DOI QR코드

DOI QR Code

Dynamic behaviour of multi-stiffened plates

  • 투고 : 2007.07.05
  • 심사 : 2009.01.18
  • 발행 : 2009.02.20

초록

The paper investigates the dynamic behaviour of stiffened panels. The coupled differential equations for eccentric stiffening configuration are first derived. Then a semi-analytical procedure for dynamic analysis of stiffened panels is presented. Unlike finite element or finite strip methods, where the plate is discretized into a set of elements or strips, the plate in this procedure is treated as a single element. The potential energy of the structure is first expressed in terms generalized functions that describe the longitudinal and transverse displacement profiles. The resulting non-linear strain energy functions are then transformed into unconstrained optimization problem in which mathematical programming techniques are employed to determine the magnitude of the lowest natural frequency and the associated mode shape for pre-selected plate/stiffener geometric parameters. The described procedure is verified with other numerical methods for several stiffened panels. Results are then presented showing the variation of the natural frequency with plate/stiffener geometric parameters for various stiffening configurations.

키워드

참고문헌

  1. Asku, G. and Ali, R. (1976), "Free vibration analysis of stiffened plates using finite difference method", J. Sound Vib., 48, 15-25 https://doi.org/10.1016/0022-460X(76)90367-9
  2. Asku, G. (1982), "Free vibration analysis of stiffened plates by including the effect of in-plane inertia", J. Appl. Mech., 49, 206-212 https://doi.org/10.1115/1.3161972
  3. Barrette, M., Berry, A. and Beslin, O. (2000), "Vibration of stiffened plates using hierarchical trigonometric functions", J. Sound Vib., 235, 727-747 https://doi.org/10.1006/jsvi.2000.2978
  4. Chan, H.C., Cai, C.W. and Cheung, Y.K. (1991), "A static solution of stiffened plates", Thin Wall. Struct., 11, 291-303 https://doi.org/10.1016/0263-8231(91)90017-D
  5. Fletcher, L. (1959), "The frequency of vibrations of rectangular plates", J. Appl. Mech., Trans., ASME, 81, 290-292
  6. Ghosh, A. and Biswal, K. (1996), "Free-vibration analysis of stiffened laminated plates using higher-order shear deformation theor"”, Finite Elem. Anal. Des., 22, 143-161 https://doi.org/10.1016/0168-874X(95)00051-T
  7. Harik, I.E. and Guo, M. (1993), "Finite element analysis of eccentrically stiffened plates in free vibration", Comput. Struct., 49, 1007-1015 https://doi.org/10.1016/0045-7949(93)90012-3
  8. Harik, I. and Salamoun, G. (1988), "The analytical strip method of solution for stiffened rectangular plates", Comput. Struct., 29, 283-291 https://doi.org/10.1016/0045-7949(88)90261-1
  9. Harris, C.M. and Crede, C.E. (1961), "Shock and vibration handbook", McGraw-Hill, New-York
  10. Kirk, C.L. (1970), "Natural frequency of stiffened rectangular plates", J. Sound Vib., 13, 375-388 https://doi.org/10.1016/S0022-460X(70)80043-8
  11. Koko, T.S. (1990), "Super finite elements for non-linear static and dynamic analysis of stiffened plate structures", Ph.D. Dissertation, University of British Columbia
  12. Koko, T.S. and Olson, M.D. (1991), "Non-linear analysis of stiffened plates using super element", Int. J. Numer. Meth. Eng., 31, 319-343 https://doi.org/10.1002/nme.1620310208
  13. Kumar, Y. and Mukhopadhyay, M. (2002), "Transient response analysis of laminated stiffened plates", Compos. Struct., 58(1), 97-107 https://doi.org/10.1016/S0263-8223(02)00036-3
  14. Long, B.R. (1971), "A stiffness-type analysis of the vibration of a class of stiffened plates", J. Sound Vib., 16, 323-335 https://doi.org/10.1016/0022-460X(71)90590-6
  15. Mead, D.J., Zhu, D.C. and Bardell, N.S. (1988), "Free vibration of orthogonally stiffened flat plate", J. Sound Vib., 127, 19-48 https://doi.org/10.1016/0022-460X(88)90348-3
  16. Mukherjee, N. and Chattopadhyay, T. (1994), "Improved free vibration analysis of stiffened plates by dynamic element method", Comput. Struct., 52, 259-264 https://doi.org/10.1016/0045-7949(94)90278-X
  17. Mukherjee, A. and Mukhopadhyay, M. (1989), "Finite element free vibration of eccentrically stiffened plates", Comput. Struct., 33, 295-305 https://doi.org/10.1016/0045-7949(89)90153-3
  18. Mukhopadhyay, M. (1989), "Vibration and stability of stiffened plates by semi-analytic finite difference method, Part I: Consideration of bending displacement only", J. Sound Vib., 130, 27-39 https://doi.org/10.1016/0022-460X(89)90517-8
  19. Mukhopadhyay, M. (1989), "Vibration and stability of stiffened plates by semi-analytic finite difference method, Part II: Consideration of bending and axial displacements", J. Sound Vib., 130, 41-53 https://doi.org/10.1016/0022-460X(89)90518-X
  20. Park, B. and Cho, S. (2006), "Simple design formulae for predicting the residual damage of unstiffened and stiffened plates under explosion loadings", Int. J. of Impact Eng., 32, 1721-1736 https://doi.org/10.1016/j.ijimpeng.2005.01.005
  21. Patel, S., Datta, P. and Sheikh, A. (2006), "Buckling and dynamic instability analysis of stiffened shell panels", Thin Wall. Struct., 44, 321-333 https://doi.org/10.1016/j.tws.2006.03.004
  22. Peng, L. and Kitipornchai, S. (2006), "Buckling and free vibration analyses of stiffened plates using the FSDT mesh-free method", J. Sound Vib., 289, 421-449 https://doi.org/10.1016/j.jsv.2005.02.023
  23. Peng-Cheng, S., Dade, H. and Zongmu, W. (1987), "Static, vibration and stability analysis of stiffened plates using B spline functions", Comput. Struct., 27, 73-78 https://doi.org/10.1016/0045-7949(87)90182-9
  24. Qing, G., Qiu, J. and Liu, Y. (2006), "Free vibration analysis of stiffened laminated plates", Int. J. Solids Struct., 43, 1357-1371 https://doi.org/10.1016/j.ijsolstr.2005.03.012
  25. Rikards, R., Chate, A. and Ozolinsh, O. (2001), "Analysis for buckling and vibrations of composite stiffened shells and plates", Compos. Struct., 51, 361-370 https://doi.org/10.1016/S0263-8223(00)00151-3
  26. Schittkowski, K. (1985), "A unified outline of non-linear programming algorithms", J. Mechanisms, Transmissions and Automation in Design, 107, 449-453 https://doi.org/10.1115/1.3260744
  27. Shen, P.C., Dade, H. and Wang, Z. (1987), "Static, vibration and stability analysis of stiffened plates using Bspline functions", Comput. Struct., 27, 73-78 https://doi.org/10.1016/0045-7949(87)90182-9
  28. Wah, T. (1964), "Vibration of stiffened plates", Aeronaut. Quart., 15, 285-298 https://doi.org/10.1017/S0001925900010891
  29. Wittrick, W.H. (1968), "General sinusoidal stiffness matrices for buckling and vibration analysis of thin flatwalled structures", Int. J. Mech. Sci., 10, 49-966 https://doi.org/10.1016/0020-7403(68)90049-0
  30. Wu, C.L. and Cheung, Y.K. (1974), "Frequency analysis of rectangular plates continuous in one or two directions", Earthq. Eng. Struct. Dyn., 3, 3-14
  31. Zhang, W., Wang, A., Vlahopoulos, N. and Wu, K. (2005), "Vibration analysis of stiffened plates under heavy fluid loading by an energy finite element analysis formulation", Finite Elem. Anal. Des., 41, 1056-1078 https://doi.org/10.1016/j.finel.2004.10.012

피인용 문헌

  1. Design space representation of channel members for industrial applications vol.14, pp.3, 2014, https://doi.org/10.1007/s13296-014-3009-6