The vibration and buckling of freely supported non-homogeneous orthotropic conical shells subjected to different uniform pressures

Sofiyev, A.H.; Korkmaz, Kasım Armağan; Mammadov, Z.; Kamanli, Mehmet

doi:10.1016/j.ijpvp.2009.03.012

Cited by 22 publications

(8 citation statements)

References 24 publications

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“…e jωt = Bφ (α) sin (nθ) e jωt w 0 (α, θ, t) = C w (α, θ) e jωt = Cφ (α) cos (nθ) e jωt (21) where ω denotes the natural frequency, n is the circumferential wave number, and A, B and C are the constant coefficients. Moreover, three functions of u (α, θ), v (α, θ) and w (α, θ) form a natural mode.…”

Section: Vibrational Analysis Using the Galerkin Methodsmentioning

confidence: 99%

“…Moreover, three functions of u (α, θ), v (α, θ) and w (α, θ) form a natural mode. By embedding equation (21) in equation 15, the following relations can be obtained…”

Section: Vibrational Analysis Using the Galerkin Methodsmentioning

confidence: 99%

“…Their results revealed that the volume fraction distributions had a significant effect on the buckling pressure of FGM hybrid truncated conical shells. Sofiyev et al [21] also studied freely supported non-homogeneous orthotropic conical shells subjected to different uniform pressures. They also extended their previous work to FGM conical shells [22].…”

Section: Introductionmentioning

confidence: 99%

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Free vibration analysis of truncated conical fiber metal laminate (FML) shells

Ghasemi

Ansari

Paskiabi

2013

Mechanics & Industry

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In this paper, an analytical solution is developed for free vibration analysis of conical fiber metal shells. In order to find constitutive relations, the assumptions of thins hells are used and the governing equations are based on Love's theory. The Galerkin method is employed to solve the governing equations in which beam functions are used to approximate the mode shapes. Using beam functions enables us to assess the effects of different boundary conditions on the frequency response of the shells. Numerical comparisons of the present and previously published results confirm the accuracy of the current approach. Additionally, the influences of geometrical parameters and embedding aluminum plies in different layers of the structure on natural frequency of the conical shells with various boundary conditions are investigated. It can be observed that the more the aluminum plies are used, the greater natural frequency of the structure will be reached. Except the clamped-free boundary conditions, the results also indicate that if the aluminum plies are embedded in the top and bottom layers of the laminate, natural frequency reaches its maximum value.

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Section: Vibrational Analysis Using the Galerkin Methodsmentioning

confidence: 99%

“…Moreover, three functions of u (α, θ), v (α, θ) and w (α, θ) form a natural mode. By embedding equation (21) in equation 15, the following relations can be obtained…”

Section: Vibrational Analysis Using the Galerkin Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Free vibration analysis of truncated conical fiber metal laminate (FML) shells

Ghasemi

Ansari

Paskiabi

2013

Mechanics & Industry

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“…16,17 Moreover, Spagnoli studied the different modes of instability in stringer-stiffened cones under axial compression through finite element. 18 For vibration of unstiffened conical shell, many papers discuss the frequency characteristics based on CLT, particularly the works done by Sivadas and Ganesan, 19 Thambiratnam and Zhuge, 20 Tong, 21,22 and Sofiyev et al 23,24 Additionally, Najafov et al derived the governing equations for non-linear free vibration of truncated, thin, laminated, orthotropic conical shells using the theory of large deformations. 25 This theory cannot be used for thick shells and even thin shells when the number of circumferential waves increases as a result of neglecting shear deformation and rotary inertia effects in CLT.…”

Section: Introductionmentioning

confidence: 99%

A Mixed Layerwise-Differential Quadrature Method for 3-D Vibration and Buckling Analyses of Orthogonally Stiffened Composite Conical Shell

Talebitooti¹

2019

The International Journal of Acoustics and Vibration

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A layerwise-differential quadrature method (LW-DQM) is developed for the vibration analysis of a stiffened laminated conical shell. The circumferential stiffeners (rings) and meridional stiffeners (stringers) are treated as discrete elements. The motion equations are derived by applying the Hamilton’s principle. In order to accurately account for the thickness effects and the displacement field of stiffeners, the layerwise theory is used to discretize the equations of motion and the related boundary conditions through the thickness. Then, the equations of motion as well as the boundary condition equations are transformed into a set of algebraic equations applying the DQM in the meridional direction. The advantage of the proposed model is its applicability to thin and thick unstiffened and stiffened shells with arbitrary boundary conditions. In addition, the axial load and external pressure is applied to the shell as a ratio of the global buckling load and pressure. This study demonstrates the accuracy, stability, and the fast rate of convergence of the present method, for the buckling and vibration analyses of stiffened conical shells. The presented results are compared with those of other shell theories and a special case where the angle of conical shell approaches zero, i.e. a cylindrical shell, and excellent agreements are achieved.

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“…Sofiyev et al. 12 performed the free vibration and buckling analyses of truncated conical shells with non-homogeneous material properties under uniform lateral and hydrostatic pressures. Free vibration and buckling analyses of a two-layered functionally graded cylindrical shell under combined static and periodic axial forces were investigated by Sepiani et al.…”

Section: Introductionmentioning

confidence: 99%

The buckling of truncated conical sandwich panels under axial compression and external pressure

Fard

Livani

2014

Proceedings of the Institution of Mechanical Engineers, Part C:

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Based on a new improved higher-order sandwich panel theory, the buckling analysis of a truncated conical composite sandwich panel with simply supported and fully clamped boundary conditions was performed for the first time. This panel was subjected to axial compression and external pressures. The governing equations were derived by using the principle of minimum potential energy. The first-order shear deformation theory was used for the composite face sheets, and for the core, a polynomial description of the displacement fields was assumed. Geometry was used for the consideration of different radii curvatures of the face sheets and the core was unique. The effects of types of boundary conditions, conical angles, length to smaller radius of core ratio, core to panel thickness ratio, and smaller radius of core to panel thickness ratio on the buckling response of truncated conical composite sandwich panels were also studied. The results were validated by the results published in the literature and the presented FE results were obtained by ABAQUS software.

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The vibration and buckling of freely supported non-homogeneous orthotropic conical shells subjected to different uniform pressures

Cited by 22 publications

References 24 publications

Free vibration analysis of truncated conical fiber metal laminate (FML) shells

Free vibration analysis of truncated conical fiber metal laminate (FML) shells

A Mixed Layerwise-Differential Quadrature Method for 3-D Vibration and Buckling Analyses of Orthogonally Stiffened Composite Conical Shell

The buckling of truncated conical sandwich panels under axial compression and external pressure

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