T. Irie, G. Yamada and Y. Kaneko, “Free Vibration of a Conical Shell with Variable Thickness,” Journal of Sound and Vibration, Vol. 82, No. 1, 1982, pp. 83-94. doi:10.1016/0022-460X(82)90544-2

has been cited by the following article:

• TITLE: Vibration and Buckling Approximation of an Axially Loaded Cylindrical Shell with a Three Lobed Cross Section Having Varying Thickness

  AUTHORS: Mousa Khalifa Ahmed

  KEYWORDS: Free Vibration, Buckling, Vibration of Continuous System, Noncircular Cylindrical Shell, Transfer Matrix Approach, Variable Thickness, Axial Loads

  JOURNAL NAME: Applied Mathematics, Vol.2 No.3, March 24, 2011

  ABSTRACT: On the basis of the thin-shell theory and on the use of the transfer matrix approach, this paper presents the vibrational response and buckling analysis of three-lobed cross-section cylindrical shells, with circumferentially varying thickness, subjected to uniform axial membrane loads. A Fourier approach is used to separate the variables, and the governing equations of the shell are formulated in terms of eight first-order differential equations in the circumferential coordinate, and by using the transfer matrix of the shell, these equations are written in a matrix differential equation. The transfer matrix is derived from the non-linear differential equations of the cylindrical shells with variable thickness by introducing the trigonometric series in the longitudinal direction and applying a numerical integration in the circumferential direction. The natural frequencies and critical loads beside the mode shapes are calculated numerically in terms of the transfer matrix elements for the symmetrical and antisymmetrical vibration modes. The influences of the thickness variation of cross- section and radius v