Vibration of cylindrical shells with ring support

doi:10.1016/S0020-7403(96)00035-5

International Journal of Mechanical Sciences

Volume 39, Issue 4, April 1997, Pages 455-471

https://doi.org/10.1016/S0020-7403(96)00035-5 Get rights and content

Abstract

In this paper, a study on the vibration of thin cylindrical shells with ring supports is presented. The cylindrical shells have ring supports which are arbitrarily placed along the shell and which imposed a zero lateral deflection. The study is carried out using Sanders' shell theory. The governing equations are obtained using an energy functional with the Ritz method. Results are presented on the frequency characteristics, influence of ring support position and the influence of boundary conditions. The present analysis is validated by comparing results with those available in the literature.

References (16)

A. Ludwig et al.
An analytical quasi-exact method for calculating eigenvibrations of thin circular shells
J. Sound Vibration
(1981)
A. Bhimaraddi
A higher order theory for free vibration analysis of circular cylindrical shells
Int. J. Solids Structures
(1984)
K.P. Soldatos et al.
Three-dimensional solution of the free vibration problem of homogeneous isotropic cylindrical shells and panels
J. Sound Vibration
(1990)
C.W. Bert et al.
Vibration of cylindrical shell of biomodulus composite materials
J. Sound Vibration
(1982)
K.P. Soldatos
A comparison of some shell theories used for the dynamic analysis of cross-ply laminated circular cylindrical panels
J. Sound Vibration
(1984)
K.Y. Lam et al.
Free vibrations of a rotating multi-layered cylindrical shell
Int. J. Solids Structures
(1995)
C.B. Sharma
Frequencies of clamped-free circular cylindrical shell
J. Sound Vibration
(1973)
R.N. Arnold et al.
Flexural vibrations of the walls of thin cylindrical shells having freely supported ends

There are more references available in the full text version of this article.

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Vibration of cylindrical shells with ring support

Abstract

J. Sound Vibration

Int. J. Solids Structures

J. Sound Vibration

J. Sound Vibration

J. Sound Vibration

Int. J. Solids Structures

J. Sound Vibration

Flexural vibrations of the walls of thin cylindrical shells having freely supported ends