International Journal of Naval Architecture and Ocean Engineering

  • 제4권3호
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  • Pages.267-280
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  • 2012
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  • 2092-6782(pISSN)
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  • 2092-6790(eISSN)
대한조선학회 (The Society of Naval Architects of Korea)
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Free vibration analysis of rectangular plate with arbitrary edge constraints using characteristic orthogonal polynomials in assumed mode method

  • Kim, Kook-Hyun (Department of Naval Architecture, Tongmyong University) ;
  • Kim, Byung-Hee (Marine Research Institute, Samsung Heavy Industries Co. Ltd.) ;
  • Choi, Tae-Muk (Createch Co. Ltd.) ;
  • Cho, Dae-Seung (Department of Naval Architecture and Ocean Engineering, Pusan National University)
  • 발행 : 2012.09.30
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초록

An approximate method based on an assumed mode method has been presented for the free vibration analysis of a rectangular plate with arbitrary edge constraints. In the presented method, natural frequencies and their mode shapes of the plate are calculated by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion. Characteristic orthogonal polynomials having the property of Timoshenko beam functions which satisfies edge constraints corresponding to those of the objective plate are used. In order to examine the accuracy of the proposed method, numerical examples of the rectangular plates with various thicknesses and edge constraints have been presented. The results have shown good agreement with those of other methods such as an analytic solution, an approximate solution, and a finite element analysis.

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참고문헌

  1. Cho, D.S., Kim, S.S. and Jung, S.M., 1998. Structural intensity analysis of stiffened plate using assumed mode method. Journal of the Society of Naval Architects of Korea, 35(4), pp.76-86.
  2. Chung, J.H., Chung, T.Y. and Kim, K.C., 1992. Vibration analysis of mindlin plates using polynomials having the property of Timoshenko beam functions. Journal of the Society of Naval Architects of Korea, 29(1), pp.158-172.
  3. Chung, J.H., Chung, T.Y. and Kim, K.C, 1993. Vibration analysis of orthotropic Mindlin plates with edges elastically restrained against rotation. Journal of Sound and Vibration, 163(1), pp.151-163. https://doi.org/10.1006/jsvi.1993.1154
  4. Dawe, D.J. and Roufaeil, O.L., 1980. Rayleigh-Ritz vibration analysis of Mindlin plates. Journal of Sound and Vibration, 69(3), pp.345-359. https://doi.org/10.1016/0022-460X(80)90477-0
  5. Gorman, D.J., 1990. A general solution for the free vibration of rectangular plates resting on uniform elastic edge supports. Journal of Sound and Vibration, 139(2), pp.325-335. https://doi.org/10.1016/0022-460X(90)90893-5
  6. Lee, J.M., 2003. Vibration analysis of thick orthotropic plates using mindlin plate characteristic functions. Journal of Ocean Engineering and Technology, 17(3), pp.21-26.
  7. Leissa, A.W., 1969. Vibration of plates, NASA Report No SP-160. Scientific and Technical Information Division, National Aeronautics and Space Administration.
  8. Li, W.L., 2004. Vibration analysis of rectangular plates with general elastic boundary supports. Journal of Sound and Vibration, 273(3), pp.619-635. https://doi.org/10.1016/S0022-460X(03)00562-5
  9. Liu, F.-L. and Liew, K.M., 1999. Analysis of vibrating thick rectangular plates with mixed boundary constraints using differential quadrature element method. Journal of Sound and Vibration, 225(5), pp.915-934. https://doi.org/10.1006/jsvi.1999.2262
  10. Mindlin, R.D., Schacknow, A. and Deresiewicz, H., 1956. Flexural vibrations of rectangular plates. Journal of Applied Mechanics, 23, pp.430-436.
  11. MSC, 2010. MD Nastran 2010 Dynamic analysis user's guide. MSC Software.
  12. Zhang, X. and Li, W.L., 2010. A unified approach for predicting sound radiation from baffled rectangular plates with arbitrary boundary conditions. Journal of Sound and Vibration, 329(25), pp.5307-5320. https://doi.org/10.1016/j.jsv.2010.07.014
  13. Zhou, D., 2001. Vibrations of Mindlin rectangular plates with elastically restrained edges using static Timoshenko beam functions with the Rayleigh-Ritz method. International Journal of Solids and Structures, 38(32-33), pp.5565-5580. https://doi.org/10.1016/S0020-7683(00)00384-X