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.

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.

Dynamic Stability of a Cylindrical Shell under Alternating Axial External Pressure

2017 ◽  
Vol 60 (4) ◽  
pp. 508-513 ◽  
Author(s):  
V. N. Bakulin ◽  
E. N. Volkov ◽  
A. I. Simonov
Keyword(s):  
Cylindrical Shell ◽  
Dynamic Stability ◽  
External Pressure

Limit Analysis for Combined Edge and Pressure Loading on a Cylindrical Shell

1971 ◽  
Vol 93 (4) ◽  
pp. 998-1006
Author(s):  
H. S. Ho ◽  
D. P. Updike
Keyword(s):  
Cylindrical Shell ◽  
Velocity Field ◽  
Axial Force ◽  
Shear Force ◽  
Circular Cylindrical Shell ◽  
Yield Condition ◽  
External Pressure ◽  
Tresca Yield Condition ◽  
Stress States ◽  
Range Of Values

Equations describing the stress field and velocity field occurring in a circular cylindrical shell at plastic collapse are derived corresponding to stress states lying on each face of a yield surface for a uniform shell of material obeying the Tresca yield condition. They are then applied to the case of a shell under combined axisymmetric loadings (moment, shear force, and axial force) at one end and uniform internal or external pressure on the lateral surface. For a sufficiently long shell, complete solutions are obtained for a fixed far end, and for a certain range of values of axial force and pressure, they are obtained for a free far end. All the solutions are represented by either closed form or by quadratures. It is shown that in many cases the radial velocity field is proportional to the shear force.

Optimal Design of Laminated-Composite Circular-Cylindrical Shells Subjected to Combined Loads

1988 ◽  
Vol 55 (1) ◽  
pp. 136-142 ◽  
Author(s):  
G. Sun ◽  
J. S. Hansen
Keyword(s):  
Circular Cylindrical Shell ◽  
Laminated Composite ◽  
Optimization Procedure ◽  
External Pressure ◽  
Buckling Load ◽  
Perturbation Approach ◽  
Combined Loads ◽  
Fixed Weight ◽  
Shell Analysis ◽  
Post Buckling

Optimization of the buckling load of a laminated-composite, circular-cylindrical shell subjected to axial compression, external pressure, torsion, or a combination thereof is undertaken. In the optimization procedure it is assumed that the shell has a fixed weight (length, radius and thickness); the buckling load is taken as the objective function which is maximized by adopting the lamina fiber orientations as the optimizing parameters. For the shell analysis a perturbation approach is used and the boundary conditions and nonlinear prebuckling effects are included; the analysis yields both the buckling load and the post-buckling character of the shell. The procedure developed is demonstrated for eight loading configurations. In addition, selected laminates were chosen for an experimental programme involving a series of graphite/epoxy shells. The predicted analytical and the measured experimental buckling loads are in very good agreement.

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.

Experimental Study on Pre-Stressed Circular Cylindrical Shell

2012 ◽  
Author(s):  
Antonio Zippo ◽  
Marco Barbieri ◽  
Matteo Strozzi ◽  
Vito Errede ◽  
Francesco Pellicano
Keyword(s):  
Experimental Study ◽  
Cylindrical Shell ◽  
Axial Load ◽  
Nonlinear Vibrations ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Experimental Studies ◽  
Element Model ◽  
Experimental Setup ◽  
Circular Cylindrical Shells

In this paper an experimental study on circular cylindrical shells subjected to axial compressive and periodic loads is presented. Even though many researchers have extensively studied nonlinear vibrations of cylindrical shells, experimental studies are rather limited in number. The experimental setup is explained and deeply described along with the analysis of preliminary results. The linear and the nonlinear dynamic behavior associated with a combined effect of compressive static and a periodic axial load have been investigated for different combinations of loads; moreover, a non stationary response of the structure has been observed close to one of the resonances. The linear shell behavior is also investigated by means of a finite element model, in order to enhance the comprehension of experimental results.

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.

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