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

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.