Cylindrical Shells Under Line Load

1957 ◽  
Vol 24 (4) ◽  
pp. 553-558
Author(s):  
R. M. Cooper
Keyword(s):  
Cylindrical Shell ◽  
Radial Displacement ◽  
Circular Cylindrical Shell ◽  
Transverse Shear Deformation ◽  
System Of Equations ◽  
Principle Of Superposition ◽  
Line Load ◽  
Simply Supported ◽  
Shell Equations ◽  
Shell Geometry

Abstract The problem of a line load along a segment of a generator of a simply supported circular cylindrical shell is treated using shallow cylindrical shell equations which include the effect of transverse-shear deformation. The line load is first treated as a sinusoidally-varying edge load over the length of the shell, with boundary conditions prescribed along the loaded generator such that the continuity of the shell is maintained. The solution for the problem of a uniform line load over a segment of a generator is obtained from the preceding solution, using the principle of superposition. By means of a numerical example it is shown that the results predicted by the Donnell equations for the stresses are in excellent agreement with those obtained from the system of equations employed here. However, the radial displacement predicted by the Donnell equations is in error by as much as 20 per cent in the range of shell geometry considered.

Response of Pressurized Cylindrical Shells Subjected to Moving Loads

1972 ◽  
Vol 39 (1) ◽  
pp. 227-234 ◽  
Author(s):  
E. N. K. Liao ◽  
P. G. Kessel
Keyword(s):  
Cylindrical Shell ◽  
Radial Displacement ◽  
Circular Cylindrical Shell ◽  
Axial Direction ◽  
Biaxial Stress ◽  
Steady State Response ◽  
Moving Loads ◽  
Simply Supported ◽  
State Response ◽  
Critical Velocities

This paper presents a theoretical analysis of the dynamic response of a thin circular cylindrical shell, simply supported at both ends, of finite length, under initial biaxial stress and subjected to a radial point force that moves uniformly either along the axial direction or the circumferential direction. The analytical solutions are obtained in explicit form for the transient response of the first problem and the steady-state response of the latter problem. Critical speeds are given for both problems. Numerical results for both problems show the effects of the various relevant parameters. The effects of initial biaxial stress on the radial displacement and the critical velocities are presented. The behavior of cylinders beyond the lowest critical velocity is also pointed out.

scholarly journals Vibrations of an elastic cylindrical shell near the lowest cut-off frequency

2016 ◽  
Vol 472 (2189) ◽  
pp. 20150753 ◽  
Author(s):  
J. Kaplunov ◽  
L. I. Manevitch ◽  
V. V. Smirnov
Keyword(s):  
Cylindrical Shell ◽  
Dispersion Relation ◽  
Ad Hoc ◽  
Circular Cylindrical Shell ◽  
Dynamic Modelling ◽  
Elastic Cylindrical Shell ◽  
Two Dimensional ◽  
Membrane Theory ◽  
Thin Walled Structures ◽  
Shell Equations

A new asymptotic approximation of the dynamic equations in the two-dimensional classical theory of thin-elastic shells is established for a circular cylindrical shell. It governs long wave vibrations in the vicinity of the lowest cut-off frequency. At a fixed circumferential wavenumber, the latter corresponds to the eigenfrequency of in-plane vibrations of a thin almost inextensible ring. It is stressed that the well-known semi-membrane theory of cylindrical shells is not suitable for tackling a near-cut-off behaviour. The dispersion relation within the framework of the developed formulation coincides with the asymptotic expansion of the dispersion relation originating from full two-dimensional shell equations. Asymptotic analysis also enables refining the geometric hypotheses underlying various ad hoc set-ups, including the assumption on vanishing of shear and circumferential mid-surface deformations used in the semi-membrane theory. The obtained results may be of interest for dynamic modelling of elongated cylindrical thin-walled structures, such as carbon nanotubes.

On Boundary Layers in a Pressurized Mooney Cylinder

1987 ◽  
Vol 54 (2) ◽  
pp. 280-286 ◽  
Author(s):  
L. A. Taber
Keyword(s):  
Boundary Layer ◽  
Shell Theory ◽  
Circular Cylindrical Shell ◽  
Small Strain ◽  
Axisymmetric Deformation ◽  
Transverse Shear Deformation ◽  
Edge Zone ◽  
Secondary Layer ◽  
Shell Equations ◽  
Pressurized Cylinder

Asymptotic expansions are developed for the equations governing large axisymmetric deformation of a circular cylindrical shell composed of a Mooney material. The shell equations allow large normal strains and thickness changes but ignore transverse shear deformation. For a pressurized cylinder with rigid end plugs, results are presented to illustrate the development of a primary and a secondary boundary layer as generalizations of those that occur in small-strain shell theory. The form of the WKB-type expansion divides the secondary layer into bending and stretching components, which lie within the wider primary boundary layer. While the bending component of the secondary layer can become significant when strains are still small, the stretching component emerges as a consequence of large geometry changes in the edge zone, becoming significant as strains grow large and material nonlinearity becomes important.

Closed-End Cylindrical Shell Under Line Load Along a Generator

1980 ◽  
Vol 102 (1) ◽  
pp. 90-97 ◽  
Author(s):  
U. S. Chawla
Keyword(s):  
Cylindrical Shell ◽  
Finite Difference ◽  
Discrete Element Method ◽  
Computer Program ◽  
Circular Cylindrical Shell ◽  
Numerical Technique ◽  
Elastic Analysis ◽  
Line Load ◽  
Shell Plate ◽  
Free Body

This paper presents a numerical technique for elastic analysis of a thin circular cylindrical shell with end plates under uniform line load along a generator. This technique is based upon the discrete element method. An accurate set of the governing differential equations due to Vlasov is used. The derivatives with respect to the circumferential coordinate are replaced by finite difference relationships. The end plate is analyzed as a free body under unit concentrated edge loads and the resulting coefficients are used to satisfy continuity conditions at the shell-plate junction. A computer program to implement this technique is developed and results are compared with those published in the literature. A number of new results are presented.

On Radial Deflections of a Cylinder Subjected to Equal and Opposite Concentrated Radial Loads: Infinitely Long Cylinder and Finite-Length Cylinder With Simply Supported Ends

1957 ◽  
Vol 24 (2) ◽  
pp. 278-282
Author(s):  
S. W. Yuan ◽  
L. Ting
Keyword(s):  
Mathematical Method ◽  
Cylindrical Shell ◽  
Finite Length ◽  
Circular Cylindrical Shell ◽  
Short Length ◽  
Simply Supported ◽  
Thin Walled ◽  
Long Cylinder

Abstract The radial deformations of a thin-walled circular cylindrical shell subjected to a pair of equal and opposite concentrated radial loads were obtained in (1) for the cases of infinitely long cylinders and cylinders of finite length simply supported at the ends. Based on the mathematical method given in (1) this problem is reexamined in the present paper by using Flügge’s equations (2, 3). It is found that the results obtained in (1) are quite satisfactory for short-length cylinders (L/α ≤ 10) with simply supported ends but not satisfactory for infinitely long cylinders.

Vibration Analysis of a Railway Carbody Model as a Non-Circular Cylindrical Shell

2007 ◽  
Author(s):  
Yukinori Kobayashi ◽  
Kotaro Ishiguri ◽  
Takahiro Tomioka ◽  
Yohei Hoshino
Keyword(s):  
Cylindrical Shell ◽  
Natural Frequencies ◽  
Circular Cylindrical Shell ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Elastic Vibration ◽  
Mode Shapes ◽  
Simply Supported ◽  
Vibration Problems ◽  
Good Agreement

Railway carbody is modeled as a non-circular cylindrical shell with simply-supported ends in this paper. The shell model doesn’t have end plates of the carbody and other equipments attached to actual carbody are neglected. We have applied the transfer matrix method (TMM) to the analysis of three-dimensional elastic vibration problems on the carbody. We also made a 1/12 size carbody model for experimental studies to verify the validity of the numerical simulation. The model has end plates and was placed on soft sponge at both ends of the model to emulate the freely-support. The modal analysis was applied to the experimental model, and natural frequencies and mode shapes of vibration were measured. Comparing the results by TMM and the experiment, natural frequencies and mode shapes of vibration for lower modes show good agreement each other in spite of differences of boundary conditions.

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