Elasticity Solution for a Radially Nonhomogeneous Hollow Circular Cylinder

1999 ◽  
Vol 66 (3) ◽  
pp. 598-606 ◽  
Author(s):  
Xiangzhou Zhang ◽  
Norio Hasebe
Keyword(s):  
Circular Cylinder ◽  
Continuous Functions ◽  
Variable Coefficients ◽  
Circular Cylinders ◽  
Explicit Solutions ◽  
Elasticity Solution ◽  
First Order ◽  
Hollow Circular Cylinder ◽  
Homogeneous Elasticity ◽  
Ordinary Differential Equation Systems

An exact elasticity solution is developed for a radially nonhomogeneous hollow circular cylinder of exponential Young’s modulus and constant Poisson’s ratio. In the solution, the cylinder is first approximated by a piecewise homogeneous one, of the same overall dimension and composed of perfectly bonded constituent homogeneous hollow circular cylinders. For each of the constituent cylinders, the solution can be obtained from the theory of homogeneous elasticity in terms of several constants. In the limit case when the number of the constituent cylinders becomes unboundedly large and their thickness tends to infinitesimally small, the piecewise homogeneous hollow circular cylinder reverts to the original nonhomogeneous one, and the constants contained in the solutions for the constituent cylinders turn into continuous functions. These functions, governed by some systems of first-order ordinary differential equations with variable coefficients, stand for the exact elasticity solution of the nonhomogeneous cylinder. Rigorous and explicit solutions are worked out for the ordinary differential equation systems, and used to generate a number of numerical results. It is indicated in the discussion that the developed method can also be applied to hollow circular cylinders with arbitrary, continuous radial nonhomogeneity.

Analysis of Thermo-Mechanical Stresses in Laminated Hollow Circular Cylinder with Finite Length

2011 ◽  
Vol 462-463 ◽  
pp. 1182-1187
Author(s):  
Hong Jin Zhao ◽  
Zhu Shan Shao ◽  
Min Zhe Wu
Keyword(s):  
Circular Cylinder ◽  
Finite Length ◽  
Present Method ◽  
Mechanical Stresses ◽  
Stress Fields ◽  
Circular Cylinders ◽  
Variable Separation ◽  
Simply Supported ◽  
Hollow Circular Cylinder ◽  
Variable Separation Approach

Thermo-mechanical stresses analysis of laminated hollow circular cylinder with finite length are carried out in this study based on the theory of laminated composites. The hollow circular cylinders with finite length are simply supported at four edges and are subjected to nonuniform thermal and mechanical loadings on the inner and outer surfaces. Analytical solutions of temperature distribution and thermo-mechanical stress fields are derived by using variable separation approach and series solving method. A four -layer laminated hollow circular cylinder with finite length is numerically analyzed by using the present method. All results are graphically presented and briefly discussed.

Designing Experiments for Model Identification of the Nitrification Process

1991 ◽  
Vol 24 (6) ◽  
pp. 9-16 ◽  
Author(s):  
P. J. Ossenbruggen ◽  
H. Spanjers ◽  
H. Aspegren ◽  
A. Klapwijk
Keyword(s):  
Mechanistic Model ◽  
Nonlinear Differential Equations ◽  
Model Identification ◽  
Reaction Rates ◽  
Variable Coefficients ◽  
Model Specification ◽  
First Order ◽  
Interactive Behavior ◽  
Batch Tests ◽  
Nitrification Process

A series of batch tests were performed to study the competition for oxygen by Nitrosomonas and Nitrobacter in the nitrification of ammonia in activated sludge. Oxygen uptake rate (OUR) and dynamic (compartment) models describing the process are proposed and tested. The OUR model is described by a Monod relationship and the biogradation process by a set of first order nonlinear differential equations with variable coefficients. The results show a mechanistic model and ten reaction rates are sufficient to capture the interactive behavior of the nitrification process. Methods for model specification, calibrating, and testing the model and the design of additional experiments are described.

scholarly journals Oscillatory Behaviour of a First-Order Neutral Differential Equation in relation to an Old Open Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
K. C. Panda ◽  
R. N. Rath ◽  
S. K. Rath
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
First Order ◽  
Neutral Delay Differential Equation ◽  
Delay Differential ◽  
Oscillation And Nonoscillation

In this paper, we obtain sufficient conditions for oscillation and nonoscillation of the solutions of the neutral delay differential equation yt−∑j=1kpjtyrjt′+qtGygt−utHyht=ft, where pj and rj for each j and q,u,G,H,g,h, and f are all continuous functions and q≥0,u≥0,ht<t,gt<t, and rjt<t for each j. Further, each rjt, gt, and ht⟶∞ as t⟶∞. This paper improves and generalizes some known results.

scholarly journals Some Further Results on Oscillations for Neutral Delay Differential Equations with Variable Coefficients

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Fatima N. Ahmed ◽  
Rokiah Rozita Ahmad ◽  
Ummul Khair Salma Din ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Variable Coefficients ◽  
Oscillatory Behaviour ◽  
Neutral Delay ◽  
Neutral Equations ◽  
First Order ◽  
All Solutions ◽  
Neutral Delay Differential Equations ◽  
Delay Differential

We study the oscillatory behaviour of all solutions of first-order neutral equations with variable coefficients. The obtained results extend and improve some of the well-known results in the literature. Some examples are given to show the evidence of our new results.

Steady approach of unsteady low-Reynolds-number flow past two rotating circular cylinders

2013 ◽  
Vol 736 ◽  
pp. 414-443 ◽  
Author(s):  
Y. Ueda ◽  
T. Kida ◽  
M. Iguchi
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Stokes Equations ◽  
Low Reynolds Number ◽  
Vortex Method ◽  
The Self ◽  
Circular Cylinders ◽  
Far Field ◽  
Flow Past ◽  
Low Reynolds

AbstractThe long-time viscous flow about two identical rotating circular cylinders in a side-by-side arrangement is investigated using an adaptive numerical scheme based on the vortex method. The Stokes solution of the steady flow about the two-cylinder cluster produces a uniform stream in the far field, which is the so-called Jeffery’s paradox. The present work first addresses the validation of the vortex method for a low-Reynolds-number computation. The unsteady flow past an abruptly started purely rotating circular cylinder is therefore computed and compared with an exact solution to the Navier–Stokes equations. The steady state is then found to be obtained for $t\gg 1$ with ${\mathit{Re}}_{\omega } {r}^{2} \ll t$, where the characteristic length and velocity are respectively normalized with the radius ${a}_{1} $ of the circular cylinder and the circumferential velocity ${\Omega }_{1} {a}_{1} $. Then, the influence of the Reynolds number ${\mathit{Re}}_{\omega } = { a}_{1}^{2} {\Omega }_{1} / \nu $ about the two-cylinder cluster is investigated in the range $0. 125\leqslant {\mathit{Re}}_{\omega } \leqslant 40$. The convection influence forms a pair of circulations (called self-induced closed streamlines) ahead of the cylinders to alter the symmetry of the streamline whereas the low-Reynolds-number computation (${\mathit{Re}}_{\omega } = 0. 125$) reaches the steady regime in a proper inner domain. The self-induced closed streamline is formed at far field due to the boundary condition being zero at infinity. When the two-cylinder cluster is immersed in a uniform flow, which is equivalent to Jeffery’s solution, the streamline behaves like excellent Jeffery’s flow at ${\mathit{Re}}_{\omega } = 1. 25$ (although the drag force is almost zero). On the other hand, the influence of the gap spacing between the cylinders is also investigated and it is shown that there are two kinds of flow regimes including Jeffery’s flow. At a proper distance from the cylinders, the self-induced far-field velocity, which is almost equivalent to Jeffery’s solution, is successfully observed in a two-cylinder arrangement.

APPROXIMATIVE PROPERTIES OF ABEL–POISSON-TYPE OPERATORS ON THE GENERALIZED HÖLDER CLASSES

2021 ◽  
Vol 1 ◽  
pp. 76-83
Author(s):  
Yuri I. Kharkevich ◽  
◽  
Alexander G. Khanin ◽  
Keyword(s):  
Modulus Of Continuity ◽  
Applied Mathematics ◽  
Continuous Functions ◽  
Elliptic Type ◽  
Periodic Functions ◽  
French Mathematician ◽  
First Order ◽  
Function Classes ◽  
In The Beginning ◽  
Poisson Type

The paper deals with topical issues of the modern applied mathematics, in particular, an investigation of approximative properties of Abel–Poisson-type operators on the so-called generalized Hölder’s function classes. It is known, that by the generalized Hölder’s function classes we mean the classes of continuous -periodic functions determined by a first-order modulus of continuity. The notion of the modulus of continuity, in turn, was formulated in the papers of famous French mathematician Lebesgue in the beginning of the last century, and since then it belongs to the most important characteristics of smoothness for continuous functions, which can describe all natural processes in mathematical modeling. At the same time, the Abel-Poisson-type operators themselves are the solutions of elliptic-type partial differential equations. That is why the results obtained in this paper are significant for subsequent research in the field of applied mathematics. The theorem proved in this paper characterizes the upper bound of deviation of continuous -periodic functions determined by a first-order modulus of continuity from their Abel–Poisson-type operators. Hence, the classical Kolmogorov–Nikol’skii problem in A.I. Stepanets sense is solved on the approximation of functions from the classes by their Abel–Poisson-type operators. We know, that the Abel–Poisson-type operators, in partial cases, turn to the well-known in applied mathematics Poisson and Jacobi–Weierstrass operators. Therefore, from the obtained theorem follow the asymptotic equalities for the upper bounds of deviation of functions from the Hölder’s classes of order from their Poisson and Jacobi–Weierstrass operators, respectively. The obtained equalities generalize the known in this direction results from the field of applied mathematics.

Second-order recombination in a parallel shear flow

1989 ◽  
Vol 200 ◽  
pp. 389-407 ◽  
Author(s):  
Ronald Smith
Keyword(s):  
Shear Flow ◽  
Concentration Distribution ◽  
Second Order ◽  
Explicit Solutions ◽  
Far Field ◽  
First Order ◽  
Parallel Shear Flow

For a reactive solute, with weak second-order recombination, an investigation is made of the near-source behaviour (where concentrations are high), and of the far field (where the recombination has an accumulative effect). Despite the loss of material and increased spread due to recombination, the far-field concentration distribution is shown to be nearly Gaussian. This permits a simplified (Gaussian) treatment of the chemical nonlinearity. Explicit solutions are given for the total amount of solute, variance and kurtosis for solutes with no first-order reactions.

A Model for High-Reynolds-Number Flow Past Rough-Walled Circular Cylinders

1977 ◽  
Vol 99 (3) ◽  
pp. 486-493 ◽  
Author(s):  
O. Gu¨ven ◽  
V. C. Patel ◽  
C. Farell
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Circular Cylinder ◽  
Turbulent Boundary Layer ◽  
Pressure Coefficient ◽  
Empirical Relation ◽  
Reynolds Numbers ◽  
Boundary Layer Separation ◽  
Circular Cylinders ◽  
Mean Flow

A simple analytical model for two-dimensional mean flow at very large Reynolds numbers around a circular cylinder with distributed roughness is presented and the results of the theory are compared with experiment. The theory uses the wake-source potential-flow model of Parkinson and Jandali together with an extension to the case of rough-walled circular cylinders of the Stratford-Townsend theory for turbulent boundary-layer separation. In addition, a semi-empirical relation between the base-pressure coefficient and the location of separation is used. Calculation of the boundary-layer development, needed as part of the theory, is accomplished using an integral method, taking into account the influence of surface roughness on the laminar boundary layer and transition as well as on the turbulent boundary layer. Good agreement with experiment is shown by the results of the theory. The significant effects of surface roughness on the mean-pressure distribution on a circular cylinder at large Reynolds numbers and the physical mechanisms giving rise to these effects are demonstrated by the model.

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