According to the framework of the Flügge's shell theory, the Winkler and Pasternak foundations model, the transfer matrix approach and the Romberg integration method, the vibration behavior of an isotropic and orthotropic cylindrical shell with variable thickness is investigated. The governing equations of the shell based on the Pasternak foundation model are formulated and solved. The analysis is formulated to overcome the mathematical difficulties related to mode coupling which comes from the variable curvature and thickness of the shell. The vibration equations of the shell are reduced to eight first order differential equations in the circumferential coordinate. Using the transfer matrix of the shell, these equations can be written in a matrix differential equation. The proposed model is adopted to get the vibration frequencies and the corresponding mode shapes for the symmetrical and antisymmetrical modes of vibration. The sensitivity of the frequency parameters and the bending deformations to the Winkler and Pasternak foundations moduli, the thickness ratio, and the orthotropic parameters are demonstrated.
A new vibration behavior is presented for an elastic oval cylindrical shell having circumferentially variable thickness with complex radius of curvature of an isotropic and orthotropic material. Based on the framework of the Flügge’s shell theory, the transfer matrix approach and the Romberg integration method, the governing equations of motion that have variable coefficients are formulated and solved. The analysis is formulated to overcome the mathematical difficulties related to mode coupling which comes from variable curvature and thickness of shell. 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 proposed model is adopted to get the vibration frequencies and the corresponding mode shapes for symmetric and anti-symmetric modes of vibration. The sensitivity of the frequency parameters and the bending deformations to the shell geometry, ovality parameter, thickness ratio, and orthotropic parameters corresponding to different types of vibration modes of shells is investigated.
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.
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