ANALYSIS OF PRESSURE AND VELOCITY EFFECTS OF ACOUSTIC WAVES ON DIFFERENT AMBIENT SURFACES USING FDTD METHOD

Abstract

In this article, the changes of pressure and speed on the various media surfaces, created by the sound waves are studied. Sound waves are used in the study due to their similarity to ultrasound waves. As the wave model, the Gaussian pulse wave pattern has been preferred. While inanimate surfaces such as air, water, metal, s-oil, polyethylene are used as ambient surfaces, and muscle and connective tissue surfaces are used as the living tissue in analyses. The pressure effects of acoustic waves on the selected media surfaces are investigated using the finite difference time domain (FDTD) method. In the study of the Gaussian sound wave, the propagation value increases as the number of iterations rises. In polyethylene layers, the effect of the pressure created by the sound is low (Pplastic = 39,5 µPa and Vplastic = 13,17 µm / sec). The study implemented on living tissues as a connective and muscle tissue depicts that a sound wave creates similar pressure (Pconnective =1,295 Pa, Pmuscle=1,282 Pa) and velocity (Vconnective=0,63 µm/sec, Vmuscle= 0,58 µm/sec) values in both tissues.

Keywords

• FDTD
• Acoustic wave analysis
• Acoustic wave propagation
• Pressure changes in the acoustic wave
• One-dimensional Gaussian model

AKUSTİK DALGALARIN FARKLI ORTAM YÜZEYLERİNDEKİ BASINÇ VE HIZ ETKİLERİNİN FDTD METODU İLE ÇÖZÜMLENMESİ

Abstract

Bu çalışmada ses dalgalarının farklı ortam yüzeylerinde meydana getirdiği basınç ve hız değişimleri ele alınmıştır. Ultrason dalgalarına benzerliği nedeniyle çalışmada ses dalgaları kullanılmıştır. Dalga modeli olarak, gauss nabız dalga modeli kullanılmıştır. Ortam yüzeyleri olarak hava, su, metal, s-oil, polietilen gibi cansız yüzeyler, doku türleri da olarak bağ doku ve kas dokusu yüzeyleri analizlerde kullanılmıştır. Seçilen bu ortam yüzeylerinde, akustik dalgalarının oluşturduğu basınç etkileri, zamanda sonlu farklar (FDTD) metodu kullanılarak incelenmiştir. Örneklenen gauss ses dalgasının analizinde, iterasyon sayısı arttıkça yayılım değeri de artmaktadır. Polietilen yapılı katmanlarda ise sesin oluşturduğu basıncın etkisinin düşük olduğu (Pplastik=39,5 µPa ve Vplastik=13,17 µm/sn ) tespit edilmiştir. Canlı dokulardan bağ dokusu ve kas dokusu üzerinde yapılan incelemede ise bir ses dalgasının bu iki doku üzerinde benzer basınç (Pbağ=1,295 Pa, Pkas=1,282 Pa) ve hız (Vbağ=0,63 µm/sn, Vkas= 0,58 µm/sn) değerleri oluşturduğu gözlenmektedir.

Keywords

• FDTD
• Akustik dalga analizi
• Akustik dalga maruziyeti
• Akustik dalgalarda basınç değişimi
• Tek boyutlu gauss modeli

References

1. A. Chaigne, A. Askenfelt, Numerical simulations of piano strings-Part I: a physical model for a struck string using finite dif-ference methods, Journal of the Acoustical Society of America 95/2 (1994) 1112-1118.
2. Abarbanel S, Gottlieb D, Hesthaven J S, Well-posed perfectly matched layers for advective acoustics, Journal of Computa-tional Physics, 1999, 154(2) 266-283.
3. Bording, R. P. and Lines, L. R. 1997. Seismic modeling and imaging with the complete wave equation. SEG Course Notes N8.
4. Carcione, J. M., Herman, G. C., and ten Kroode, A. P. E. 2002. Y2K review article: Seismic modeling. Geophysics67, pp. 1304-1325.
5. D. Razansky, P. D. Einziger, and D. R. Adam, Increased Acoustic and Electromagnetic Energy Deposition in a Layered Tissue Model, Proceedings of the 26th Annual International Conference of the IEEE EMBS, San Francisco, CA, USA, September 1-5, 2004.
6. D.M. Sullivan, Electromagnetic simulation using the FDTD method, IEEE Press, 2000.
7. Hong Wei Yang, Ze Kun Yang, Jian Xiao Liu, Ai Ping Li, Xiong You, A novel DGS microstrip antenna simulated by FDTD, Optik 124/16 (2013) 2277-2260.
8. Hongwei Guo, A simple algorithm for fitting a Gaussian function, IEEE Sign. Proc. Mag. 28(9): 134-137 (2011).

9. https://itis.swiss/virtual-population/tissue-properties/database/acoustic-properties/ Date of Access: 20 March 2020.
10. https://itis.swiss/virtual-population/tissue-properties/database/acoustic-properties/ Date of Access: 20 March 2020
11. J. G. Maloney and K. E. Cummings, Adaptation of FDTD techniques to Acoustic modeling, 11th Annual Review of Progress in Applied Computational Electromagnetic , Monterey, CA, vol. 2, March 1995, pp. 724-731.
12. J. J. Bowman, T. B. A. Senior, and P. L. E. Uslenghi, Electromagnetic and Acoustical Scattering by Simple Shapes. New York, Hemisphere, 1987.
13. J. Lovetri, D. Mardare, G. Soulodre, Modeling of the seat dip effect using the finite-difference time-domain method, Journal of the Acoustical Society of America 100 (1996) 2204-2212.
14. J.-E Berenger, A perfectly matched layer for the absorption of electromagnetic waves, J. Comput. Phys. 1994, 114. 185-200.
15. K. Yee, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media, IEEE Trans-actions on Antennas and Propagation 14/3 (1966) 302-307.
16. L. Beranek, Acoustics, New York, McGraw-Hill, 1954
17. Liu Q H, Tao J, The perfectly matched layer for acoustic waves in absorptive media, The Journal of the Acoustical Society of America, 1997, 102(4): 2072-2082.
18. M. N. H. Zahari, S. H. Dahlan and A. Madun, A review of acoustic FDTD Simulation technique and its application to under-ground cavity detection, ARPN Journal of Engineering and Applied Sciences, vol. 10, no.19, October 2015, Malaysia.
19. N. Hagen, M. Kupinski, and E. L. Dereniak, Gaussian profile estimation in one dimension, Appl. Opt. 46:5374-5383 (2007).
20. S.D. Gedney, An anisotropic perfectly matched layer absorbing media for the truncation of FDTD lattices, Antennas and Propagation, IEEE Transactions, 1996, 44 (12): 1630–1639.
21. Sukru Ozen, Selcuk Helhel, and O. Halil Colak, Electromanetic Field Measurements of Radio Transmıtters in Urban Area and Exposure Analysis, Microwave and Optical Technology Letters / Vol. 49, No. 7, July 2007.
22. Tauseef Qamar Dmrd, Mtıdu, Musp, Member American Institute of Ultrasound in Medicine, Punjap Ultrasound Socıety, 2014, ICEAF (USA).
23. Turkel E, Yefet A, Absorbing PML boundary layers for wave-like equations, Applied Numerical Mathematics, 1998, 27(4): 533-557.
24. V. Ostashev, D. Wilson, L. Liu, D. Aldridge, N. Symons, D. Marlin, Equations for finite-difference time-domain simulation of sound propagation in moving inhomogeneous media and numerical implementation, Journal of the Acoustical Society of America 117 (2005) 503-517.
25. W. C. Chew and W. H. Weedon, A 3d perfectly matched medium from modified Maxwell's equations with stretched coordi-nates, Microwave Optical Tech. Letters, 1994, 7 (13): 599–604.
26. Weisstein, Eric W. "Fourier Transform–Gaussian". MathWorld. Retrieved 19 December 2013.
27. Y. Pennec, J.O. Vasseur, B. Djafari-Rouhani, L. Dobrzynski, P.A. Deymier, Two-dimensional phononic crystals, Examples and application, Surface Science Reports, 65/8 ,2010, 229-291.
28. Z. Zhan, P. Wei, Influences of anisotropy on band gaps of 2D photonic crystal, Acta Mechanica Solida Sinica 23/2, 2010, 181-18.
29. Zhang, H., Liu, B., A New Genetic Algorithm for Order-Picking of Irregular Warehouse. International Conference on Envi-ronmental Science and Information Application Technology, 1, 2009, 121-124.