A study of free vibration of a circumferentially non-uniform cylindrical shell with a four-lobed cross-section

Abstract

The transfer matrix approach is used and the Flügge's shell theory is modeled to investigate the free vibration behaviour of a cylindrical shell with a four-lobed cross-section with reduced thickness over part of its circumference. Modal displacements of the shell can be described by trigonometric functions and Fourier's approach is used to separate the variables. The vibration equations of the shell are reduced to eight first-order differential equations in the circumferential coordinate, and by using the transfer matrix of the shell, these equations can be written in a matrix differential equation. The transfer matrix is derived from the nonlinear differential equations of the cylindrical shells by introducing the trigonometric functions in the longitudinal direction and applying a numerical integration in the circumferential direction. The proposed method is used to get the vibration frequencies and the corresponding mode shapes of symmetrical and antisymmetrical type-modes. Computed results indicate the sensitivity of the frequency parameters and the bending deformations to the geometry of the non-uniformity of the shell, and also to the radius of curvature at the lobed corners.

Exact solutions for the vibration of circumferentially stepped orthotropic circular cylindrical shells

“…Other related references may be found in the well-known works, see [5][6][7][8][9][10]. Some of researchers have considerable interest in the study of vibration behaviour of circular cylindrical shells with variable thickness such as [11][12][13][14][15][16][17][18] in which their investigations have been made into different forms of thickness, i.e. axial, circumferential and step-wise thickness variations for isotropic shells.…”

A new vibration approach of an elastic oval cylindrical shell with varying circumferential thickness

“…oval, elliptical, three and four-lobed cross-section. In contrast, the vibration study of non-uniform cylindrical shells with variable thickness has received much less attention, but some implementations are well documented by Suzuki and Leissa (1985), Mitao et al (1996) and Khalifa (2010) in which their treatments have been modeled into different forms of shell theories. The vibration problems of cylindrical shells with an oval profile are rather limited, which is due to the difficulty introduced in governing equations of motion.…”