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급수 함수를 이용한 임의 형상 고정단 평판의 자유 진동 해석

Free Vibration Analysis of Clamped Plates with Arbitrary Shapes Using Series Functions

  • 강상욱 (한성대학교 기계시스템공학과)
  • 발행 : 2007.06.20

초록

A new method for free nitration analysis using series functions is proposed to obtain the eigenvalues of arbitrarily shaped, polygonal plates with clamped edges. Since a general solution used in the method satisfies the equation of motion for the transverse vibration of a plate, the method offers very accurate eigenvalues, compared to FEM or BEM results. In addition, the method can minimize the amount of numerical calculation because it has the advantage of not needing to divide the plate of interest. 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 (NASTRAN) or another analytical method.

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참고문헌

  1. Blevins, R. D., 1979, 'Formulas for Natural Frequency and Mode Shape', New York: Litton Educational Publishing
  2. Conway, H. D. and Farnham, K. A., 1965, 'The Free Flexural Vibration of Triangular, Rhombic and Parallelogram Plates and Some Analogies', International Journal of Mechanical Sciences, Vol. 7, pp. 811-816 https://doi.org/10.1016/0020-7403(65)90034-2
  3. Dickinson, S. M., 1978, 'The Buckling and Frequency of Flexural Vibration of Rectangular, Isotropic and Orthotropic Plates Using Rayleigh's Method', Journal of Sound and Vibration Vol. 61, pp. 1-8 https://doi.org/10.1016/0022-460X(78)90036-6
  4. Mclachlan, N. W., 1947, 'Vibrational Problems In Elliptical Coordinates', Quarterly Applied Mathematics, Vol. 5, pp. 289-297 https://doi.org/10.1090/qam/23185
  5. Conway, H. D., 1961, 'The Bending, Buckling, and Flexural Vibration of Simply Supported Polygonal Plates by Point-matching', American Society of Mechanical Engineers Journal of Applied Mechanics, Vol. 28, pp. 288-291 https://doi.org/10.1115/1.3641670
  6. Singh, B. and Chakraverty, S. 1992, 'Transverse Vibration of Simply Supported Elliptical and Circular Plates Using Boundary Characteristic Orthogonal Polynomials in Two Variables', Journal of Sound and Vibration, Vol. 152, No.1, pp. 149-155 https://doi.org/10.1016/0022-460X(92)90071-5
  7. Bathe, K., 1982, Finite Element Procedures in Engineering Analysis. New Jersey: Prentice-Hall
  8. Mavriplis, D. J., 1990, 'Accurate Multigrid Solution of the Euler Equations on Unstructured and Adaptive Meshes', AIAA Journal, Vol. 28, No.2, pp. 213-221 https://doi.org/10.2514/3.10377
  9. Brebbia, C. A., Telles, J. C. F. and Wrobel, L. C., 1984, Boundary Element Techniques, New York: Springer-Verlag
  10. 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
  11. 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
  12. 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
  13. 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
  14. Kang, S. W., et. al., 2003, 'Free Vibration Analysis of Arbitrarily Shaped Plates With Free Edges Using Non-dynamic Influence Functions', Transactions of the Korea Society for Noise and Vibration Engineering, Vol. 13, No. 10, pp. 821-827 https://doi.org/10.5050/KSNVN.2003.13.10.821
  15. Kang, S. W., 2007, 'Free Vibration Analysis of Arbitrarily Shaped Polygonal Plates with Free Edges by Considering the Phenomenon of Stress Concentration at Comers', Transactions of the Korea Society for Noise and Vibration Engineering, Vol. 17, No. 3, pp. 220-225 https://doi.org/10.5050/KSNVN.2007.17.3.220
  16. Kim, Y. Y. and Kang, J. H., 1996, 'Free Vibration Analysis of Membranes Using Wave-Type Base Functions', J. Acoust. Soc. Amer., Vol. 99, No. 5, pp, 2938-2946 https://doi.org/10.1121/1.414822
  17. Kim, Y. Y. and Kim, D. K., 1999, 'Applications of Waveguide-Type Base Functions for the Eigenproblems of Two-dimensional Cavities', J. Acoust. Soc. Amer. Vol. 106, pp. 1704-1711 https://doi.org/10.1121/1.427919
  18. Meirovitch, L., 1967, Analytic Methods in Vibrations, New York: Nacmillan Publishing, pp. 179-182