DOI QR코드

DOI QR Code

Eigenvalue Analysis of Arbitrarily Shaped, Concave Membranes With a Deep Groove Using a Sub-domain Method

영역 분할법을 이용한 깊은 홈을 가진 임의 형상 오목 멤브레인의 고유치 해석

  • 강상욱 (한성대학교 기계시스템공학과) ;
  • 윤주일 (한성대학교 기계시스템공학과)
  • Published : 2009.10.20

Abstract

A sub-domain method for free vibration analysis of arbitrarily shaped, concave membranes with a deep groove is proposed in the paper. The proposed method divides the concave membrane of interest into two convex regions. The vibration displacement(approximate solution) of each convex region is assumed by linearly superposing plane waves generated at edges of the region. A sub-system matrix for each convex region is extracted by applying a provisional boundary condition to the approximate solution. Finally, a system matrix, which of the determinant gives eigenvalues of the concave membrane, is made by considering the fixed boundary condition(displacement zero condition) at edges and the compatibility condition(the condition of continuity in displacement and slope) at the interface between the two regions. Case studies show that the proposed method is valid and accurate when the eigenvalues by the proposed are compared to those by NDIF method, FEM, or the exact method.

Keywords

References

  1. Bathe, K., 1982, “Finite Element Procedures in Engineering Analysis,” Prentice-Hall, New Jersey
  2. Brebbia, C. A., Telles, J. C. F. and Wrobel, L. C., 1984, “Boundary Element Techniques, Springer-Verlag,” New York
  3. 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
  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. 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 Nondimensional 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., Kim, I. S. and Lee, J. M., 2003, “Free Vibration Analysis of Arbitrarily Shaped Plates with Free Edges Using Nondynamic 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
  9. 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
  10. 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, Transactions of ASME. Vol. 130, No. 4, pp. 041010.1-041010.8
  11. Kang, S. W. and Atluri, S. N., “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
  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. Meirovitch, L., 1967, “Analytical methods in vibrations,” Macmillan Publishing, New York
  14. Blevins, R. D., 1979, “Formulas for Natural Frequency and Mode Shape,” Litton Educational Publishing, New York

Cited by

  1. 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