A Method for Approximate Stability Analysis and Its Application to Circular Cylindrical Shells Under Circumferentially Varying Edge Loads

1973 ◽  
Vol 40 (4) ◽  
pp. 971-976 ◽  
Author(s):  
A. Libai ◽  
D. Durban
Keyword(s):  
Stress Distribution ◽  
Boundary Conditions ◽  
Stability Problem ◽  
Circular Cylindrical Shell ◽  
Symmetric Matrix ◽  
Circumferential Stress ◽  
Characteristic Roots ◽  
Circular Cylindrical Shells ◽  
The Stability ◽  
Simple Stress

A procedure is presented which relates the solution of the stability problem for an elastic structure subjected to a complex prebuckling stress distribution, to that of a solved stability problem for the same structure but with a “simple” stress distribution. The procedure reduces to obtaining the characteristic roots of a symmetric matrix. It is then applied to the buckling problem of a circular cylindrical shell subjected to a circumferentially varying compressive stress field and boundary conditions of the SS1-2 types. The main result is that for the boundary conditions and number of harmonic terms in the edge load taken, the buckling parameter approaches, as h/R → 0, that of a cylinder uniformly subjected to the maximum circumferential stress.

Buckling of Circular Cylindrical Shells Using a Displacement Function

1974 ◽  
Vol 96 (4) ◽  
pp. 1322-1327
Author(s):  
Shun Cheng ◽  
C. K. Chang
Keyword(s):  
Boundary Conditions ◽  
Axial Compression ◽  
Cylindrical Shells ◽  
External Pressure ◽  
Displacement Function ◽  
Combined Loading ◽  
Trial Solution ◽  
Governing Differential Equation ◽  
Circular Cylindrical Shells ◽  
The Stability

The buckling problem of circular cylindrical shells under axial compression, external pressure, and torsion is investigated using a displacement function φ. A governing differential equation for the stability of thin cylindrical shells under combined loading of axial compression, external pressure, and torsion is derived. A method for the solutions of this equation is also presented. The advantage in using the present equation over the customary three differential equations for displacements is that only one trial solution is needed in solving the buckling problems as shown in the paper. Four possible combinations of boundary conditions for a simply supported edge are treated. The case of a cylinder under axial compression is carried out in detail. For two types of simple supported boundary conditions, SS1 and SS2, the minimum critical axial buckling stress is found to be 43.5 percent of the well-known classical value Eh/R3(1−ν2) against the 50 percent of the classical value presently known.

scholarly journals On the equilibrium and stability of a row of point vortices

1995 ◽  
Vol 290 ◽  
pp. 167-181 ◽  
Author(s):  
Hassan Aref
Keyword(s):  
Vortex Dynamics ◽  
Stability Problem ◽  
Regular Polygon ◽  
Symmetric Matrix ◽  
Classical Problem ◽  
Point Vortices ◽  
Instability Modes ◽  
Systematic Enumeration ◽  
The Stability ◽  
Accessible Form

The equilibrium and stability of a single row of equidistantly spaced identical point vortices is a classical problem in vortex dynamics, which has been addressed by several investigators in different ways for at least a century. Aspects of the history and the essence of these treatments are traced, stating some in more accessible form, and pointing out interesting and apparently new connections between them. For example, it is shown that the stability problem for vortices in an infinite row and the stability problem for vortices arranged in a regular polygon are solved by the same eigenvalue problem for a certain symmetric matrix. This result also provides a more systematic enumeration of the basic instability modes. The less familiar theory of equilibria of a finite number of vortices situated on a line is also recalled.

scholarly journals STABILITY OF ROTATING CIRCULAR CYLINDRICAL SHELL SUBJECT TO AN AXIAL AND ROTATIONAL FLUID FLOW

2017 ◽  
Vol 18 (9) ◽  
pp. 84-97
Author(s):  
S.A. Bochkarev ◽  
V.P. Matveenko
Keyword(s):  
Finite Element Method ◽  
Fluid Flow ◽  
Boundary Conditions ◽  
Circular Cylindrical Shell ◽  
Loss Of Stability ◽  
Rotating Fluid ◽  
The Finite Element Method ◽  
The Stability ◽  
Rotating Shell ◽  
Simultaneous Rotation

This paper is concerned with the stability analysis of rotating cylindrical shells conveying a co-rotating fluid. The problem is solved by the finite element method for shells subjected to different boundary conditions. It has been found that the loss of stability for a rotating shell under the action of the fluid having both axial and circumferential velocity components depends on the type of boundary conditions imposed on the shell ends. The results of numerical calculations have shown that for different variants of boundary conditions a simultaneous rotation of shell and the fluid causes an increase or decrease in the critical velocity of axial fluid flow.

Temperature stresses in thick circular cylindrical shells used in nuclear reactors with exponential heat generation within the shell wall thickness

1998 ◽  
Vol 212 (7) ◽  
pp. 555-565 ◽  
Author(s):  
G Guerreri ◽  
L M Cossa
Keyword(s):  
Heat Generation ◽  
Wall Thickness ◽  
Nuclear Reactors ◽  
Circular Cylindrical Shell ◽  
Circumferential Stress ◽  
Preceding Paper ◽  
Quantitative Measure ◽  
Principle Of Superposition ◽  
Heat Flows ◽  
Circular Cylindrical Shells

In the preceding paper, formulae and graphs were given which enabled estimates to be made of heat flow, temperature and stresses through the thickness of the circular cylindrical shell, when heat was not generated inside the thickness and when it was generated according to a uniform path. Situations of heat generation in shell thickness are commonly encountered in the shields of nuclear reactors. All the expressions given for stress in the preceding paper may be reduced to the following form: σ{ Eα qa2/[(1 - ν) k]}η, where η is a factor associated with the stress which depends upon heat generation profiles, internal and external temperatures T a and T b of the shell and its thermal conductivity k, for each radius r. Another common heat generation which occurs in these shells has an exponential path. For these cases, the circumferential thermal stress σϑ may be given in the following form: σϑ = { Eα q(β−1)2/[(1 - ν) k]}ηϑ, where β is the exponential absorption factor which is related to the quantitative measure of the generated heat and ηϑ is the non-dimensional circumferential stress. In the present paper graphs are furnished to estimate the parameter ηϑ in order to foresee the values of stresses in the circumferential directions at the internal and external radii of the shell for the case of exponential heat generation through the wall thickness. They apply only when: (a) all generated heat flows inside the vessel or (b) all heat flows outside the vessel or ( c) T a = T b. Application of the principle of superposition shows how to evaluate the stresses where the generated heat paths are not uniform, triangular or exponential.

Vibration Characteristics of the Respiratory Branched Network-Comparative Study

2005 ◽  
Author(s):  
P. M. Au ◽  
A. M. Al-Jumaily
Keyword(s):  
Boundary Conditions ◽  
Comparative Study ◽  
Circular Cylindrical Shell ◽  
Vibration Characteristics ◽  
The Finite Element Method ◽  
Resonant Frequencies ◽  
Membrane Shell ◽  
Classical Boundary ◽  
Circular Cylindrical Shells ◽  
Shell Approximation

Determining the vibration characteristics of a realistic branched biological network, such as the respiratory system, faces many hurdles, which includes using the appropriate theory, specifying suitable boundary conditions and selecting accurate physical properties. Further, dichotomized or bifurcated structures beyond a simple circular cylindrical shell induce problems and difficulties in boundary matching between generations. This paper determines the natural frequencies using the Donnell-Mushtari formulation, membrane-shell approximation, a simplified limiting ring formula and the finite element method using COSMOS/Works™ for circular cylindrical shells with classical boundary conditions. Some experimental data are used for comparison and validation. Comparative study between the various methods sets the pros, cons, limitations of each method and the boundaries for the resonant frequencies of each individual generation of this system.

Analysis of Fiberglass Winding Angle on Natural Frequency of Cylindrical Shell with Symmetric Boundary Conditions

2013 ◽  
Vol 765-767 ◽  
pp. 106-109
Author(s):  
Zhi Wei Wang ◽  
Yan Fu Wang ◽  
Bai Qin
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Circular Cylindrical Shell ◽  
Glass Fiber Reinforced Plastic ◽  
Glass Fiber Reinforced ◽  
Reinforced Plastic ◽  
Circular Cylindrical Shells ◽  
Winding Angle

In order to obtain approximate solution of natural frequencies for the free vibration of anisotropic circular cylindrical shells made of GFRP (glass fiber-reinforced plastic) with symmetric boundary conditions, Loves theory and energy method are used. Computation results show that the fundamental natural frequency comes from different vibration modes while the winding angle varies, the effect of number of axial half waves is stronger than number of circumferential waves on natural frequency of free vibration of anisotropic circular cylindrical shell.

Vibrations of Circular Cylindrical Shells With General Elastic Boundary Restraints

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
W. L. Li
Keyword(s):  
Boundary Conditions ◽  
Solution Method ◽  
Circular Cylindrical Shell ◽  
Cylindrical Shells ◽  
Elastic Boundary ◽  
Special Cases ◽  
Ritz Procedure ◽  
Circular Cylindrical Shells ◽  
Elastically Restrained ◽  
Structural Engineers

Vibration of a circular cylindrical shell with elastic boundary restraints is of interest to both researchers and structural engineers. This class of problems, however, is far less attempted in the literature than its counterparts for beams and plates. In this paper, a general solution method is presented for the vibration analysis of cylindrical shells with elastic boundary supports. This method universally applies to shells with a wide variety of boundary conditions including all 136 classical (homogeneous) boundary conditions which represent the special cases when the stiffnesses for the restraining springs are set as either zero or infinity. The Rayleigh–Ritz procedure based on the Donnell–Mushtari theory is utilized to find the displacement solutions in the form of the modified Fourier series expansions. Numerical examples are given to demonstrate the accuracy and reliability of the current solution method. The modal characteristics of elastically restrained shells are discussed against different supporting stiffnesses and configurations.

scholarly journals Effects of Boundary Conditions on the Parametric Resonance of Cylindrical Shells under Axial Loading

1998 ◽  
Vol 5 (5-6) ◽  
pp. 343-354 ◽  
Author(s):  
T.Y. Ng ◽  
K.Y. Lam
Keyword(s):  
Boundary Conditions ◽  
Cylindrical Shells ◽  
Axial Loading ◽  
Various Boundary Conditions ◽  
Transverse Modes ◽  
First Approximation ◽  
Ritz Procedure ◽  
Circular Cylindrical Shells ◽  
The Stability ◽  
Parametric Response

In this paper, a formulation for the dynamic stability analysis of circular cylindrical shells under axial compression with various boundary conditions is presented. The present study uses Love’s first approximation theory for thin shells and the characteristic beam functions as approximate axial modal functions. Applying the Ritz procedure to the Lagrangian energy expression yields a system of Mathieu–Hill equations the stability of which is analyzed using Bolotin’s method. The present study examines the effects of different boundary conditions on the parametric response of homogeneous isotropic cylindrical shells for various transverse modes and length parameters.

An Improved Approach to Conductive Boundary Conditions for the Rayleigh-Be´nard Instability

1987 ◽  
Vol 109 (2) ◽  
pp. 378-387 ◽  
Author(s):  
J. H. Lienhard
Keyword(s):  
Thermal Conductivity ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Stability Problem ◽  
Stability Limit ◽  
Fluid Layers ◽  
The Stability ◽  
Rayleigh Numbers ◽  
Layer Problem

A technique is developed for predicting the stability limit of conductively coupled horizontal fluid layers heated from below and cooled above. The approach presented gives exact solutions of the stability problem and is numerically much simpler than previous multilayer solutions. Critical Rayleigh numbers are obtained for the case of three and four fluid layers separated by equally spaced identical midlayers of various thicknesses and conductivities with isothermal outer walls and for the symmetric two-layer problem with outer walls of finite thermal conductivity. Other configurations are considered briefly.

scholarly journals The two-dimensional hydrodynamical theory of moving aerofoils. IV

1947 ◽  
Vol 188 (1015) ◽  
pp. 439-463
Keyword(s):  
Stability Problem ◽  
Two Dimensional ◽  
Centre Of Gravity ◽  
First Approximation ◽  
Von Karman ◽  
Moving Cylinder ◽  
Period Equation ◽  
The Stability ◽  
Von Kármán ◽  
Hydrodynamical Theory

In the first part of this paper opportunity has been taken to make some adjustments in certain general formulae of previous papers, the necessity for which appeared in discussions with other workers on this subject. The general results thus amended are then applied to a general discussion of the stability problem including the effect of the trailing wake which was deliberately excluded in the previous paper. The general conclusion is that to a first approximation the wake, as usually assumed, has little or no effect on the reality of the roots of the period equation, but that it may introduce instability of the oscillations, if the centre of gravity of the element is not sufficiently far forward. During the discussion contact is made with certain partial results recently obtained by von Karman and Sears, which are shown to be particular cases of the general formulae. An Appendix is also added containing certain results on the motion of a vortex behind a moving cylinder, which were obtained to justify certain of the assumptions underlying the trail theory.

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