DOI QR코드

DOI QR Code

Finite Element Modeling for the Analysis of In- and Out-of-plane Bulk Elastic Wave Propagation in Piezoelectric Band Gap Structures

압전 밴드 갭 구조물의 면내·외 방향 체적 탄성파 전파 특성 해석을 위한 유한요소 모델링

  • Kim, Jae-Eun (Faculty of Mechanical and Automotive Engineering, Catholic Univ. of Daegu) ;
  • Kim, Yoon-Young (School of Mechanical and Aerospace Engineering, Seoul Nat'l Univ.)
  • 김재은 (대구가톨릭대학교 기계자동차공학부) ;
  • 김윤영 (서울대학교 기계항공공학부)
  • Received : 2011.05.11
  • Accepted : 2011.06.08
  • Published : 2011.08.01

Abstract

This investigation presents a finite element method to obtain the transmission properties of bulk elastic waves in piezoelectric band gap structures(phonon crystals) for varying frequencies and modes. To this end, periodic boundary conditions are imposed on a three-dimensional model while both in-plane and out-of-plane modes are included. In particular, the mode decoupling characteristics between in-plane and out-of-plane modes are identified for each electric poling direction and the results are incorporated in the finite element modeling. Through numerical simulations, the proposed modeling method was found to be a useful, effective one for analyzing the wave characteristics of various types of piezoelectric phononic band gap structures.

본 연구에서는 압전 밴드 갭 구조물(포논 결정) 에 대한 체적 탄성파의 전파 특성을 주파수 및 모드 별로 파악하기 위한 유한 요소법의 적용 방안을 제안하였다. 이를 위해 체적 탄성 진행파의 면내 모드 뿐만 아니라 면외 모드를 포함하도록 3 차원 주기 경계 조건을 고려하였다. 특히, 체적 탄성파 모드 간의 비연성 특성을 전기 분극 방향에 따라 유도한 다음, 그 결과를 유한 요소 모델링에 반영하였다. 제안된 방법은 실제 시뮬레이션을 통해 다양한 형태의 압전 밴드 갭 구조물의 파동 특성 분석에 적용될 수 있는 일반적이고 효율적인 방법임을 확인하였다.

Keywords

References

  1. Brillouin, L., 1946, Wave Propagation in Periodic Structures, McGraw-Hill Book Company, New York.
  2. Kushwaha, M. S., Halevi, P., Dobrzynski, L. and Djafari-Rouhani, B., 1993, "Acoustic Band Structure of Periodic Elastic Composites," Phys. Rev. Lett. B, Vol. 71, No. 13, pp. 2022-2025. https://doi.org/10.1103/PhysRevLett.71.2022
  3. Sigmund, O., Jensen, J. S., 2003, "Systematic Design of Phononic Band-Gap Materials and Structures by Topology Optimization," Phil. Trans. R. Soc. Lond. A, Vol. 361, pp. 1001-1009. https://doi.org/10.1098/rsta.2003.1177
  4. Pennec, Y., Djafari-Rouhani, B., Larabi, H., Vasseur, J. and Hladky-Hennion, A-C., 2009, "Phononic Crystals and Manipulation of Sound," Phys. Status Solidi C., Vol. 6, No. 9, 2080-2085. https://doi.org/10.1002/pssc.200881760
  5. Armenise, M. N., Campanella, C. E., Ciminelli, C., Dell'Olio, F. and Passaro, V. M. N., 2010, "Phononic and Photonic Band Gap Structures: Modeling and Applications," Physics Procedia, Vol. 3, No. 1, pp. 357-364. https://doi.org/10.1016/j.phpro.2010.01.047
  6. Solymar, L. and Shamonina, E., 2009, Waves in Metamaterials, Oxford University Press, New York.
  7. Hou, Z., Wu, F. and Liu, Y., 2004, "Phononic Crystals Containing Piezoelectric Material," Solid State Commun. Vol. 130, pp. 745-749. https://doi.org/10.1016/j.ssc.2004.03.052
  8. Wang, Y., Li, F., Wang, Y., Kishimoto, K. and Huang, W., 2009, "Tuning of Band Gaps for a Two-Dimensional Piezoelectric Phononic Crystal with a Rectangular Lattice," Acta. Mech. Sin., Vol. 25, pp. 65-71. https://doi.org/10.1007/s10409-008-0191-9
  9. Robillard, J.-F., Matar, O. B., Vasseur, J. O., Deymier, P. A., Stippinger, M., Hladky-Hennion, A.-C., Pennec, Y. and Djafari-Rouhani, B., 2009, "Tunable Magnetoelastic Phononic Crystals, " Appl. Phys. Lett., Vol. 95, 124104. https://doi.org/10.1063/1.3236537
  10. Vasseur, J. O., Deymier, P. A., Djafari-Rouhani, B., Pennec, Y. and Hladky-Hennion, A.-C., "Absolute Forbidden Bands and Waveguiding in Two-Dimensional Phononic Crystal Plates," Phys. Rev. B, Vol. 77, 085415. https://doi.org/10.1103/PhysRevB.77.085415
  11. Wilm, M., Ballandras, S., Laude, V. and Pastureaud, T., 2002, "A Full 3D Plane-Wave-Expansion Model for 1-3 Piezoelectric Composite Structures," J. Acoust. Soc. Am., Vol. 112, No. 3, pp. 943-952. https://doi.org/10.1121/1.1496081
  12. Kafesaki, M., 1999, "Multiple-Scattering Theory for Three-Dimensional Periodic Acoustic Composites," Phys. Rev. B, Vol. 60, pp. 993-1001.
  13. Garcia-Pablos, D., Sigalas, M., Montero de Espinosa, F. R., Torres, M., Kafesaki, M. and Garcia, N., 2000, "Theory and Experiments on Elastic Band Gaps," Phys. Rev. Lett., Vol. 84, No. 19, pp. 4349-4352. https://doi.org/10.1103/PhysRevLett.84.4349
  14. Hou, Z. and Fu, X., 2004, "Calculation Method to Study the Transmission Properties of Phononic Crystals," Phys. Rev. B, Vol. 70, 014304. https://doi.org/10.1103/PhysRevB.70.014304
  15. Langlet, P., Hladky-Hennion, A-C. and Decarpigny, J-N., 1995, "Analysis of the Propagation of Plane Acoustic Waves in Passive Periodic Materials Using the Finite Element Method," J. Acoust. Soc. Am., Vol. 98, No. 5, pp. 2792-2800. https://doi.org/10.1121/1.413244
  16. Aberg, M. and Gudmundson, P., 1997, "The Usage of Standard Finite Element Codes for Computation of Dispersion Relations in Materials with Periodic Microstructure," J. Acoust. Soc. Am., Vol. 102, No. 4, pp. 2007-2013. https://doi.org/10.1121/1.419652
  17. IEEE Standards Board, 1987, IEEE Standard on Piezoelectricity, IEEE, New York.
  18. Lerch, R.,1990, "Simulation of Piezoelectric Devices by Two-and Three-Dimensional Finite Elements," IEEE Trans. Ultrason. Ferroelectr. Freq. Control, Vol. 37, pp. 233-247. https://doi.org/10.1109/58.55314
  19. Kim, J. E., Kim, D. S., Ma, P. S. and Kim, Y. Y., 2010, "Multi-Physics Interpolation for the Topology Optimization of Piezoelectric Systems," Comput. Methods Appl. Mech. Engrg., Vol. 199, pp. 3153-3168. https://doi.org/10.1016/j.cma.2010.06.021
  20. Ewins, D. J., 2000, Modal Testing: Theory, Practice and Application, Research Studies Press Ltd., England.
  21. Ha, Y. and Cho, S., 2006, "Design Sensitivity Analysis and Topology Optimization of Eigenvalue Problems for Piezoelectric Resonators," Smart Mater. Struct., Vol. 15, 1513-1524. https://doi.org/10.1088/0964-1726/15/6/002