
  19. [19] Y. Liu. “Research on Acoustic Radiation and Propagation Characteristics of Leakage Sources in Boiler Tube Arrays". (mathesis). North China Electric Power University, 2014.
  20. [20] A. L. Wang Lin Jiang GenShan, (2010) “Research status of the acoustic detection and location system for boiler tube leakage" Applied Acoustics 29: 1–10.
  21. [21] Y. S. L. Chiu, C.-F. Chen, and M.-H. Lin. “Study of focusing structure in time-reversal-mirror tcechnique”. In: Oceans. 2007. 2006, 1–7. DOI: 10.1109/OCEANSAP.20.
  22. [22] G. X. Wang SuPing and D. ShuanPing, (2005) “Active time reversal focusing technology" Acoustics and Electronics Engineering: 12–14+27.
  23. [23] A. Derode, A. Tourin, and M. Fink, (2001) “Random multiple scattering of ultrasound. II. Is time reversal a self-averaging process" Physical Review E 64: 036606. DOI: 10.1103/PhysRevE.64.036606.



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