scholarly journals ON THE EXPLICIT SOLUTIONS OF VARIOUS ISOTROPIC THIN CLOSED CIRCULAR CYLINDRICAL SHELL EQUATIONS APPLIED TO G. W. HOUSNER, S DYNAMIC FLUID PRESSURE

1976 ◽  
Vol 14 ◽  
pp. 141-144
Author(s):  
Hirohumi Ogata
Keyword(s):  
Cylindrical Shell ◽  
Circular Cylindrical Shell ◽  
Fluid Pressure ◽  
Explicit Solutions ◽  
Shell Equations

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.

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.

Stresses in Eccentric Nonuniform Rings Reinforcing Cylindrical Shells

1967 ◽  
Vol 11 (02) ◽  
pp. 73-88
Author(s):  
Arnold Kempner ◽  
Joseph Kempner
Keyword(s):  
Cylindrical Shell ◽  
Hydrostatic Pressure ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Approximate Solutions ◽  
Ring Theory ◽  
Stress Distributions ◽  
Membrane Stress ◽  
Shell Equations ◽  
Interaction Problem

Bending and membrane stresses are determined in nonuniform frames of an infinitely long reinforced circular cylindrical shell subjected to hydrostatic pressure. The Donnell shell equations and deep-ring theory are used to solve the interaction problem. The frames, periodically spaced along the shell, are composed of two uniform but different sections. Each section of each frame has a different centroidal radius. Analyses of bending and membrane stress distributions in the frames are presented. Approximate solutions of different degrees of simplicity and accuracy are also given.

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