Vibration analysis of a thin eccentric rotating circular cylindrical shell

2018 ◽  
Vol 233 (5) ◽  
pp. 1588-1600 ◽  
Author(s):  
Zhihua Wu ◽  
Guo Yao ◽  
Yimin Zhang
Keyword(s):  
Cylindrical Shell ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Initial Stresses ◽  
Eccentric Rotation ◽  
Element Analysis ◽  
Coriolis Forces ◽  
Rotating Speed ◽  
Irregular Frequency ◽  
Thin Shell Theory

In this study, the vibration characteristics of a thin eccentric rotating circular cylindrical shell with simply supported boundary conditions are studied. Energy formulations based on Flügge’s thin shell theory, Hamilton’s principle, and the method of linear approximation are applied to derive the governing equations of motion. In addition to the effects of centrifugal and Coriolis forces, the effect of nonuniform initial stresses resulting from eccentric rotation are taken into account. The natural frequencies of the shell with respect to rotating speed and eccentricity are obtained using Galerkin’s method. To validate the present analysis, comparisons are carried out with the results in published literatures and finite element analysis, and good agreements are obtained. The effect of the eccentricity on the natural frequency of the eccentric rotating cylindrical shell is investigated. Some further numerical results are given to illustrate the irregular frequency mutation behaviors resulting from the eccentricity. The effects of the eccentricity on the critical speed and flutter speed of the eccentric rotating circular cylindrical shell are also investigated.

Approximate Formulas for Cylindrical Shell Free Vibration Based on Vlasov’s and Enhanced Vlasov’s Semi-Momentless Theory

2018 ◽  
Author(s):  
Igor Orynyak ◽  
Yaroslav Dubyk
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Middle Surface ◽  
Axial Direction ◽  
Mode Shapes ◽  
Natural Mode ◽  
Transverse Deflection ◽  
Approximate Formulas

Simple approximate formulas for the natural frequencies of circular cylindrical shells are presented for modes in which transverse deflection dominates. Based on the Donnell-Mushtari thin shell theory the equations of motion of the circular cylindrical shell are introduced, using Vlasov assumptions and Fourier series for the circumferential direction, an exact solution in the axial direction is obtained. To improve the results assumptions of Vlasov’s semimomentless theory are enhanced, i.e. we have used only the hypothesis of middle surface inextensibility to obtain a solution in axial direction. Nonlinear characteristic equations and natural mode shapes, are derived for all type of boundary conditions. Good agreement with experimental data and FEM is shown and advantage over the existing formulas for a variety of boundary conditions is presented.

Free vibration of bi-material cylindrical shells

2016 ◽  
Vol 230 (15) ◽  
pp. 2637-2649 ◽  
Author(s):  
Saeed Sarkheil ◽  
Mahmud S Foumani ◽  
Hossein M Navazi
Keyword(s):  
Exact Solution ◽  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
State Space ◽  
Thin Shell ◽  
Shell Theory ◽  
Circular Cylindrical Shell ◽  
Space Technique ◽  
Thin Shell Theory

Based on the Sanders thin shell theory, this paper presents an exact solution for the vibration of circular cylindrical shell made of two different materials. The shell is sub-divided into two segments and the state-space technique is employed to derive the homogenous differential equations. Then continuity conditions are applied where the material of the cylindrical shell changes. Shells with various combinations of end boundary conditions are analyzed by the proposed method. Finally, solving different examples, the effect of geometric parameters as well as BCs on the vibration of the bi-material shell is studied.

Internal Resonance and Nonlinear Vibrations of Eccentric Rotating Composite Laminated Circular Cylindrical Shell

2019 ◽  
Author(s):  
Tao Liu ◽  
Wei Zhang ◽  
Yan Zheng ◽  
Yufei Zhang
Keyword(s):  
Cylindrical Shell ◽  
Differential Equations ◽  
Internal Resonance ◽  
Nonlinear Vibrations ◽  
Multiple Scales ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Nonlinear Partial Differential Equations ◽  
Shear Deformation Theory ◽  
Internal Resonances

Abstract This paper is focused on the internal resonances and nonlinear vibrations of an eccentric rotating composite laminated circular cylindrical shell subjected to the lateral excitation and the parametric excitation. Based on Love thin shear deformation theory, the nonlinear partial differential equations of motion for the eccentric rotating composite laminated circular cylindrical shell are established by Hamilton’s principle, which are derived into a set of coupled nonlinear ordinary differential equations by the Galerkin discretization. The excitation conditions of the internal resonance is found through the Campbell diagram, and the effects of eccentricity ratio and geometric papameters on the internal resonance of the eccentric rotating system are studied. Then, the method of multiple scales is employed to obtain the four-dimensional nonlinear averaged equations in the case of 1:2 internal resonance and principal parametric resonance-1/2 subharmonic resonance. Finally, we study the nonlinear vibrations of the eccentric rotating composite laminated circular cylindrical shell systems.

Dynamic Response Analysis and Comparative Study of Circular Cylindrical Shell Subjected to Radial Impact

2007 ◽  
Vol 51 (02) ◽  
pp. 94-103
Author(s):  
Li Xuebin
Keyword(s):  
Cylindrical Shell ◽  
Dynamic Response ◽  
Normal Mode ◽  
Shell Theory ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Response Analysis ◽  
Mode Theory ◽  
Normal Mode Theory ◽  
Exact Derivation

Following Flu¨ gge's exact derivation for the buckling of cylindrical shells, the equations of motion for dynamic loading of a circular cylindrical shell under external hydrostatic pressure have been formulated. The normal mode theory is used to provide transient dynamic response for the equations of motion. The responses of displacements, strain, and stress are obtained for the area of impact, while those outside the area of impact are also calculated. The accuracy of normal mode theory and Timoshenko shell theory are examined in this paper.

Nonlinear Finite Element Analysis of a Toroidal Shell With Ring-Stiffened Ribs

2010 ◽  
Author(s):  
Qing-Hai Du ◽  
Wei-Cheng Cui ◽  
Zheng-Quan Wan
Keyword(s):  
Finite Element ◽  
Cylindrical Shell ◽  
Circular Cylindrical Shell ◽  
Structural Characteristics ◽  
External Pressure ◽  
Nonlinear Finite Element ◽  
Toroidal Shell ◽  
Shells Of Revolution ◽  
Element Analysis ◽  
Stiffened Cylindrical Shell

The toroidal shell is a special type of shells of revolution, which is hardly solved by analytical method. To show the nonlinear structural characteristics of a circular toroidal shell with ring-stiffened ribs due to external pressure, both material nonlinear and geometric nonlinear Finite Element Analyses (FEA) have been presented in this paper, especially for the stability to the type of pressure hull. In the presented Finite Element Method (FEM), the elastic-plastic stress-strain relations have been adopted, and the initial deflection of toroidal shell created by manufacture was also taken into account. The analytic results eventually indicate that by nonlinear FEA such a new type of ring-stiffened circular toroidal shell could be used to a main pressure hull as the traditional ring-stiffened circular cylindrical shell, which could obtain kinds of performance in underwater engineering, such as better stability and more reserve buoyancy to the classical ring-stiffened cylindrical shell.

Nonlinear Response of a Cylindrical Shell to an Impulsive Pressure

1969 ◽  
Vol 36 (2) ◽  
pp. 277-284 ◽  
Author(s):  
E. G. Lovell ◽  
I. K. McIvor
Keyword(s):  
Cylindrical Shell ◽  
Nonlinear Response ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Fundamental Difference ◽  
Large Displacements ◽  
Flexural Response ◽  
Modal Coupling ◽  
Impulsive Pressure

When a circular cylindrical shell (plane strain) is subjected to a uniform radial impulse, the resulting circular mode may be unstable. In such a case flexural motion is excited, resulting in rather large displacements and stress. A previous nonlinear analysis [1]1 used a linear inextensionality constraint and displacement representation for the flexural response. A formulation employing a nonlinear inextensionality constraint is presented in this paper, and a comparison is made with the earlier work. The most significant result is a fundamental difference between the equations of motion; in this analysis the nonlinear modal coupling is primarily inertial. The condition for stability of the circular mode is unaffected, but substantial differences may occur in the long-term (nonlinear) response.

Reduced-Order Nonlinear Modal Equations of Circular Cylindrical Shells Based on the Finite-Element Method

2004 ◽  
Author(s):  
Yukinori Kobayashi ◽  
Tomoaki Furukawa ◽  
Gen Yamada
Keyword(s):  
Finite Element ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Nonlinear Finite Element ◽  
Element Analysis ◽  
Reduced Order ◽  
Finite Element Equation ◽  
Displacement Vectors ◽  
Circular Cylindrical Shells

This paper presents a procedure to derive reduced-order nonlinear modal equations of circular cylindrical shells. Modal analysis is applied to the nonlinear finite element equation by using base vectors obtained by the finite element analysis. Reduced-order modal equations are derived by transforming the equations of motion from the physical coordinates to the modal coordinates. Base vectors for the transformation consist of dominant linear eigenmodes and nonlinear displacement vectors derived approximately from the nonlinear finite element equation. Asymmetry of the deformation of the circular cylindrical shell with respect to its neutral surface is taken into consideration to determine the base vectors. Numerical results show good agreement with those presented in other papers.

Dynamic Stability of an Isotropic Metal Foam Cylindrical Shell Subjected to External Pressure and Axial Compression

2011 ◽  
Vol 78 (4) ◽  
Author(s):  
Tomasz Belica ◽  
Marek Malinowski ◽  
Krzysztof Magnucki
Keyword(s):  
Cylindrical Shell ◽  
Dynamic Stability ◽  
Metal Foam ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Element Model ◽  
External Pressure ◽  
Combined Loads ◽  
Nonlinear Approach ◽  
Isotropic Metal

This paper presents a nonlinear approach with regard to the dynamic stability of an isotropic metal foam circular cylindrical shell subjected to combined loads. The mechanical properties of metal foam vary in the thickness direction. Combinations of external pressure and axial load are taken into account. A nonlinear hypothesis of deformation of a plane cross section is formulated. The system of partial differential equations of motion for a shell is derived on the basis of Hamilton’s principle. The system of equations is analytically solved by Galerkin’s method. Numerical investigations of dynamic stability for the family of cylindrical shells with regard to analytical solution are carried out. Moreover, finite element model analysis is presented, and the results of the numerical calculations are shown in figures.

Bending of a Thin Cylindrical Shell Subjected to a Line Load Around a Circumference

1961 ◽  
Vol 28 (3) ◽  
pp. 427-433 ◽  
Author(s):  
H. R. Meck
Keyword(s):  
Cylindrical Shell ◽  
Circular Cylindrical Shell ◽  
Thin Cylindrical Shell ◽  
Radial Line ◽  
Eighth Order ◽  
Line Load ◽  
Bending Stresses ◽  
Center Section ◽  
Fourth Order Equations ◽  
Thin Shell Theory

An analysis is developed for bending of a thin circular cylindrical shell under a varying radial line load distributed around the circumference at the center section. The problem is solved by reducing the eighth-order differential equation of thin-shell theory to two approximate fourth-order equations. Deflections, bending stresses, and membrane stresses are evaluated. Both simply supported and clamped ends are considered.

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