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Frequency parameter versus thickness ratio for orthotropic oval cylindrical shells with (η = 0.5, μ = 0.35, m = 1) η = 0.1, η = 0.5, η = 1.
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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 tha...
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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 foundatio...
Citations
... They applied the Ritz method in conjunction with Bezier functions to investigate the free vibration behavior of the shells. In another research, Ahmed [21] calculated the frequency parameters and corresponding mode shapes of the oval cylindrical shells having circumferentially variable thickness by the usage of the transfer matrix approach. The finite strip method and non-uniform rational B-splines (NURBS) formulation were simultaneously used by Borković et al. [22] to obtain natural frequencies of singly curved shells such as cubic and quartic cylinders. ...
... Lakis and Selmane [18] conducted the thin shell theory, fluid theory, and the hybrid FEM to study the influence of large amplitude vibration of orthotropic, circumferentially nonuniform cylindrical shells. Ahmed [19] analyzed the isotropic and orthotropic cylindrical shell with variable circumferentially thickness and complex curvature radius by Flugge's shell theory. e transfer-matrix method and the Longberg integral method were proposed in the establishment of the motion control equation. ...
The wave-based method (WBM) is a feasible method which investigates the free vibration characteristics of orthotropic cylindrical shells under general boundary conditions. Based on Reissner–Naghid’s shell theory, the governing motion equation is established, and the displacement variables are transformed into wave functions formed to satisfy the governing equations. On the basis of the kinematic relationship between the force resultant and displacement vector, the overall matrix of the shell is established. Comparison studies of this paper with the solutions in the literatures were carried out to validate the accuracy of the present method. Furthermore, by analyzing some numerical examples, the free vibration characteristics of orthogonal anisotropic cylindrical shells under classical boundary conditions, elastic boundary conditions, and their combinations are studied. Also, the effects of the material parameter and geometric constant on the natural frequencies for the orthotropic circular cylindrical shell under general boundary conditions are discussed. The conclusions obtained can be used as data reference for future calculation methods.
... The dynamic behavior of cylindrical shells conveying fluid is of substantial practical applications, for instance, in heat exchangers, hydraulic systems, power plants and nuclear reactor systems, etc. It is not surprising, therefore, that the dynamic problems of fluidconveying shells have been extensively investigated both theoretically (Tang and Paı¨doussis, 2009;Ahmed, 2010Ahmed, , 2012Sofiyev and Kuruoglu, 2013) and experimentally (Zhang et al., 2000;Liu et al., 2009;Chebair et al., 1989;Karagiozis et al., 2005Karagiozis et al., , 2008. ...
The characteristics of the beam-mode stability of the fluid-conveying shell systems are investigated in this paper, under the clamped-clamped condition. A finite element model algorithm is developed to conduct the investigation. A periodic structure of functionally graded material (FGM) for the shell system, termed as PFGM shell here, is designed to enhance the stability for the shell systems, and to eliminate the stress concentration problems that exist in periodic structures. Results show that (i) the dynamical behaviors, either the divergence or the coupled-mode flutter, are all improved in such a periodic shell system; (ii) the critical velocities ucr for the divergent form of instability is independent of the normalized fluid density β; (iii) various critical values of β exist in the system, for indentifying the coupled modes of flutter (Païdoussis-type or Hamiltonian Hopf bifurcation flutter) and for determining the mode exchange; (iv) changes of some key parameters, e.g., lengths of segments and/or ‘grading profiles’ could result in appreciable improvement on the stability of the system.
... Cylindrical shells have widespread application as structural elements in advanced structures, such as high-speed trains, pressure vessels, airplanes, rockets and submarine hulls. A considerable number of researchers have committed themselves to analysing the dynamics of cylindrical shells because they give rise to the optimum condition for dynamical behaviour [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. In other words, an optimised shell improves its dynamics through its geometrical shape or advanced materials; therefore, undesired vibrations or sounds could be eliminated or depressed. ...
This research aimed to study the analysis of free vibrations of cylindrical shells made of functionally graded materials (FGMs). The studied shells were thin and had been selected in a way that their thickness varies linearly along the length. A combination of different boundary conditions was applied, and vibrational analysis was performed through finite element method. Then, the effects of different parameters, including varying thickness along the length, shell length, and radius, on the frequency behavior of the shell were extracted. Afterward, the frequency behaviors of the shells made of different materials were compared. The numerical results obtained in this article have been verified by the results derived from the analytical relations of previous research, which indicated the high accuracy of the finite element method for the vibrational analysis of the shells with variable thickness. The analysis indicated significant effects of thickness changes and boundary conditions on the natural frequencies.
This paper is aimed to investigate how the corrugation parameters and the Winkler foundation affect the buckling behavior of isotropic and orthotropic thin-elliptic cylindrical shells with cosine-shaped meridian subjected to radial loads. The buckling three-dimensional equations of the shell are amended by including the Winkler foundation modulus based on the Flügge thin shell theory and Fourier's approach is used to deform the displacement fields as trigonometric functions in the longitudinal direction of shell. Using the transfer matrix of the shell, the governing equations of buckling can be written in a matrix differential equation of variable coefficients as a one-dimensional boundary-value problem that is solved numerically as an initial-value problem by the Romberg integration approach. The proposed model is adopted to determine the basic loads and the corresponding buckling deformations for the symmetrical and antisymmetrical modes of buckling. The sensitivity of the buckling behavior and bending deformations to the corrugation parameters, Winkler foundation moduli, ellipticity and orthotropy of the shell structure is studied for different type-modes of buckling. The obtained results indicate that this design model allows us to find out how the local properties of the shell and its stiffness in existence of an elastic foundation are related and would serve as benchmarks for future works in this important area.
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.
Based on the framework of Flügge's shell theory, transfer matrix approach and Romberg integration method, this paper investigates how corrugation parameters and material homogeneity affect the vibration behavior of isotropic and orthotropic oval cylindrical shells with sine-shaped hoop. Assume that the Young's moduli, shear moduli and density of the orthotropic material are continuous functions of the coordinate in the circumferential direction. The governing equations of non-homogeneous, orthotropic oval cylindrical shells with variable homogeneity along its circumference are derived and put in a matrix differential equation as a boundary-value problem. The trigonometric functions are used with Fourier's approach to approximate the solution in the longitudinal direction, and also to reduce the two-dimensional problem to a one-dimensional one. Using the transfer matrix approach, the equations can be written in a matrix differential equation of the first order and solved numerically as an initial-value problem. The proposed model is applied to get the vibration frequencies and mode shapes of the symmetric and antisymmetric vibration modes. The sensitivity of the vibration behavior to the corrugation parameters, homogeneity variation, ovality, and orthotropy of the shell is studied for different type modes of vibration.
Flügge's shell theory and solution for the vibration analysis of a non-homogeneous orthotropic elliptical cylindrical shell resting on a non-uniform Winkler foundation are presented. The theoretical analysis of the governing equations of the shell is formulated to overcome the mathematical difficulties of mode coupling of variable curvature and homogeneity of shell. Using the transfer matrix of the shell, the vibration equations based on the variable Winkler foundation are written in a matrix differential equation of first order in the circumferential coordinate and solved numerically. The proposed model is applied to get the vibration frequencies and the corresponding mode shapes of the symmetrical and antisymmetrical vibration modes. The sensitivity of the vibration behavior and bending deformations to the non-uniform Winkler foundation moduli, homogeneity variation, elliptical and orthotropy of the shell is studied for different type-modes of vibrations.
In this paper, based on the framework of the Flügge's shell theory, the transfer matrix approach and the Romberg integration method, the vibration behavior of an elastic oval cylindrical shell with parabolically varying thickness along of its circumference resting on the Winkler-Pasternak foundations is investigated. The theoretical analysis of the governing equations of the shell is formulated to overcome the mathematical difficulties of mode coupling of variable curvature and thickness of shell. Using the transfer matrix of the shell, the vibration equations based on the Winkler-Pasternak foundations are written in a matrix differential equation of first order in the circumferential coordinate and solved numerically. The proposed model is applied to get the vibration frequencies and the corresponding mode shapes of the symmetrical and antisymmetrical vibration modes. The sensitivity of the vibration characteristics and bending deformations to the Winkler-Pasternak foundations moduli, thickness variation, ovality and orthotropy of the shell is studied for different type-modes of vibration.
