DOI QR코드

DOI QR Code

Free Vibration Analysis of Arbitrarily Shaped Polygonal Plates with Free Edges by Considering the Phenomenon of Stress Concentration at Corners

꼭지점에서의 응력 집중 현상을 고려한 자유단 경계조건을 가진 임의 다각형 형상 평판의 자유 진동 해석

  • 강상욱 (한성대학교 기계시스템공학과)
  • Published : 2007.03.20

Abstract

Free vibration analysis using the method of NDIF (non-dimensional dynamic influence function), which was developed by the author, is extended to arbitrarily shaped polygonal plates with free edges. Local Cartesian coordinate systems are employed to apply the free boundary condition to nodes distributed along the edges of the plate of interest. Furthermore, a new way for applying the free boundary condition to nodes located at corners of the plate is for the first time introduced by considering the phenomenon of stress concentration at the corners. Two case studies show that the proposed method is valid and accurate when the eigenvalues by the proposed method are compared to those by FEM(ANSYS).

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. 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
  3. 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
  4. Kang, S. W., 2002, 'Free Vibration Analysis of Arbitrarily Shaped Plates with a Mixed Boundary Condition Using Non-dimensional Dynamics Influence Function' , Journal of Sound and Vibration, Vol. 256, No.3, pp,533-549 https://doi.org/10.1006/jsvi.2002.5009
  5. Kang, S. W., et. al., 2003, 'Free Vibration Analysis of Arbitrarily Shaped Plates with Free Edges Using Non-dimensional 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
  6. Brebbia, C. A., 1978, The Boundary Element Method for Engineers, New York: John Wiley & Sons
  7. Meirovitch, L., 1967, Analytic Methods In Vibrations, New York: Nacmillan Publishing, pp. 179-182
  8. Timoshenko, S., 1959, Theory of Plates and Shells, New York: McGRAW-HILL, pp.83-85
  9. Hughes, T. J. R., 1987, The Finite Element Method, Englewood Cliffs: Prentice-Hall

Cited by

  1. New Formulation of MNDIF Method for Extracting Accurate Natural Frequencies of Plates vol.23, pp.8, 2013, https://doi.org/10.5050/KSNVE.2013.23.8.725
  2. Efficient Meshless Method for Accurate Eigenvalue Analysis of Clamped Plates vol.25, pp.10, 2015, https://doi.org/10.5050/KSNVE.2015.25.10.653
  3. Extraction of Accurate Eigenvalues of Plates Using a Meshless Method vol.25, pp.11, 2015, https://doi.org/10.5050/KSNVE.2015.25.11.779
  4. Meshless Method Based on Wave-type Function for Accurate Eigenvalue Analysis of Arbitrarily Shaped, Clamped Plates vol.26, pp.5, 2016, https://doi.org/10.5050/KSNVE.2016.26.5.602