DOI QR코드

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Numerical procedure for the vibration analysis of arbitrarily constrained stiffened panels with openings

  • Cho, Dae Seung (Department of Naval Architecture and Ocean Engineering, Pusan National University) ;
  • Vladimir, Nikola (University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture) ;
  • Choi, Tae Muk (Createch Co. Ltd.)
  • 발행 : 2014.12.31

초록

A simple and efficient vibration analysis procedure for stiffened panels with openings and arbitrary boundary conditions based on the assumed mode method is presented. Natural frequencies and modes are determined by solving an eigenvalue problem of a multi-degree-of-freedom system matrix equation derived by using Lagrange's equations of motion, where Mindlin theory is applied for plate and Timoshenko beam theory for stiffeners. The effect of stiffeners on vibration response is taken into account by adding their strain and kinetic energies to the corresponding plate energies whereas the strain and kinetic energies of openings are subtracted from the plate energies. Different stiffened panels with various opening shapes and dispositions for several combinations of boundary conditions are analyzed and the results show good agreement with those obtained by the finite element analysis. Hence, the proposed procedure is especially appropriate for use in the preliminary design stage of stiffened panels with openings.

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참고문헌

  1. Aksu, G. and Ali, R., 1976. Determination of dynamic characteristics of rectangular plates with cut-outs using a finite difference formulation. Journal of Sound and Vibration, 44(8), pp.147-158. https://doi.org/10.1016/0022-460X(76)90713-6
  2. Cho, D.S., Vladimir, N. and Choi, T.M., 2013. Approximate natural vibration analysis of rectangular plates with openings using assumed mode method. International Journal of Naval Architecture and Ocean Engineering, 5(3), pp.478-491. https://doi.org/10.3744/JNAOE.2013.5.3.478
  3. Cho, D.S., Vladimir, N. and Choi, T.M., 2014. Natural vibration analysis of stiffened panels with arbitrary edge constraints using the assumed mode method. Proceedings of the IMechE, Part M: Journal of Engineering for the Maritime Environment. DOI:10.1177/1475090214521179 (published online).
  4. 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
  5. Grossi, R.O., del V. Arenas B. and Laura, P.A.A., 1997. Free vibration of rectangular plates with circular openings. Ocean Engineering, 24(1), pp.19-24. https://doi.org/10.1016/0029-8018(96)83604-3
  6. Kim, K., Kim, B.H., Choi, T.M. and Cho, D.S., 2012. Free vibration analysis of rectangular plate with arbitrary edge constraints using characteristic orthogonal polynomials in assumed mode method. International Journal of Naval Architecture and Ocean Engineering, 4(3), pp.267-280. https://doi.org/10.3744/JNAOE.2012.4.3.267
  7. Kwak, M.K. and Han, S., 2007. Free vibration analysis of rectangular plate with a hole by means of independent coordinate coupling method. Journal of Sound and Vibration. 306(1-2), pp.12-30. https://doi.org/10.1016/j.jsv.2007.05.041
  8. Mindlin, R.D., Schacknow, A. and Deresiewicz, H., 1956. Flexural vibrations of rectangular plates. Journal of Applied Mechanics. 23, pp.430-436.
  9. Monahan, L.J., Nemergut, P.J. and Maddux, G.E., 1970. Natural frequencies and mode shapes of plates with interior cutouts. The Shock and Vibration Bulletin. 41, pp.37-49.
  10. MSC, 2010. MD Nastran 2010 Dynamic analysis user's guide. Newport Beach, California, USA: MSC Software.
  11. Paramasivam, P., 1973. Free vibration of square plates with square openings. Journal of Sound and Vibration. 30(2), pp. 173-178. https://doi.org/10.1016/S0022-460X(73)80111-7
  12. Samanta, A. and Mukhopadhyay, M., 2004. Free vibration analysis of stiffened shells by the finite element technique. European Journal of Mechanics, A Solids, 23(1), pp.159-179. https://doi.org/10.1016/j.euromechsol.2003.11.001
  13. Sapountzakis, E.J. and Mokos, V.G., 2008. An improved model for the dynamic analysis of plates stiffened by parallel beams. Engineering Structures, 30, pp.1720-1733. https://doi.org/10.1016/j.engstruct.2007.11.016
  14. Sivasubramonian, B., Kulkarni, A.M., Rao, G.V. and Krishnan, A., 1997. Free vibration of curved panels with cutouts. Journal of Sound and Vibration, 200(2), pp.227-234. https://doi.org/10.1006/jsvi.1996.0637
  15. Sivasubramonian, B., Rao, G.V. and Krishnan, A., 1999. Free vibration of longitudinally stiffened curved panels with cutout. Journal of Sound and Vibration, 226(1), pp. 41-55. https://doi.org/10.1006/jsvi.1999.2281
  16. Srivastava, A.K.L., 2012. Vibration of stiffened plates with cutout subjected to partial edge loading. Journal of the Institution of Engineers (India) Series A, 93(2), pp.129-135. https://doi.org/10.1007/s40030-012-0018-3
  17. Szilard, R., 2004. Theories and applications of plate analysis. Hoboken, New Jersey, USA: John Wiley & Sons.