Abstract
In this paper, an analytical solution for the free vibration of rotating composite conical shells with axial stiffeners (stringers) and circumferential stiffener (rings), is presented using an energy-based approach. Ritz method is applied while stiffeners are treated as discrete elements. The conical shells are stiffened with uniform interval and it is assumed that the stiffeners have the same material and geometric properties. The study includes the effects of the coriolis and centrifugal accelerations, and the initial hoop tension. The results obtained include the relationship between frequency parameter and circumferential wave number as well as rotating speed at various angles. Influences of geometric properties on the frequency parameter are also discussed. In order to validate the present analysis, it is compared with other published works for a non-stiffened conical shell; other comparison is made in the special case where the angle of the stiffened conical shell goes to zero, i.e., stiffened cylindrical shell. Good agreement is observed and a new range of results is presented for rotating stiffened conical shells which can be used as a benchmark to approximate solutions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Leissa, A.W.: Vibration of shells. NASA. SP-288 (1973)
Soedel W.: Vibrations of Shells and Plates, Revised and Expanded, 2nd edn. Marcel Dekker, New York (1996)
Reddy J.N.: Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd edn. CRC press, New York (2004)
Chen Y., Zhao H.B., Shea Z.P.: Vibrations of high speed rotating shells with calculations for cylindrical shells. J. Sound Vib. 160, 137–160 (1993)
Lam K.Y., Loy C.T.: On vibrations of thin rotating laminated composite cylindrical shells. Compos. Eng. 4, 1153–1167 (1994)
Lam K.Y., Loy C.T.: Free vibrations of a rotating multi-layered cylindrical shell. Int. J. Solids Struct. 32, 647–663 (1995)
Lam K.Y., Loy C.T.: Analysis of rotating laminated cylindrical shells by different thin shell theories. J. Sound Vib. 186, 23–25 (1995)
Hua L., Lam K.Y.: Frequency characteristics of a thin rotating cylindrical shell using the generalized differential quadrature method. Int. J. Mech. Sci. 40, 443–459 (1998)
Lam K.Y., Hua L.: Vibration analysis of a rotating truncated circular conical shell. Int. J. Solids Struct. 34(17), 2183–2197 (1997)
Zhao X., Liew K.M., Ng T.Y.: Vibration of rotating cross-ply laminated circular cylindrical shells with stringer and ring stiffeners. Int. J. Solids Struct. 39, 529–545 (2002)
Jafari A.A., Bagheri M.: Free vibration of rotating ring stiffened cylindrical shells with non-uniform stiffener distribution. J. Sound Vib. 296, 353–376 (2006)
Lim C.W., Liew K.M.: Vibratory behaviour of shallow conical shells by a global Ritz formulation. Eng. Struct. 17(1), 63–70 (1995)
Rao S.S.: Vibration of Continuous Systems. Wiley, London (2007)
Lam K.Y., Hua L.: Influence of boundary conditions on the frequency characteristics of a rotating truncated circular conical shell. J. Sound Vib. 223(2), 171–195 (1999)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Talebitooti, M., Ghayour, M., Ziaei-Rad, S. et al. Free vibrations of rotating composite conical shells with stringer and ring stiffeners. Arch Appl Mech 80, 201–215 (2010). https://doi.org/10.1007/s00419-009-0311-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-009-0311-4