Transients During a Railway Air Brake Release Demand

1990 ◽  
Vol 204 (1) ◽  
pp. 31-38 ◽  
Author(s):  
M A Murtaza ◽  
S B L Garg
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Difference Method ◽  
Laboratory Data ◽  
One Dimensional ◽  
The Finite Difference Method ◽  
Air Brake System ◽  
Good Agreement

This paper deals with the simulation of railway air brake release demand of a twin-pipe graduated release railway air brake system based on the solution of partial differential equations governing one-dimensional flow by the finite difference method supported by extrapolation/interpolation. Air brake release demand is simulated as an exponential input of pressure. The analysis incorporates the corrections needed to be used for various restrictions in the brake pipeline. Results are in good agreement with the laboratory data.

Chaotic Vibrations of Beams: Numerical Solution of Partial Differential Equations

1993 ◽  
Vol 60 (1) ◽  
pp. 167-174 ◽  
Author(s):  
N. S. Abhyankar ◽  
E. K. Hall ◽  
S. V. Hanagud
Keyword(s):  
Differential Equation ◽  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Difference Method ◽  
Chaotic Dynamics ◽  
Partial Differential ◽  
Galerkin Approximations ◽  
The Finite Difference Method

The objective of this paper is to examine the utility of direct, numerical solution procedures, such as finite difference or finite element methods, for partial differential equations in chaotic dynamics. In the past, procedures for solving such equations to detect chaos have utilized Galerkin approximations which reduce the partial differential equations to a set of truncated, nonlinear ordinary differential equations. This paper will demonstrate that a finite difference solution is equivalent to a Galerkin solution, and that the finite difference method is more powerful in that it may be applied to problems for which the Galerkin approximations would be difficult, if not impossible to use. In particular, a nonlinear partial differential equation which models a slender, Euler-Bernoulli beam in compression issolvedto investigate chaotic motions under periodic transverse forcing. The equation, cast as a system of firstorder partial differential equations is directly solved by an explicit finite difference scheme. The numerical solutions are shown to be the same as the solutions of an ordinary differential equation approximating the first mode vibration of the buckled beam. Then rigid stops of finite length are incorporated into the model to demonstrate a problem in which the Galerkin procedure is not applicable. The finite difference method, however, can be used to study the stop problem with prescribed restrictions over a selected subdomain of the beam. Results obtained are briefly discussed. The end result is a more general solution technique applicable to problems in chaotic dynamics.

scholarly journals Vibration Analysis of Axially Functionally Graded Non-Prismatic Euler-Bernoulli Beams Using the Finite Difference Method

2021 ◽  
Author(s):  
Valentin Fogang
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Difference Method ◽  
Vibration Analysis ◽  
Mass Density ◽  
Functionally Graded ◽  
Partial Differential ◽  
The Finite Difference Method

This paper presents an approach to the vibration analysis of axially functionally graded (AFG) non-prismatic Euler-Bernoulli beams using the finite difference method (FDM). The characteristics (cross-sectional area, moment of inertia, elastic moduli, and mass density) of AFG beams vary along the longitudinal axis. The FDM is an approximate method for solving problems described with differential or partial differential equations. It does not involve solving differential equations; equations are formulated with values at selected points of the structure. The model developed in this paper consists of formulating differential or partial differential equations with finite differences and introducing new points (additional or imaginary points) at boundaries and positions of discontinuity (concentrated loads or moments, supports, hinges, springs, and brutal change of stiffness). The introduction of additional points allows satisfying boundary and continuity conditions. Vibration analysis of AFG non-prismatic Euler-Bernoulli beams was conducted with this model, and natural frequencies were determined. Finally, the direct time integration method (DTIM) was presented. The FDM-based DTIM enabled the analysis of forced vibration of AFG non-prismatic Euler-Bernoulli beams, considering the damping. The efforts and displacements could be determined at any time.

scholarly journals Vibration Analysis of Axially Functionally Graded Non-Prismatic Timoshenko Beams Using the Finite Difference Method

2021 ◽  
Author(s):  
Valentin Fogang
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Difference Method ◽  
Vibration Analysis ◽  
Functionally Graded ◽  
Timoshenko Beams ◽  
Partial Differential ◽  
The Finite Difference Method

This paper presents an approach to the vibration analysis of axially functionally graded non-prismatic Timoshenko beams (AFGNPTB) using the finite difference method (FDM). The characteristics (cross-sectional area, moment of inertia, elastic moduli, shear moduli, and mass density) of axially functionally graded beams vary along the longitudinal axis. The Timoshenko beam theory covers cases associated with small deflections based on shear deformation considerations. The FDM is an approximate method for solving problems described with differential or partial differential equations. It does not involve solving differential equations; equations are formulated with values at selected points of the structure. The model developed in this paper consists of formulating differential or partial differential equations with finite differences and introducing new points (additional or imaginary points) at boundaries and positions of discontinuity (concentrated loads or moments, supports, hinges, springs, and brutal change of stiffness). The introduction of additional points allows satisfying boundary and continuity conditions. Vibration analysis of AFGNPTB was conducted with this model, and natural frequencies were determined. Finally, the direct time integration method (DTIM) was presented. The FDM-based DTIM enabled the analysis of forced vibration of AFGNPTB, considering the damping. The efforts and displacements could be determined at any time.

An Efficient Modified Taylor Wavelet Galerkin Method for One Dimensional Partial Differential Equations

2021 ◽  
Vol 14 ◽  
Author(s):  
Ankit Kumar ◽  
Sag Ram Verma
Keyword(s):  
Partial Differential Equations ◽  
Numerical Methods ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Galerkin Method ◽  
Difference Method ◽  
Partial Differential ◽  
One Dimensional ◽  
Wavelet Galerkin Method

Background: In this paper, a modified Taylor wavelet Galerkin method (MTWGM) based on approximation scheme is used to solve partial differential equations (PDEs), which is play an important role in electrical circuit models. Objective: The objective of this work is to give fine and accurate implementation of proposed method for the solution of PDEs, which is the best tool for the analysis of electric circuit problems. Methods: In this work, we used an effective, modified Taylor wavelet Galerkin method with its residual technique and we obtained more accurate numerical solution of the one dimensional PDEs. The Introduced wavelet method is more efficiently applicable in the comparison of some existing numerical methods such as, finite difference method, finite element method, finite volume method, spectral method etc. This method is the best tool for solving PDEs. Therefore, it has significance in the field of electrical engineering and others. Results: The experimentally four numerical problems are given which are showing the numerical results extractive by introduced method and those results compared with exact solution and other available numerical methods i.e., Hermite wavelet Galarkin method (HWGM), Finite difference method (FDM) and spectral procedures which shows that proposed method is more effective. Conclusion: This work is significantly helpful for the electrical circuits in which the governing models are available in the form of PDEs.

scholarly journals Computer modelling of a bacteria dynamics

2010 ◽  
Vol 51 ◽  
Author(s):  
Pranas Katauskis ◽  
Vladas Skakauskas
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Differential Equations ◽  
Oxygen Concentration ◽  
Difference Method ◽  
Computer Modelling ◽  
Numerical Schemes ◽  
Shallow Layer ◽  
The Finite Difference Method

The system of partial differential equations, describing the dynamics of the oxygen consuming bacteria in a chamber with an open top, is investigated. The finite difference method is used for solving the problem. Solutions of two different numerical schemes are compared and analyzed when values of oxygen concentration become negative in the case of a shallow layer.

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