scholarly journals Model of an electro-rheological shock absorber and coupled problem for partial and ordinary differential equations with variable unknown domain

2007 ◽  
Vol 18 (4) ◽  
pp. 513-536 ◽  
Author(s):  
W. G. LITVINOV ◽  
T. RAHMAN ◽  
R. H. W. HOPPE
Keyword(s):  
Numerical Simulation ◽  
Exact Solution ◽  
Shock Absorber ◽  
Linear Equations ◽  
Approximate Solutions ◽  
Electrorheological Fluid ◽  
Coupled Problem ◽  
Uniqueness Of The Solution ◽  
Convergence Of Approximate Solutions ◽  
Non Linear Equations

Amortization of a shock in an electro-rheological shock absorber is carried out in the motion of a piston in an electrorheological fluid. The drag force acting on the piston is regulated by varying the voltage applied to electrodes. A model of an electrorheological shock absorber is constructed. A problem on shock absorber reduces to the solution of a coupled problem for motion equation of the piston and non-linear equations of fluid flow in an unknown domain that varies with the time. A method of semi-discretization for approximate solution of the coupled problem is considered. Results on the existence and on the uniqueness of the solution of the coupled problem are obtained. Convergence of approximate solutions to the exact solution is proved. Numerical simulation of the operation of the shock absorber is performed.

scholarly journals On a class of non-linear differential equations with exact solution

2012 ◽  
Vol 34 (1) ◽  
pp. 7-17
Author(s):  
Dao Huy Bich ◽  
Nguyen Dang Bich
Keyword(s):  
Exact Solution ◽  
Differential Equations ◽  
Exact Solutions ◽  
Solid Mechanics ◽  
Linear Equations ◽  
Linear Differential Equations ◽  
Second Order Differential Equations ◽  
Non Linear ◽  
Linear Differential ◽  
Non Linear Equations

The present paper deals with a class of non-linear ordinary second-order differential equations with exact solutions. A procedure for finding the general exact solution based on a known particular one is derived. For illustration solutions of some non-linear equations occurred in many problems of solid mechanics are considered.

Dynamic modelling of planar flexible manipulators: Computational and algorithmic efficiency

1997 ◽  
Vol 211 (2) ◽  
pp. 119-133 ◽  
Author(s):  
Y-J Shyu ◽  
K F Gill
Keyword(s):  
Linear Equations ◽  
Dynamic Modelling ◽  
Approximate Solutions ◽  
Experimental Information ◽  
Open Loop ◽  
Flexible Manipulator ◽  
Time Step ◽  
End Effector ◽  
And Control ◽  
Non Linear Equations

Traditionally, many robot arms are very rigid in construction; this was believed to be necessary for accurate placement and repeatability but led to higher material costs and increased energy consumption. Higher operational speeds and the use of lightweight materials cause elastic deformations to occur during the operation of the manipulator. These deformations degrade the path-tracking performance of the end-effector. The dynamic behaviour of a flexible manipulator is described mathematically by non-linear equations which are difficult to solve analytically. Unfortunately, there is currently no experimental information available with which to compare this design of flexible structure. For design and control purposes, it is suggested in this paper that it is more appropriate to employ approximate solutions with the emphasis on the development of a fast computational algorithm. An analytical study was undertaken to investigate the relevant uncertainties that are either inappropriately described or unavailable in the literature. The purpose of the paper is essentially to include the initial deflections in the simulation, to select the size of the time step, to select the models for emulating the end-effector, payload and joint actuator and, finally, to suppress the uncontrollable off-plane vibrations when encountered. When this knowledge has been obtained, the design and development of the simulation process can begin. In order to demonstrate the practicability of the open-loop simulation proposed and test the software, two representative models were investigated.

scholarly journals Fuzzy Version of Secant Method to Solve Fuzzy Non-Linear Equations

2016 ◽  
Vol 35 ◽  
pp. 127-134
Author(s):  
Goutam Kumar Saha ◽  
Shapla Shirin
Keyword(s):  
Linear Equation ◽  
Linear Equations ◽  
Approximate Solutions ◽  
Secant Method ◽  
Graphical Representations ◽  
Non Linear Equation ◽  
Non Linear ◽  
Optimum Solution ◽  
Non Linear Equations

In this paper fuzzy version of secant method has been introduced to obtain approximate solutions of a fuzzy non-linear equation. Graphical representations of the approximate solutions have also been shown. The idea of converging to the root to the desired degree of accuracy, which is the optimum solution, of a fuzzy non-linear equation has been focused.GANIT J. Bangladesh Math. Soc.Vol. 35 (2015) 127-134

THE STRONG-NORM CONVERGENCE OF A PROJECTION-DIFFERENCE METHOD OF SOLUTION OF A PARABOLIC EQUATION WITH THE PERIODIC CONDITION ON THE SOLUTION

2018 ◽  
pp. 617-623
Author(s):  
Andrei Sergeevich Bondarev
Keyword(s):  
Exact Solution ◽  
Parabolic Equation ◽  
Difference Method ◽  
Approximate Solutions ◽  
Linear Parabolic Equation ◽  
Periodic Condition ◽  
Method Of Solution ◽  
The Galerkin Method ◽  
Convergence Of Approximate Solutions ◽  
Strong Norm

A smooth soluble abstract linear parabolic equation with the periodic condition on the solution is treated in a separable Hilbert space. This problem is solved approximately by a projection-difference method using the Galerkin method in space and the implicit Euler scheme in time. Effective both in time and in space strong-norm error estimates for approximate solutions, which imply convergence of approximate solutions to the exact solution and order of convergence rate depending of the smoothness of the exact solution, are obtained.

Analytic Approximate Solutions and Numerical Results for Stagnation Point Flow of Jeffrey Fluid Towards an Off-Centered Rotating Disk

2014 ◽  
Vol 31 (2) ◽  
pp. 201-215 ◽  
Author(s):  
N. A. Khan ◽  
S. Khan ◽  
F. Riaz
Keyword(s):  
Linear Equations ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Approximate Solutions ◽  
Jeffrey Fluid ◽  
Analysis Method ◽  
Convergence Region ◽  
Homotopy Analysis ◽  
Special Case ◽  
Non Linear Equations

AbstractThe present paper studies the three-dimensional, off centered stagnation flow of a Jeffrey fluid over a rotating disk. The governing non-linear equations and their associated boundary conditions are transformed into coupled ordinary differential equations by utilizing an appropriate similarity transformation. Homotopy analysis method is utilized to evaluate the analytical solution in the form of infinite series. Also, the convergence region of the obtained solution is determined and plotted. The effects of pertaining parameters on radial, azimuthal and induced velocities of the fluid flow are presented graphically and discussed. Moreover comparisons have also been made with the previous results as a special case.

scholarly journals Exact solution and high frequency asymptotic methods in the wedge diffraction problem

2016 ◽  
Vol 14 (38) ◽  
pp. 9-28
Author(s):  
Hernan G. Triana ◽  
Andrés Navarro Cadavid
Keyword(s):  
Numerical Simulation ◽  
Exact Solution ◽  
Asymptotic Solution ◽  
High Frequency ◽  
Asymptotic Methods ◽  
Diffraction Problem ◽  
Approximate Solutions ◽  
Point Of View ◽  
Simulation Tool ◽  
Computational Point

AbstractThe Sommerfeld exact solution for canonical 2D wedge diffraction problem with perfectly conducting surfaces is presented. From the integral formulation of the problem, the Malyuzhinets solution is obtained and this result is extended to obtain the general impedance solution of canonical 2D wedge problem. Keller’s asymptotic solution is developed and the general formulation of exact solution it’s used to obtain general asymptotic methods for approximate solutions useful from the computational point of view. A simulation tool is used to compare numerical calculations of exact and asymptotic solutions. The numerical simulation of exact solution is compared to numerical simulation of an asymptoticmethod, and a satisfactory agreement found.  Accuracy dependence with frequency is verified.

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