Exact Two-Dimensional Theory of Spherical Spiral Groove Bearings

1980 ◽  
Vol 102 (4) ◽  
pp. 430-438 ◽  
Author(s):  
Susumu Murata ◽  
Yutaka Miyake ◽  
Nobuyoshi Kawabata
Keyword(s):  
Exact Solution ◽  
Iterative Method ◽  
Load Capacity ◽  
Perturbation Technique ◽  
Fluid Film ◽  
Two Dimensional ◽  
Spiral Groove ◽  
Dimensional Theory ◽  
New Iterative Method ◽  
Spiral Groove Bearing

This paper is concerned with a method of obtaining exact solution for the flow of fluid film of spherical spiral groove bearing. The problem is analyzed for three cases where the centers of two elements of a bearing coincide, slightly offset vertically and arbitrarily offset vertically. Effects of bearing parameters on the load capacity are examined. A perturbation technique is applied for the case of slight offset of centers of two spheres, and the stiffness is calculated. For the case of large offset, a new iterative method is developed in this paper.

scholarly journals By using a new iterative method to the generalized system Zakharov-Kuznetsov and estimate the best parameters via applied the pso algorithm

2020 ◽  
Vol 19 (2) ◽  
pp. 1055 ◽  
Author(s):  
Abeer Aldabagh
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Iterative Method ◽  
Numerical Method ◽  
Pso Algorithm ◽  
Accurate Solution ◽  
Generalized System ◽  
A New Technique ◽  
Best Parameters ◽  
New Iterative Method

In this paper, a new iterative method was applied to the Zakharov-Kuznetsov system to obtain the approximate solution and the results were close to the exact solution, A new technique has been proposed to reach the lowest possible error, and the closest accurate solution to the numerical method is to link the numerical method with the pso algorithm which is denoted by the symbol (NIM-PSO). The results of the proposed Technique showed that they are highly efficient and very close to the exact solution, and they are also of excellent effectiveness for treating partial differential equation systems.

scholarly journals New Iterative Method for the Solution of Fractional Damped Burger and Fractional Sharma-Tasso-Olver Equations

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Mohammad Jibran Khan ◽  
Rashid Nawaz ◽  
Samreen Farid ◽  
Javed Iqbal
Keyword(s):  
Exact Solution ◽  
Iterative Method ◽  
Fractional Order ◽  
Approximate Solutions ◽  
Differential Transform Method ◽  
Transform Method ◽  
Order Solution ◽  
Differential Transform ◽  
New Iterative Method ◽  
Good Agreement

The new iterative method has been used to obtain the approximate solutions of time fractional damped Burger and time fractional Sharma-Tasso-Olver equations. Results obtained by the proposed method for different fractional-order derivatives are compared with those obtained by the fractional reduced differential transform method (FRDTM). The 2nd-order approximate solutions by the new iterative method are in good agreement with the exact solution as compared to the 5th-order solution by the FRDTM.

scholarly journals The best parameters selection using pso algorithm to solving for ito system by new iterative technique

2020 ◽  
Vol 18 (3) ◽  
pp. 1638
Author(s):  
Karam Adel Abed ◽  
Abeer Abdulkhaleq Ahmad
Keyword(s):  
Exact Solution ◽  
Iterative Method ◽  
Approximate Solutions ◽  
Pso Algorithm ◽  
High Accuracy ◽  
Iterative Technique ◽  
Parameters Selection ◽  
A New Technique ◽  
Best Parameters ◽  
New Iterative Method

<p>The main aim of this study is to obtain the best approximate solution for the nonlinear Ito system by applying the new iterative method, A new technique has been proposed that combines the new iterative method with the particle optimization algorithm. The most important distinctive of this work is the analysis of errors between the exact solution of the system and the approximate solutions, which showed us that these approximate solutions of the proposed technique in particular have high accuracy because they converge significantly from the exact solution.</p>

scholarly journals Solutions of Two-Dimensional Nonlinear Sine-Gordon Equation via Triple Laplace Transform Coupled with Iterative Method

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Alemayehu Tamirie Deresse ◽  
Yesuf Obsie Mussa ◽  
Ademe Kebede Gizaw
Keyword(s):  
Exact Solution ◽  
Iterative Method ◽  
Laplace Transform ◽  
Gordon Equation ◽  
Type Systems ◽  
Mathematical Physics ◽  
Test Problems ◽  
Two Dimensional ◽  
Sine Gordon Equation ◽  
The Given

This article presents triple Laplace transform coupled with iterative method to obtain the exact solution of two-dimensional nonlinear sine-Gordon equation (NLSGE) subject to the appropriate initial and boundary conditions. The noise term in this equation is vanished by successive iterative method. The proposed technique has the advantage of producing exact solution, and it is easily applied to the given problems analytically. Four test problems from mathematical physics are taken to show the accuracy, convergence, and the efficiency of the proposed method. Furthermore, the results indicate that the introduced method is promising for solving other type systems of NLPDEs.

Exact Two-Dimensional Analysis of Circular Disk Spiral Groove Bearing (Part II)

1979 ◽  
Vol 101 (4) ◽  
pp. 431-436
Author(s):  
S. Murata ◽  
Y. Miyake ◽  
N. Kawabata
Keyword(s):  
Velocity Field ◽  
Infinite Number ◽  
Thrust Bearing ◽  
Pressure Field ◽  
Circular Disk ◽  
Pressure Jump ◽  
Two Dimensional ◽  
Spiral Groove ◽  
Bearing Part ◽  
Spiral Groove Bearing

Two-dimensional pressure field of circular disk grooved thrust bearing when it does three kinds of elementary unsteady motions has been successfully analyzed using potential flow theory. The cancellation of the pressure jump by putting line vortices on the groove-land boundaries is demonstrated to be useful. The analysis of the velocity field can be carried out only in one basic domain, while the pressure field must be calculated in every domain by doing rather complicated selection among infinite number of values of inverse tangent.

scholarly journals Analytic and numerical solution for duffing equations

2016 ◽  
Vol 5 (2) ◽  
pp. 115 ◽  
Author(s):  
Majeed AL-Jawary ◽  
Sayl Abd- AL- Razaq
Keyword(s):  
Exact Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Iterative Method ◽  
Numerical Solution ◽  
Ordinary Differential Equations ◽  
Numerical Solutions ◽  
Duffing Equations ◽  
Linear And Nonlinear ◽  
New Iterative Method

<p>Daftardar Gejji and Hossein Jafari have proposed a new iterative method for solving many of the linear and nonlinear equations namely (DJM). This method proved already the effectiveness in solved many of the ordinary differential equations, partial differential equations and integral equations. The main aim from this paper is to propose the Daftardar-Jafari method (DJM) to solve the Duffing equations and to find the exact solution and numerical solutions. The proposed (DJM) is very effective and reliable, and the solution is obtained in the series form with easily computed components. The software used for the calculations in this study was MATHEMATICA<sup>®</sup> 9.0.</p>

Exact Two-Dimensional Analysis of Circular Disk Spiral Groove Bearing (Part I)

1979 ◽  
Vol 101 (4) ◽  
pp. 424-430 ◽  
Author(s):  
S. Murata ◽  
Y. Miyake ◽  
N. Kawabata
Keyword(s):  
Circular Disk ◽  
Inviscid Flow ◽  
Fluid Film ◽  
Two Dimensional ◽  
Spiral Groove ◽  
Singularity Method ◽  
Load Carrying ◽  
Circular Wing ◽  
Basic Equations ◽  
Detailed Technique

Basic equations and idea of the method are described concerning the new two-dimensional theory of thin fluid film of spiral groove bearings. Two-dimensional inviscid flow theory of circular wing lattice is the basis of the proposed method. Detailed technique to perform numerical calculation has been established utilizing singularity method. Two-dimensional pressure formation of the fluid film is calculated together with load carrying capacity.

Membrane theory

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Three Dimensional ◽  
Thin Sheets ◽  
Two Dimensional ◽  
Leading Order ◽  
Membrane Theory ◽  
Dimensional Theory ◽  
Small Thickness

This chapter develops two-dimensional membrane theory as a leading order small-thickness approximation to the three-dimensional theory for thin sheets. Applications to axisymmetric equilibria are developed in detail, and applied to describe the phenomenon of bulge propagation in cylinders.

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