Transactions of the Korean Society for Noise and Vibration Engineering (한국소음진동공학회논문집)

The Korean Society for Noise and Vibration Engineering (한국소음진동공학회)
권호 표지
DOI QR코드

DOI QR Code

Development of an Improved NDIF Method for Efficiently Extracting Eigenvalues and Eigenmodes of Arbitrarily Shaped Acoustic Cavities

임의 형상 음향 공동의 효율적인 고유치 및 고유모드 추출을 위한 개선된 NDIF법 개발

  • 강상욱 (한성대학교 기계시스템공학과) ;
  • 윤주일 (한성대학교 기계시스템공학과)
  • Received : 2011.08.08
  • Accepted : 2011.09.19
  • Published : 2011.10.20
Download PDF
⟨ Previous Next ⟩

Abstract

An improved NDIF method is introduced to efficiently extract eigenvalues and eigenmodes of two-dimensional, arbitrarily shaped acoustic cavities. The NDIF method, which was developed by the authors for the eigen-mode analysis of arbitrarily shaped acoustic cavities, membranes, and plates, has the feature that it yields highly accurate eigenvalues compared with other analytical methods or numerical methods(FEM and BEM). However, the NDIF method has the weak point that the system matrix of the NDIF method depends on the frequency parameter and, as a result, a final system equation doesn's take the form of an algebra eigenvalue problem. The system matrix of the improved NDIF method developed in the paper is independent of the frequency parameter and eigenvalues and mode shapes can be efficiently obtained by solving a typical algebraic eigenvalue problem. Finally, the validity and accuracy of the proposed method is verified in two case studies, which indicate that eigenvalues and mode shapes obtained by the proposed method are very accurate compared to the exact method, the NDIF method or FEM(ANSYS).

Keywords

References

  1. Kang, S. W. and Lee, J. M., 1999, Vibration Analysis of Arbitrarily Shaped Membrane Using Non-dimensional Dynamics Influence Function, Journal of Sound and Vibration, Vol. 221, pp. 117-132. https://doi.org/10.1006/jsvi.1998.2009
  2. Bathe, K., 1982, Finite Element Procedures in Engineering Analysis, Prentice-Hall, New Jersey.
  3. Brebbia, C. A., Telles, J. C. F. and Wrobel, L. C., 1984, Boundary Element Techniques, Springer-Verlag, New York.
  4. Kang, S. W. and Lee, J. M., 2000, Application of Free Vibration Analysis of Membranes Using the Non-dimensional Dynamics Influence Function, Journal of Sound and Vibration, Vol. 234, No. 3, pp. 455-470. https://doi.org/10.1006/jsvi.1999.2872
  5. Kang, S. W. and Lee, J. M., 2000, Eigenmode Analysis of Arbitrarily Shaped Two-dimensional Cavities by the Method of Point-matching, Journal of the Acoustical Society of America, Vol. 107, No. 3, pp. 1153-1160. https://doi.org/10.1121/1.428456
  6. Kang, S. W. and Lee, J. M., 2001, Free Vibration Analysis of Arbitrarily Shaped Plates with Clamped Edges Using Wave-type Functions, Journal of Sound and Vibration, Journal of Sound and Vibration, Vol. 242. No, 1, pp. 9-26. https://doi.org/10.1006/jsvi.2000.3347
  7. Kang, S. W., 2002, Free Vibration Analysis of Arbitrarily Shaped Plates with a Mixed Boundary Condition Using Non-dimensional Dynamic Influence Functions, Journal of Sound and Vibration, Vol. 256, No. 3, pp. 533-549. https://doi.org/10.1006/jsvi.2002.5009
  8. Kang, S. W. and Lee J. M., 2002, Free Vibration Analysis of Composite Rectangular Membranes with an Oblique Interface, Journal of Sound and Vibration, Vol. 251, No. 3, pp. 505-517. https://doi.org/10.1006/jsvi.2001.4015
  9. Kang, S. W., Kim, I. S. and Lee, J. M., 2003, Free Vibration Analysis of Arbitrarily Shaped Plates with Free Edges Using Non-dynamic Influence Functions, Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 13, No. 10, pp. 821-827. https://doi.org/10.5050/KSNVN.2003.13.10.821
  10. Kang, S. W., 2004, Free Vibration Analysis of Composite Rectangular Membranes with a Bent Interface, Journal of Sound and Vibration, Vol. 272, No. 1, pp. 39-53. https://doi.org/10.1016/S0022-460X(03)00305-5
  11. Kang, S. W. and Lee J. M., 2004, Free Vibration Analysis of an Unsymmetric Trapezoidal Membrane, Journal of Sound and Vibration, Vol. 272, No. 2, pp. 450-460. https://doi.org/10.1016/S0022-460X(03)00798-3
  12. Kang, S. W., 2007, Free Vibration Analysis of Clamped Plates with Arbitrary Shapes Using Series Functions, Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 13, No. 10, pp. 531-538.
  13. Kang, S. W., 2007, Free Vibration Analysis of Arbitrarily Shaped Polygonal Plates with Free Edges by Considering the Phenomenon of Stress Concentration at Corners, Transactions of the Korean Society for Noise and Vibration Engineering, Vol.17, No. 3, pp. 220-225. https://doi.org/10.5050/KSNVN.2007.17.3.220
  14. Kang, S. W., Kim, I. S. and Lee, J. M., 2008, Free Vibration Analysis of Arbitrarily Shaped Plates with Smoothly Varying Free Edges Using NDIF Method, Journal of Vibration and Acoustics, Transaction of ASME, Vol. 130, No. 4, pp. 041010.1-041010.8.
  15. Kang, S. W. and Atluri, S. N., 2008, Development of Meshless Method for Free Vibration Analysis of Arbitrarily Shaped Free Plates Using Local Polar Coordinates, Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 18, No. 6, pp. 674-680. https://doi.org/10.5050/KSNVN.2008.18.6.674
  16. Kang, S. W. and Kim, S. H., 2008, Vibration Analysis of Simply Supported Rectangular Plates with Unidirectionally, Arbitrarily Varying Thickness, Journal of Sound and Vibration, Vol. 312, pp. 551-562. https://doi.org/10.1016/j.jsv.2007.12.032
  17. Kang, S. W. and Kim, J. G., 2009, A Formulation of NDIF Method to the Algebraic Eigenvalue Problem for Efficiently Extracting Natural Frequencies of Arbitrarily Shaped Plates with the Simply Supported Boundary Condition, Transactions of the Korean Society for Noise and Vibration Engineering, Vol. 19, No. 6, pp. 607-613. https://doi.org/10.5050/KSNVN.2009.19.6.607
  18. Spiegel, M. R., 1983, Advanced Mathematics, McGraw-Hill, Inc, Singapore.
  19. Gohberg, I., Lancaster, P. and Rodman, L., 1982, Matrix Polynomials, Academic Press, New York.
  20. Blevins, R. D., 1979, Formulas for Natural Frequency and Mode Shape, Litton Educational Publishing, New York.

Cited by

  1. New Formulation of MNDIF Method for Accurate Eigenvalue Analysis of Concave Acoustic Cavities vol.23, pp.11, 2013, https://doi.org/10.5050/KSNVE.2013.23.11.1003
  2. Extraction of Highly Accurate Eigenvalues of Arbitrarily Shaped Acoustic Cavities with a Mixed Boundary vol.28, pp.5, 2018, https://doi.org/10.5050/KSNVE.2018.28.5.542
  3. Eigenvalue Analysis of Arbitrarily Shaped, Acoustic Cavities Using Two-domain Method vol.28, pp.4, 2018, https://doi.org/10.5050/KSNVE.2018.28.4.410