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
Highlights
In recent years, structural engineers have been gradually concerned with the analysis of vibration and stability problems of circular cylindrical shells which have noncircular profiles because of the greatest important in many engineering applications such as in the design of machines and structures
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
The vibration and stability of circular cylindrical shells have been studied by many researchers since the basic equations for these were established by Flügge [1] and Donnell [2]
Summary
Structural engineers have been gradually concerned with the analysis of vibration and stability problems of circular cylindrical shells which have noncircular profiles because of the greatest important in many engineering applications such as in the design of machines and structures. If the determining functions vary from point to point of the neutral surface localization of the vibration and buckling modes lies near the weakest lines on the shell surface, and this kind from problems is too difficult because the radius of its curvature varies with the circumferential coordinate, closed-form or analytic solutions cannot be obtained, in general, for this class of shells, numerical or approximate techniques are necessary for their analysis. The purpose of this paper is to present the vibration and buckling analysis of an isotropic cylindrical shell with a three lobed cross section of circumferentially varying thickness, subjected to uniformly distributed axial compressive loads, by using the transfer matrix method.
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