DOI QR코드

DOI QR Code

Sound transmission of multi-layered micro-perforated plates in a cylindrical impedance tube

원통형 임피던스 튜브 내 다중 미세천공 판의 음향투과

  • 김현실 (한국기계연구원 음향소음팀) ;
  • 마평식 (한국기계연구원 음향소음팀) ;
  • 김봉기 (한국기계연구원 음향소음팀) ;
  • 이성현 (한국기계연구원 음향소음팀) ;
  • 서윤호 (한국기계연구원 음향소음팀)
  • Received : 2020.05.11
  • Accepted : 2020.07.03
  • Published : 2020.07.31

Abstract

In this paper, sound transmission of Micro-Perforated Plates (MPPs) installed in an impedance tube with a circular cross-section is described using an analytic method. Vibration of the plates is expressed in terms of an infinite series of modal functions, where modal function in the radial direction is given by the Bessel function. Under the plane wave assumption, a low frequency approximation is derived, and a formula for the sound transmission coefficient of multi-layered MPPs is presented using the transfer matrix method. The Sound Transmission Losses (STLs) of single and double MPPs are computed using the proposed method and compared with those done by the Finite Element Method (FEM), which shows an excellent agreement. As the perforation increases, the STL is degraded, since the STL becomes dominated by the perforation ratio rather than by vibration of the plate. The STL shows dips at natural frequencies as well as at the mass-spring-mass resonance frequency. The proposed model for the STL prediction in this study can be applied to an arbitrary number of MPPs, where each MPP may or may not have a perforation.

본 논문은 원통형 임피던스 튜브내에 설치된 다중 미세천공판(Micro-Perforated Plate, MPP)의 음향투과를 해석적으로 구하는 방법을 다루었다. 판의 진동을 무한 급수의 합으로 전개하였는데 반경방향으로는 Bessel 함수를 포함한다. 평면파 가정하에서 저주파수 대역의 근사식을 유도하였으며 전달함수법을 이용하여 다중 MPP에 대한 음향투과율 공식을 제시하였다. 단일과 이중 MPP의 음향투과손실(Sound Transmission Loss, STL)을 본 논문에서 제안한 공식을 이용하여 계산하였으며 유한요소법(Finite Element Method, FEM)을 사용한 결과와 잘 일치 하였다. 천공율이 증가할수록 STL은 감소하는데 이는 판의 진동보다는 천공율이 더 큰 영향을 주기 때문이다. STL은 판의 공진주파수에서 골(dip)을 보이며 이중 MPP의 STL은 질량-스프링-질량 진동에 해당하는 공진주파수에서 골을 보인다. 본 연구에서 제안한 STL 예측 모델은 임의의 개수의 다중 MPP에 적용이 가능하며 각각의 판은 미세천공을 포함하거나 포함하지 않는 두 가지 경우가 모두 가능하다.

Keywords

References

  1. M. Toyoda and D. Takahashi, "Sound transmission through a microperforated-panel structure with subdivided air cavities," J. Acoust. Soc. Am. 124, 3594-3603 (2008). https://doi.org/10.1121/1.3001711
  2. D. Y. Maa, "Microperforated-panel wideband absorbers," Noise Cont. Eng. J. 29, 77-84 (1987). https://doi.org/10.3397/1.2827694
  3. S. Min, K. Nagamura, N. Nakagawa, and M. Okamura, "Design of compact micro-perforated membrane absorbers for polycarbonate pane in automobile," Appl. Acoust. 74, 622-627 (2013). https://doi.org/10.1016/j.apacoust.2012.05.009
  4. M. Yairi, K. Sakagami, K. Takebayashi, and M. Morimoto, "Excess sound absorption at normal incidence by two microperforated panel absorbers with different impedance," Acoust. Sci. Technol. 32, 194-200 (2011). https://doi.org/10.1250/ast.32.194
  5. H.-S. Kim, P.-S. Ma, B.-K. Kim, S.-R. Kim, and Y.-H. Seo, "Low-frequency sound absorption of elastic microperforated plates in a parallel arrangement," J. Sound Vib. 460, 114884 (2019). https://doi.org/10.1016/j.jsv.2019.114884
  6. Y. Y. Lee and E. W. M. Lee, "Widening the sound absorption bandwidths of flexible micro-perforated curved absorbers using structural and acoustic resonances," Int. J. Mech. Sci. 49, 925-934 (2007). https://doi.org/10.1016/j.ijmecsci.2007.01.008
  7. Y. Y. Lee, E. W. M. Lee, and C. F. Ng, "Sound absorption of a finite flexible micro-perforated panel backed by an air cavity," J. Sound Vib. 287, 227-243 (2005). https://doi.org/10.1016/j.jsv.2004.11.024
  8. R. L. Mu, M. Toyoda, and D. Takahashi, "Improvement of sound insulation performance of multilayer windows by using microperforated panel," Acoust. Sci. Technol. 32, 79-81 (2011). https://doi.org/10.1250/ast.32.79
  9. T. Dupont, G. Pavic, and B. Laulagnet, "Acoustic properties of lightweight micro-perforated plate systems," Acta Acust. united Ac. 89, 201-212 (2003).
  10. H.-S. Kim, S.-R. Kim, B.-K. Kim, P.-S. Ma, and Y.-H. Seo, "Sound transmission loss of multi-layered infinite micro-perforated plates," J. Acoust. Soc. Am. 147, 508-515 (2020). https://doi.org/10.1121/10.0000600
  11. T. Bravo, C. Maury, and C. Pinhede, "Sound absorption and transmission through flexible micro-perforated panels backed by an air layer and a thin plate," J. Acoust. Soc. Am. 131, 3853-3863 (2012). https://doi.org/10.1121/1.3701987
  12. T. Bravo, C. Maury, and C. Pinhede, "Enhancing sound absorption and transmission through flexible multi-layer micro-perforated structures," J. Acoust. Soc. Am. 134, 3663-3673 (2013). https://doi.org/10.1121/1.4821215
  13. H.-S. Kim, P.-S. Ma, B.-K. Kim, S.-H. Lee, and Y.-H. Seo, "Sound transmission loss of multi-layered elastic micro-perforated plates in an impedance tube," Appl. Acoust. 166, No. 107348 (2020).
  14. M. L. Munjal, Acoustics of Ducts and Muffler, 2nd Ed. (John Wiley and Sons Ltd, United Kingdom, 2014), Section 1.2.
  15. D. Takahashi and M. Tanaka, "Flexural vibration of perforated plates and porous elastic materials under acoustic loading," J. Acoust. Soc. Am. 112, 1456-1464 (2002). https://doi.org/10.1121/1.1497624
  16. A. W. Leissa, Vibration of Plates (Acoustical Society of America, New York, 1993), Chap. 2.
  17. H.-S. Kim, B.-K. Kim, S.-R. Kim, S.-H. Lee, and P.-S. Ma, "Sound absorption of micro-perforated elastic plates in a cylindrical impedance tube" (In Korean), J. Acoust. Soc. Kr. 37, 181-187 (2018).
  18. COMSOL, COMSOL Multiphysics reference manual, version 4.4, 2013.
  19. H.-S. Kim, S.-R. Kim, S.-H. Lee, Y.-H. Seo, and P.-S. Ma, "Sound transmission loss of double plates with an air cavity between them in a rigid duct," J. Acoust. Soc. Am. 139, 2324-2333 (2016). https://doi.org/10.1121/1.4946987