Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Natural frequencies and mode shapes of thin-walled members with shell type cross section

  • Ohga, M. (Department of Civil and Environmental Engineering, Ehime University) ;
  • Shigematsu, T. (Tokuyama Technical College) ;
  • Hara, T. (Tokuyama Technical College)
  • Published : 2002.06.25
⟨ Previous Next ⟩

Abstract

An analytical procedure based on the transfer matrix method to estimate not only the natural frequencies but also vibration mode shapes of the thin-walled members composed of interconnected cylindrical shell panels is presented. The transfer matrix is derived from the differential equations for the cylindrical shell panels. The point matrix relating the state vectors between consecutive shell panels are used to allow the transfer procedures over the cross section of the members. As a result, the interactions between the shell panels of the cross sections of the members can be considered. Although the transfer matrix method is naturally a solution procedure for the one-dimensional problems, this method is well applied to thin-walled members by introducing the trigonometric series into the governing equations of the problem. The natural frequencies and vibration mode shapes of the thin-walled members composed of number of interconnected cylindrical shell panels are observed in this analysis. In addition, the effects of the number of shell panels on the natural frequencies and vibration mode shapes are also examined.

Keywords

References

  1. Bardell, N.S. and Mead, D.J. (1989), "Free vibration of an orthgonally stiffened cylindrical shell, Part 1: Descrete line simple supports, J. Sound Vib. 134(4), 29-54. https://doi.org/10.1016/0022-460X(89)90735-9
  2. Leissa, A.W. (1969), Vibration of Plates, Washington, D.C., NASA SSSSP-160.
  3. Maddox, N.R., Plumblee, H.E. and King, W.W. (1970), "Frequency analysis of a cylindrically curved panel with clamped and elastic boundaries", J Sound Vib. 12(2), 225-249. https://doi.org/10.1016/0022-460X(70)90091-X
  4. Mizusawa, T. (1988), "Application of Spline Strip Method to Analyze Vibration of Open Cylindrical Shells", Int. J. Num. Meth. Eng., 26, 663-676. https://doi.org/10.1002/nme.1620260310
  5. Ohga, M., Hara, T. and Kawaguchi, K. (1995a), "Buckling mode shapes of thin-walled members", Comput Struct. 54(4), 767-773. https://doi.org/10.1016/0045-7949(94)00371-9
  6. Ohga, M., Shigematsu, T. and Kawaguchi, K. (1995b), "Buckling analysis of thin-walled members with variable thickness", J. Struct. Engrg., ASCE 121(6), 919-924. https://doi.org/10.1061/(ASCE)0733-9445(1995)121:6(919)
  7. Ohga, M., Takao, H. and Shigematsu, T. (1995c), "Natural frequencies and modes of open cylindrical shells with a circumferential thickness taper", J. Sound Vib. 183(1), 143-156. https://doi.org/10.1006/jsvi.1995.0244
  8. Petyt, M. (1971), "Vibration of curved plates". J. Sound Vib. 15(3), 381-395. https://doi.org/10.1016/0022-460X(71)90432-9
  9. Petyt, M. and Deb Math, J.M. (1971), "Vibration analysis of singly curved rectangular plates", J. Sound Vib. 13(4), 485-497.
  10. Sewall, J.L. (1967), "Vibration analysis of cylindrically curved panels with simply supported or clamped edges and comparison with some experiments", NASA TN D-3791.
  11. Sheinman, I. and Reichman Y. (1992), "A study of buckling and vibration of laminated shallow curved panels", Int. J. Solids Struct. 29(11), 1329-1338. https://doi.org/10.1016/0020-7683(92)90081-4
  12. Tesar, A. and Fillo, L. (1988), Transfer Matrix Method, Dordrecht, Kluwer Academic.
  13. To, C.W.S. and Wang, B. (1991), "An axisymmetric thin shell finite element for vibration analysis", Comput. Struct. 40(3), 555-568. https://doi.org/10.1016/0045-7949(91)90226-C
  14. Tsui, E.Y.W. (1968), "Natural vibrations of cylindrical panels", american society of civil engineers, J. Eng. Mech. Div., 94(6), 1425-1444.
  15. Uhrig, R. (1973), Elastostatik und Elastokinetik in Matrizenschreibweise, Berlin, Springer-Verlag.
  16. Webster, J.J. (1971), "Free vibrations of rectangular curved panels", Int. J. Mech. Sci., 10, 571-582.

Cited by

  1. Vibration analysis of thin-walled composite beams with I-shaped cross-sections vol.93, pp.2, 2011, https://doi.org/10.1016/j.compstruct.2010.08.001