On the Stresses in a Rotating Disk of Variable Thickness

1952 ◽  
Vol 19 (3) ◽  
pp. 263-266
Author(s):  
Ti-Chiang Lee
Keyword(s):  
Variable Thickness ◽  
Stress Function ◽  
Hypergeometric Functions ◽  
Analytic Solution ◽  
Radial Distance ◽  
Rotating Disk ◽  
Numerical Examples ◽  
Confluent Hypergeometric Functions ◽  
Method Of Solution ◽  
Two Parameters

Abstract This paper presents an analytic solution of the stresses in a rotating disk of variable thickness. By introducing two parameters, the profile of the disk is assumed to vary exponentially with any power of the radial distance from the center of the disk. In some respects this solution may be considered as a generalization of Malkin’s solution, but it differs essentially from the latter in the method of solution. Here, the stresses are solved through a stress function instead of being solved directly. The required stress function is expressed in terms of confluent hypergeometric functions. Numerical examples are also shown for illustration.

On Transverse Vibrations of a Rotating Disk of Uniform Strength

1992 ◽  
Vol 59 (1) ◽  
pp. 234-235 ◽  
Author(s):  
Ugˇur Gu¨ven
Keyword(s):  
Closed Form ◽  
Hypergeometric Functions ◽  
Closed Form Solution ◽  
Rotating Disk ◽  
Form Solution ◽  
Transverse Motion ◽  
Confluent Hypergeometric Functions ◽  
Transverse Vibrations ◽  
Uniform Strength

Transverse, axisymmetric vibrations of a rotating disk of uniform strength is studied. Closed-form solution for the equation of transverse motion is obtained in terms of confluent hypergeometric functions.

Stresses in a Perforated Wedge

1973 ◽  
Vol 40 (3) ◽  
pp. 759-766 ◽  
Author(s):  
Chih-Bing Ling ◽  
Chang-Ming Hsu
Keyword(s):  
Boundary Conditions ◽  
Circular Hole ◽  
Stress Function ◽  
The Other ◽  
Numerical Examples ◽  
Biharmonic Functions ◽  
Method Of Solution ◽  
The Given ◽  
Infinite Wedge

This paper presents a method of solution for an infinite wedge containing a symmetrically located circular hole. The solution is formulated separately according to the given in-plane edge tractions being even or odd with respect to the axis of the wedge. In either case, the stress function is constructed as the sum of four parts of biharmonic functions, two in the form of integrals and the other two in the form of series, in addition to a basic stress function for an otherwise unperforated wedge. The four parts as a whole give no traction along the edges and no stress at infinity of the wedge. Together with the basic stress function, the boundary conditions of no traction at the rim of hole are adjusted. Complex expressions are used in adjusting the boundary conditions. Finally, numerical examples are given for illustration.

Stresses in a Perforated Strip

1957 ◽  
Vol 24 (3) ◽  
pp. 365-375
Author(s):  
Chih-Bing Ling
Keyword(s):  
Stress Function ◽  
Harmonic Functions ◽  
Analytic Solution ◽  
Complete Solution ◽  
Classical Problem ◽  
Stress System ◽  
Infinite Strip ◽  
Numerical Examples ◽  
Biharmonic Functions ◽  
Transverse Bending

Abstract This paper presents an analytic solution of the classical problem dealing with the stresses in an infinite strip having an unsymmetrically located perforating hole. The solution is applicable to any stress system acting in the strip, which is symmetrical with respect to the line of symmetry of the strip. The required stress function is constructed by using four series of biharmonic functions and a bihamonic integral. The four series of biharmonic functions are formed from a class of periodic harmonic functions specially constructed for the purpose. The solution can be regarded as a complete solution of the problem in the sense that, unlike the previous solutions by Howland, Stevenson, and Knight for a symmetrically perforated strip, it is valid in the entire strip. Numerical examples are given for the fundamental cases of longitudinal tension and transverse bending.

scholarly journals Some results on (p, k)-extension of the hypergeometric functions

2021 ◽  
Author(s):  
Mohamed Abdalla ◽  
H Hidan
Keyword(s):  
Differential Equations ◽  
Hypergeometric Functions ◽  
Special Functions ◽  
Natural Extension ◽  
Convergence Properties ◽  
Basic Properties ◽  
Confluent Hypergeometric Functions ◽  
Derivative Formulas ◽  
Two Parameters

Abstract In this study, we investigate a new natural extension of hypergeometric functions with the two parameters p and k which is so called (p, k)-extended hypergeometric functions”. In particular, we introduce the (p, k)-extended Gauss and Kummer (or confluent) hypergeometric functions. The basic properties of the (p, k)-extended Gauss and Kummer hypergeometric functions, including convergence properties, integral and derivative formulas, contiguous function relations and differential equations. Since the latter functions contain many of the familiar special functions as sub-cases, this extension is enriches theory of k-special functions.

scholarly journals Impact of autocatalytic chemical reaction in an Ostwald-de-Waele nanofluid flow past a rotating disk with heterogeneous catalysis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bai Yu ◽  
Muhammad Ramzan ◽  
Saima Riasat ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Differential Equations ◽  
Chemical Reaction ◽  
Power Law ◽  
Variable Thickness ◽  
Rotating Disk ◽  
Thermal Profile ◽  
Nanofluid Flow ◽  
Power Law Index

AbstractThe nanofluids owing to their alluring attributes like enhanced thermal conductivity and better heat transfer characteristics have a vast variety of applications ranging from space technology to nuclear reactors etc. The present study highlights the Ostwald-de-Waele nanofluid flow past a rotating disk of variable thickness in a porous medium with a melting heat transfer phenomenon. The surface catalyzed reaction is added to the homogeneous-heterogeneous reaction that triggers the rate of the chemical reaction. The added feature of the variable thermal conductivity and the viscosity instead of their constant values also boosts the novelty of the undertaken problem. The modeled problem is erected in the form of a system of partial differential equations. Engaging similarity transformation, the set of ordinary differential equations are obtained. The coupled equations are numerically solved by using the bvp4c built-in MATLAB function. The drag coefficient and Nusselt number are plotted for arising parameters. The results revealed that increasing surface catalyzed parameter causes a decline in thermal profile more efficiently. Further, the power-law index is more influential than the variable thickness disk index. The numerical results show that variations in dimensionless thickness coefficient do not make any effect. However, increasing power-law index causing an upsurge in radial, axial, tangential, velocities, and thermal profile.

scholarly journals On the birthday problem: some generalizations and applications

2003 ◽  
Vol 2003 (60) ◽  
pp. 3827-3840 ◽  
Author(s):  
P. N. Rathie ◽  
P. Zörnig
Keyword(s):  
Probability Distribution ◽  
Random Graph ◽  
Generating Functions ◽  
Hypergeometric Functions ◽  
Exact Probability ◽  
Confluent Hypergeometric Functions ◽  
Birthday Problem ◽  
Exact Probability Distribution

We study the birthday problem and some possible extensions. We discuss the unimodality of the corresponding exact probability distribution and express the moments and generating functions by means of confluent hypergeometric functionsU(−;−;−)which are computable using the software Mathematica. The distribution is generalized in two possible directions, one of them consists in considering a random graph with a single attracting center. Possible applications are also indicated.

scholarly journals FOUR-PARTICLE ANYON EXCITON: BOSON APPROXIMATION

1995 ◽  
Vol 09 (02) ◽  
pp. 123-133 ◽  
Author(s):  
M. E. Portnoi ◽  
E. I. Rashba
Keyword(s):  
Angular Momentum ◽  
Electron Density ◽  
Ground State ◽  
Hypergeometric Functions ◽  
Energy Levels ◽  
Confluent Hypergeometric Functions ◽  
Full Symmetry ◽  
Hole Confinement ◽  
Boson Approximation

A theory of anyon excitons consisting of a valence hole and three quasielectrons with electric charges –e/3 is presented. A full symmetry classification of the k = 0 states is given, where k is the exciton momentum. The energy levels of these states are expressed by quadratures of confluent hypergeometric functions. It is shown that the angular momentum L of the exciton ground state depends on the distance between the electron and hole confinement planes and takes the values L = 3n, where n is an integer. With increasing k the electron density shows a spectacular splitting on bundles. At first a single anyon splits off of the two-anyon core, and finally all anyons become separated.

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