On the Buckling of Rings Subject to Impulsive Pressures

1965 ◽  
Vol 32 (3) ◽  
pp. 511-518 ◽  
Author(s):  
W. Stuiver
Keyword(s):  
Experimental Data ◽  
Plastic Flow ◽  
Analytical Procedure ◽  
Cylindrical Shells ◽  
Elastic Instability ◽  
Circular Cylindrical Shells ◽  
Single Approach

It is shown in this paper that previous, independent analyses of the phenomena of dynamic elastic instability and dynamic plastic-flow buckling of circular cylindrical shells can be combined in a single approach leading to results consistent with those that follow from these analyses. The response of the shell in both cases is governed by the interaction between the fundamental radial, purely extensional mode of deformation and inextensional flexural modes always present in the response. An analytical procedure is given for the determination of dominant modes in the elastic and plastic phases of the response, and the results of this procedure are verified by comparison with numerical and experimental data.

Energy Expressions and Differential Equations …. for Stress and Displacement Analyses of Arbitrary Cylindrical Shells

1958 ◽  
Vol 2 (02) ◽  
pp. 8-19
Author(s):  
Joseph Kempner
Keyword(s):  
Differential Equations ◽  
Cylindrical Shells ◽  
Arbitrary Cross Section ◽  
Natural Boundary ◽  
Equilibrium Equations ◽  
Small Deflection ◽  
Circular Cylindrical Shells ◽  
Natural Boundary Conditions ◽  
Theory Of Shells

Energy expressions and the related equilibrium equations and natural boundary conditions for the determination of the stresses in and displacements of uniform, thin-walled cylinders of arbitrary cross section loaded in an arbitrary manner by surface and edge forces and moments are presented. The derivations are based upon the Kirchhoff-Love assumptions of the classical theory of shells and are performed to within a degree of accuracy employed by Flügge in his derivation of the equilibrium equations applicable to circular cylindrical shells; hence, in terms of stress resultants, the exact, small-deflection equilibrium equations are obtained. Methods of simplification of the relations derived and of solution of the differential equations presented are indicated.

ON THE INSTABILITY OF SPINNING CYLINDRICAL SHELLS PARTIALLY FILLED WITH LIQUID

2012 ◽  
Vol 12 (03) ◽  
pp. 1250018 ◽  
Author(s):  
R. D. FIROUZ-ABADI ◽  
M. R. PERMOON ◽  
H. HADDADPOUR
Keyword(s):  
Stokes Equations ◽  
Cylindrical Shells ◽  
Fluid Pressure ◽  
Ideal Liquid ◽  
Navier Stokes ◽  
Nonpenetration Condition ◽  
Navier Stokes Equations ◽  
Circular Cylindrical Shells ◽  
Shear Deformable

The dynamics and stability of rotating circular cylindrical shells partially filled with ideal liquid is analyzed. The structural dynamics of the shell is modeled by using the first-order shear deformable shell theory and the flow inside the cylinder is simulated by a quasi 2D model based on the Navier–Stokes equations for ideal liquid. The fluid and structural models are combined using the nonpenetration condition of the flow on the wetted surface of the cylinder and the fluid pressure on the flexible shell. The obtained fluid–structure model is employed for the determination of the stable regions of the spinning frequency of the cylinder. A series of case studies are performed on the governing parameters of the instability of the cylinder and some conclusions are outlined.

Multimode Approach to Nonlinear Supersonic Flutter of Imperfect Circular Cylindrical Shells

2001 ◽  
Vol 69 (2) ◽  
pp. 117-129 ◽  
Author(s):  
M. Amabili ◽  
F. Pellicano
Keyword(s):  
Experimental Data ◽  
Degrees Of Freedom ◽  
Dynamic Pressure ◽  
Cylindrical Shells ◽  
Travelling Wave ◽  
Finite Amplitude ◽  
Research Center ◽  
Piston Theory ◽  
Nasa Ames Research ◽  
Circular Cylindrical Shells

The aeroelastic stability of simply supported, circular cylindrical shells in supersonic flow is investigated by using both linear aerodynamics (first-order piston theory) and nonlinear aerodynamics (third-order piston theory). Geometric nonlinearities, due to finite amplitude shell deformations, are considered by using the Donnell’s nonlinear shallow-shell theory, and the effect of viscous structural damping is taken into account. The system is discretized by Galerkin method and is investigated by using a model involving up to 22 degrees-of-freedom, allowing for travelling-wave flutter around the shell and axisymmetric contraction of the shell. Asymmetric and axisymmetric geometric imperfections of circular cylindrical shells are taken into account. Numerical calculations are carried out for a very thin circular shell at fixed Mach number 3 tested at the NASA Ames Research Center. Results show that the system loses stability by travelling-wave flutter around the shell through supercritical bifurcation. Nonsimple harmonic motion is observed for sufficiently high post-critical dynamic pressure. A very good agreement between theoretical and existing experimental data has been found for the onset of flutter, flutter amplitude, and frequency. Results show that onset of flutter is very sensible to small initial imperfections of the shells. The influence of pressure differential across the shell skin has also been deeply investigated. The present study gives, for the first time, results in agreement with experimental data obtained at the NASA Ames Research Center more than three decades ago.

scholarly journals Effects of Elastic Foundation on the Vibration of Laminated Non-Homogeneous Orthotropic Circular Cylindrical Shells

2004 ◽  
Vol 11 (2) ◽  
pp. 89-101 ◽  
Author(s):  
A.H. Sofiyev ◽  
S.N. Keskin ◽  
Ali H. Sofiyev
Keyword(s):  
Elastic Foundation ◽  
Analytical Procedure ◽  
Linear Time ◽  
Cylindrical Shells ◽  
Finite Deformations ◽  
Displacement Amplitude ◽  
Time Dependent ◽  
Thickness Direction ◽  
Young’S Moduli ◽  
Circular Cylindrical Shells

In this paper an analytical procedure is given to study the free vibration characteristics of laminated non-homogeneous orthotropic thin circular cylindrical shells resting on elastic foundation, accounting for Karman type geometric non-linearity. At first, the basic relations and modified Donnell type stability equations, considering finite deformations, have been obtained for laminated thin orthotropic circular cylindrical shells, the Young's moduli of which varies piecewise continuously in the thickness direction. Applying Galerkin method to the latter equations, a non-linear time dependent differential equation is obtained for the displacement amplitude. The frequency is obtained from this equation as a function of the shell displacement amplitude. Finally, the effect of elastic foundation, non-linearity, non-homogeneity, the number and ordering of layers on the frequency is found for different mode numbers. These results are given in the form of tables and figures. The present analysis is validated by comparing results with those in the literature.

Prediction of natural frequencies for thin circular cylindrical shells

2000 ◽  
Vol 214 (10) ◽  
pp. 1313-1328 ◽  
Author(s):  
M N Naeem ◽  
C B Sharma
Keyword(s):  
Variational Approach ◽  
Analytical Procedure ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Polynomial Functions ◽  
Simply Supported ◽  
Analytical Results ◽  
General Eigenvalue Problem ◽  
Circular Cylindrical Shells ◽  
Good Agreement

In this paper an analytical procedure is given to study the free-vibration characteristics of thin circular cylindrical shells. Ritz polynomial functions are assumed to model the axial modal dependence and the Rayleigh-Ritz variational approach is employed to formulate the general eigenvalue problem. Influence of some commonly used boundary conditions, viz. simply supported-simply supported, clamped-clamped and clamped-free, and also the effects of variations of shell parameters on the vibration frequencies are examined. Natural frequencies for a number of particular cases are evaluated and compared with some available experimental and other analytical results in the literature on this topic. These results are given in the form of tables and figures. A very good agreement between the results of the present analysis and the corresponding experimental and analytical results available in the literature is obtained to confirm the validity and accuracy as well as the efficiency of the method.

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