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Fononik Kristalerde Ses Dalgasının Dispersiyon Özellikleri: Sonlu Elemanlar Analizi

Year 2018, Volume: 33 Issue: 3, 145 - 152, 30.09.2018
https://doi.org/10.21605/cukurovaummfd.504561

Abstract

Bu çalışmada farklı tasarımlardaki fononik kristallerin dispersiyon özellikleri deneysel olarak FFT algoritması ve nümerik olarak sonlu elemanlar yöntemi kullanılarak araştırılmıştır. Periyodik olarak yerleştirilmiş kompozit silindirlerden oluşan kare örgü ve yarı-periyodik (Fibonacci dizilimi) yapıdaki iki boyutlu fononik kristal de, birinci Brillouin bölgesinde dalga vektörüne (k) karşılık frekanslar elde edilerek M–Г–X–M yolu boyunca fononik bant yapıları çizdirildi. Periyodik fononik kristal tasarımlarından dolu kompozit silindirlerden oluşan yapıda 4 kHz–7 kHz aralığında Г–X yönünde kısmi bant, nümerik olarak incelenen c-şekilli fononik kristalde 2 kHz–3 kHz aralığında tam bant, Fibonacci dizilimindeki fononik kristalde ise 3 kHz–4 kHz ve 3,5 kHz–6,7 kHz aralıklarına Г–X yönünde kısmi bantlar gözlendi. Sonuçların geçerliliğini test etmek için sonlu yapıda iletim kayıpları nümerik olarak hesaplandı ve deneysel olarak ölçüldü. Fononik bant yapısı ile elde edilen iletim kayıpları karşılaştırıldığında sonuçların uyumlu oldukları gözlendi.

References

  • 1. Elford, D.P., 2010. Band Gap Formation in Acoustically Resonant Phononic Crystals, Doctoral Thesis, Loughborough University Institutional Repository, Loughborough.
  • 2. Liu, X.J., Fan, Y.H., 2013. Band Structure Characteristics of T-square Fractal Phononic Crystals, Chin. Phys. B, 22, 036101.
  • 3. Khelif, A., Abidi, A., 2016. Phononic Crystal Fundamental and Applications, Springer, p.23-24, New York.
  • 4. Korozlu, N., 2017. Fononik Kristal Kaplama ile Gösteri Salonlarında Akustik Yalıtımın Sayısal İncelenmesi, Dokuz Eylül Üniversitesi- Mühendislik Fakültesi, Fen ve Mühendislik Dergisi, 19, 56.
  • 5. Hongqing, D., Baizhan, X., Dejie, Y., 2017. Dirac Cones in Two-dimensional Acoustic Metamaterials, Journal of Applied Physics, 122, 065103.
  • 6. Maetani, N., Kurose, T., Tsuruta, K., 2010. Numerical Simulation of Acoustic Waves in Two-Dimesional Phononic Crystal: Negative Refraction, Memoirs of Faculty of Engineering, -Okayama University, 44, 7-12.
  • 7. Su, M.F., Olsson R.H., Leseman, Z.C., El-Kady, I., 2010. Realization of a Phononic Crystal Operating at Gigahertz Frequencies, Applied Physics Letters, 96, 053111.
  • 8. Kurose, T., Tsuruta, K., Totsuji, C., Totsuji, H., 2009. Negative Refraction of Acoustic Waves in a Two-Dimensional Phononic Crystal via FDTD Simulation, Materials Transactions, 50, 1004-1007.
  • 9. Alaie, S., Su, M.F., Goettler, D.F., El-Kady, I., Leseman, Z., 2013. Effects of Flexural and Extensional Excitation Modes on the Transmission Spectrum of Phononic Crystals Operating at Gigahertz Frequencies, J. Appl. Phys., 113, 103513.
  • 10.Xue-Feng, Z., Sheng-Chun, L., Tao, X., T., Tie- Hai, W., Jian-Chun, C., 2010. Investigation of a Silicon-based One-dimensional Phononic Crystal Plate Via the Super-cell Plane Wave Expansion Method, Chin. Phys. B, 19, 044301.
  • 11. Meidani, M., Kim, E., Li, F., Yang, J., Ngo, D., 2015. Tunable Evolutions of Wave Modes and Band Gaps in Quasi-1D Cylindrical Phononic Crystals, Journal of Sound and Vibration, 334, 270–281.
  • 12. Lucklum, R., Zubtsov, M., Oseev, A., Schmidt, M.P., Hirsch, S., Hagemann, F., 2013. Phononic Crystals and Applications, doi 10.5162/sensor2013/A3.1.
  • 13. Pachiu, C., Ion, M.J., Izbicki, L., Moagar, V., 2011. Congrès Français de Mécanique, Besançon, 29 août au 2 Septembre 2011.
  • 14. Chiyan, L., Johnson, S.G., Joannopoulos, J.D., 2002. All-angle Negative Refraction Without Negative Effective Index, Phys. Rev. B, 65, 201104-201107.
  • 15. Pashchenko, V., Yankin, S., 2013. Surface Acoustic Wave Ferroelectric Phononic Crystal Based on Electric Field Induced Periodic Domains, COMSOL Conference 2013.
  • 16.Olsson, R.H., El-Kady, I., 2008. Microfabricated Phononic Crystal Devices and Applications, Measurement Science and Technology, 20, 1.
  • 17. Gkantzounis, G., Florescu, M., 2017. Freeform Phononic Waveguides, Crystals, 12, 353.
  • 18. Chung, G., Phan, D.T., 2010. Finite Element Modeling of Surface Acoustic Waves in Piezoelectric Thin Films, Journal of the Korean Physical Society, 57, 446-450.
  • 19. Brûlé, S., Javelaud, E.H., Enoch, S., Guenneau S., 2014. Experiments on Seismic Metamaterials, Physical Reviewletters, 112, 133901.
  • 20. Qian, D., Shi, Z., 2016. Bandgap Properties in Locally Resonant Phononic Crystal Double Panel Structures with Periodically Attached Spring–mass Resonators, Physics Letters A, 380, 41.
  • 21. Oltulu, O., Simsek, Ş., Mamedov, A.M., Ozbay, E., 2016. Phononic Band Gap and Wave Propagation on Polyvinylidene fluoride Based Acoustic Metamaterials, Cogent Physics, 2: 1169570.
  • 22.Wang, Z., 2011. Development of Acoustic Models for High Frequency Resonators for Turbocharged Ic-Engines, Master Thesis in Sound & Vibration Stockholm, Sweden.
  • 23. http://www.audiotechnica. com/cms/wired_mics/8ba9f72f1fc02b c5/index.html (18.05.2018)

Dispersion Features of the Sound Waves in Phononic Crystals: Finite Element Analysis

Year 2018, Volume: 33 Issue: 3, 145 - 152, 30.09.2018
https://doi.org/10.21605/cukurovaummfd.504561

Abstract

In this study, dispersion properties of phononic crystals in different design were investigated experimentally by using FFT algorithm and numerically by using finite elements method. In the first Brillouin zone, frequencies corresponding to the wave vector (k) obtained and phononic band diagram were plotted along the M–Г–X–M path for the two dimensional phononic crystals which were periodically placed composite cylinders with square lattice and quasi-periodic (Fibonacci sequence). In the periodic phononic crystal designs, partial band in Г–X direction between 4 kHz–7 kHz in the structure consist of full composite cylinders, full band between 2 kHz–3 kHz range in the numerically studied C-shaped phononic crystal, and partial bands in Г–X direction between in the 3 kHz–4 kHz and 3.5 kHz–6.7 kHz ranges in Fibonacci phononic crystal were observed. In order to compare validity of the results, in the finite structure the transmission losses were calculated numerically and measured experimentally. When the phononic band structure compare with the obtained transmission losses, it was observed that the results were compatible. 

References

  • 1. Elford, D.P., 2010. Band Gap Formation in Acoustically Resonant Phononic Crystals, Doctoral Thesis, Loughborough University Institutional Repository, Loughborough.
  • 2. Liu, X.J., Fan, Y.H., 2013. Band Structure Characteristics of T-square Fractal Phononic Crystals, Chin. Phys. B, 22, 036101.
  • 3. Khelif, A., Abidi, A., 2016. Phononic Crystal Fundamental and Applications, Springer, p.23-24, New York.
  • 4. Korozlu, N., 2017. Fononik Kristal Kaplama ile Gösteri Salonlarında Akustik Yalıtımın Sayısal İncelenmesi, Dokuz Eylül Üniversitesi- Mühendislik Fakültesi, Fen ve Mühendislik Dergisi, 19, 56.
  • 5. Hongqing, D., Baizhan, X., Dejie, Y., 2017. Dirac Cones in Two-dimensional Acoustic Metamaterials, Journal of Applied Physics, 122, 065103.
  • 6. Maetani, N., Kurose, T., Tsuruta, K., 2010. Numerical Simulation of Acoustic Waves in Two-Dimesional Phononic Crystal: Negative Refraction, Memoirs of Faculty of Engineering, -Okayama University, 44, 7-12.
  • 7. Su, M.F., Olsson R.H., Leseman, Z.C., El-Kady, I., 2010. Realization of a Phononic Crystal Operating at Gigahertz Frequencies, Applied Physics Letters, 96, 053111.
  • 8. Kurose, T., Tsuruta, K., Totsuji, C., Totsuji, H., 2009. Negative Refraction of Acoustic Waves in a Two-Dimensional Phononic Crystal via FDTD Simulation, Materials Transactions, 50, 1004-1007.
  • 9. Alaie, S., Su, M.F., Goettler, D.F., El-Kady, I., Leseman, Z., 2013. Effects of Flexural and Extensional Excitation Modes on the Transmission Spectrum of Phononic Crystals Operating at Gigahertz Frequencies, J. Appl. Phys., 113, 103513.
  • 10.Xue-Feng, Z., Sheng-Chun, L., Tao, X., T., Tie- Hai, W., Jian-Chun, C., 2010. Investigation of a Silicon-based One-dimensional Phononic Crystal Plate Via the Super-cell Plane Wave Expansion Method, Chin. Phys. B, 19, 044301.
  • 11. Meidani, M., Kim, E., Li, F., Yang, J., Ngo, D., 2015. Tunable Evolutions of Wave Modes and Band Gaps in Quasi-1D Cylindrical Phononic Crystals, Journal of Sound and Vibration, 334, 270–281.
  • 12. Lucklum, R., Zubtsov, M., Oseev, A., Schmidt, M.P., Hirsch, S., Hagemann, F., 2013. Phononic Crystals and Applications, doi 10.5162/sensor2013/A3.1.
  • 13. Pachiu, C., Ion, M.J., Izbicki, L., Moagar, V., 2011. Congrès Français de Mécanique, Besançon, 29 août au 2 Septembre 2011.
  • 14. Chiyan, L., Johnson, S.G., Joannopoulos, J.D., 2002. All-angle Negative Refraction Without Negative Effective Index, Phys. Rev. B, 65, 201104-201107.
  • 15. Pashchenko, V., Yankin, S., 2013. Surface Acoustic Wave Ferroelectric Phononic Crystal Based on Electric Field Induced Periodic Domains, COMSOL Conference 2013.
  • 16.Olsson, R.H., El-Kady, I., 2008. Microfabricated Phononic Crystal Devices and Applications, Measurement Science and Technology, 20, 1.
  • 17. Gkantzounis, G., Florescu, M., 2017. Freeform Phononic Waveguides, Crystals, 12, 353.
  • 18. Chung, G., Phan, D.T., 2010. Finite Element Modeling of Surface Acoustic Waves in Piezoelectric Thin Films, Journal of the Korean Physical Society, 57, 446-450.
  • 19. Brûlé, S., Javelaud, E.H., Enoch, S., Guenneau S., 2014. Experiments on Seismic Metamaterials, Physical Reviewletters, 112, 133901.
  • 20. Qian, D., Shi, Z., 2016. Bandgap Properties in Locally Resonant Phononic Crystal Double Panel Structures with Periodically Attached Spring–mass Resonators, Physics Letters A, 380, 41.
  • 21. Oltulu, O., Simsek, Ş., Mamedov, A.M., Ozbay, E., 2016. Phononic Band Gap and Wave Propagation on Polyvinylidene fluoride Based Acoustic Metamaterials, Cogent Physics, 2: 1169570.
  • 22.Wang, Z., 2011. Development of Acoustic Models for High Frequency Resonators for Turbocharged Ic-Engines, Master Thesis in Sound & Vibration Stockholm, Sweden.
  • 23. http://www.audiotechnica. com/cms/wired_mics/8ba9f72f1fc02b c5/index.html (18.05.2018)
There are 23 citations in total.

Details

Primary Language Turkish
Subjects Architecture, Engineering
Journal Section Articles
Authors

Zafer Özer

Publication Date September 30, 2018
Published in Issue Year 2018 Volume: 33 Issue: 3

Cite

APA Özer, Z. (2018). Fononik Kristalerde Ses Dalgasının Dispersiyon Özellikleri: Sonlu Elemanlar Analizi. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, 33(3), 145-152. https://doi.org/10.21605/cukurovaummfd.504561
AMA Özer Z. Fononik Kristalerde Ses Dalgasının Dispersiyon Özellikleri: Sonlu Elemanlar Analizi. cukurovaummfd. September 2018;33(3):145-152. doi:10.21605/cukurovaummfd.504561
Chicago Özer, Zafer. “Fononik Kristalerde Ses Dalgasının Dispersiyon Özellikleri: Sonlu Elemanlar Analizi”. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi 33, no. 3 (September 2018): 145-52. https://doi.org/10.21605/cukurovaummfd.504561.
EndNote Özer Z (September 1, 2018) Fononik Kristalerde Ses Dalgasının Dispersiyon Özellikleri: Sonlu Elemanlar Analizi. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi 33 3 145–152.
IEEE Z. Özer, “Fononik Kristalerde Ses Dalgasının Dispersiyon Özellikleri: Sonlu Elemanlar Analizi”, cukurovaummfd, vol. 33, no. 3, pp. 145–152, 2018, doi: 10.21605/cukurovaummfd.504561.
ISNAD Özer, Zafer. “Fononik Kristalerde Ses Dalgasının Dispersiyon Özellikleri: Sonlu Elemanlar Analizi”. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi 33/3 (September 2018), 145-152. https://doi.org/10.21605/cukurovaummfd.504561.
JAMA Özer Z. Fononik Kristalerde Ses Dalgasının Dispersiyon Özellikleri: Sonlu Elemanlar Analizi. cukurovaummfd. 2018;33:145–152.
MLA Özer, Zafer. “Fononik Kristalerde Ses Dalgasının Dispersiyon Özellikleri: Sonlu Elemanlar Analizi”. Çukurova Üniversitesi Mühendislik-Mimarlık Fakültesi Dergisi, vol. 33, no. 3, 2018, pp. 145-52, doi:10.21605/cukurovaummfd.504561.
Vancouver Özer Z. Fononik Kristalerde Ses Dalgasının Dispersiyon Özellikleri: Sonlu Elemanlar Analizi. cukurovaummfd. 2018;33(3):145-52.