International Science Index
Perturbation Based Modelling of Differential Amplifier Circuit
This paper presents the closed form nonlinear
expressions of bipolar junction transistor (BJT) differential amplifier
(DA) using perturbation method. Circuit equations have been derived
using Kirchhoff’s voltage law (KVL) and Kirchhoff’s current law
(KCL). The perturbation method has been applied to state variables
for obtaining the linear and nonlinear terms. The implementation
of the proposed method is simple. The closed form nonlinear
expressions provide better insights of physical systems. The derived
equations can be used for signal processing applications.
Nonlinear Propagation of Acoustic Soliton Waves in Dense Quantum Electron-Positron Magnetoplasma
Propagation of nonlinear acoustic wave in dense electron-positron (e-p) plasmas in the presence of an external magnetic field and stationary ions (to neutralize the plasma background) is studied. By means of the quantum hydrodynamics model and applying the reductive perturbation method, the Zakharov-Kuznetsov equation is derived. Using the bifurcation theory of planar dynamical systems, the compressive structure of electrostatic solitary wave and periodic travelling waves is found. The numerical results show how the ion density ratio, the ion cyclotron frequency, and the direction cosines of the wave vector affect the nonlinear electrostatic travelling waves. The obtained results may be useful to better understand the obliquely nonlinear electrostatic travelling wave of small amplitude localized structures in dense magnetized quantum e-p plasmas and may be applicable to study the particle and energy transport mechanism in compact stars such as the interior of massive white dwarfs etc.
Analytical Solutions for Corotational Maxwell Model Fluid Arising in Wire Coating inside a Canonical Die
The present paper applies the optimal homotopy perturbation method (OHPM) and the optimal homotopy asymptotic method (OHAM) introduced recently to obtain analytic approximations of the non-linear equations modeling the flow of polymer in case of wire coating of a corotational Maxwell fluid. Expression for the velocity field is obtained in non-dimensional form. Comparison of the results obtained by the two methods at different values of non-dimensional parameter l10, reveal that the OHPM is more effective and easy to use. The OHPM solution can be improved even working in the same order of approximation depends on the choices of the auxiliary functions.
Finite Element Analysis of Oil-Lubricated Elliptical Journal Bearings
Fixed-geometry hydrodynamic journal bearings are
one of the best supporting systems for several applications of rotating
machinery. Cylindrical journal bearings present excellent loadcarrying
capacity and low manufacturing costs, but they are subjected
to the oil-film instability at high speeds. An attempt of overcoming
this instability problem has been the development of non-circular
journal bearings. This work deals with an analysis of oil-lubricated
elliptical journal bearings using the finite element method. Steadystate
and dynamic performance characteristics of elliptical bearings
are rendered by zeroth- and first-order lubrication equations obtained
through a linearized perturbation method applied on the classical
Reynolds equation. Four-node isoparametric rectangular finite
elements are employed to model the bearing thin film flow. Curves of
elliptical bearing load capacity and dynamic force coefficients are
rendered at several operating conditions. The results presented in this
work demonstrate the influence of the bearing ellipticity on its
performance at different loading conditions.
Nonplanar Ion-acoustic Waves in a Relativistically Degenerate Quantum Plasma
Using the quantum hydrodynamic (QHD) model the
nonlinear properties of ion-acoustic waves in are lativistically
degenerate quantum plasma is investigated by deriving a nonlinear
Spherical Kadomtsev–Petviashvili (SKP) equation using the
standard reductive perturbation method equation. It was found that
the electron degeneracy parameter significantly affects the linear
and nonlinear properties of ion-acoustic waves in quantum plasma.
Numerical Buckling of Composite Cylindrical Shells under Axial Compression Using Asymmetric Meshing Technique (AMT)
This paper presents the details of a numerical study of
buckling and post buckling behaviour of laminated carbon fiber
reinforced plastic (CFRP) thin-walled cylindrical shell under axial
compression using asymmetric meshing technique (AMT) by
ABAQUS. AMT is considered to be a new perturbation method to
introduce disturbance without changing geometry, boundary
conditions or loading conditions. Asymmetric meshing affects both
predicted buckling load and buckling mode shapes. Cylindrical shell
having lay-up orientation [0^o/+45^o/-45^o/0^o] with radius to thickness
ratio (R/t) equal to 265 and length to radius ratio (L/R) equal to 1.5 is
analysed numerically. A series of numerical simulations
(experiments) are carried out with symmetric and asymmetric
meshing to study the effect of asymmetric meshing on predicted
buckling behaviour. Asymmetric meshing technique is employed in
both axial direction and circumferential direction separately using
two different methods, first by changing the shell element size and
varying the total number elements, and second by varying the shell
element size and keeping total number of elements constant. The
results of linear analysis (Eigenvalue analysis) and non-linear
analysis (Riks analysis) using symmetric meshing agree well with
analytical results. The results of numerical analysis are presented in
form of non-dimensional load factor, which is the ratio of buckling
load using asymmetric meshing technique to buckling load using
symmetric meshing technique. Using AMT, load factor has about 2%
variation for linear eigenvalue analysis and about 2% variation for
non-linear Riks analysis. The behaviour of load end-shortening curve
for pre-buckling is same for both symmetric and asymmetric meshing
but for asymmetric meshing curve behaviour in post-buckling
becomes extraordinarily complex. The major conclusions are:
different methods of AMT have small influence on predicted
buckling load and significant influence on load displacement curve
behaviour in post buckling; AMT in axial direction and AMT in
circumferential direction have different influence on buckling load
and load displacement curve in post-buckling.
Analysis of a Self-Acting Air Journal Bearing: Effect of Dynamic Deformation of Bump Foil
A theoretical investigation on the effects of both
steady-state and dynamic deformations of the foils on the dynamic
performance characteristics of a self-acting air foil journal bearing
operating under small harmonic vibrations is proposed. To take into
account the dynamic deformations of foils, the perturbation method is
used for determining the gas-film stiffness and damping coefficients
for given values of excitation frequency, compressibility number, and
compliance factor of the bump foil. The nonlinear stationary
Reynolds’ equation is solved by means of the Galerkins’ finite
element formulation while the finite differences method are used to
solve the first order complex dynamic equations resulting from the
perturbation of the nonlinear transient compressible Reynolds’
equation. The stiffness of a bump is uniformly distributed throughout
the bearing surface (generation I bearing). It was found that the
dynamic properties of the compliant finite length journal bearing are
significantly affected by the compliance of foils especially whenthe
dynamic deformation of foils is considered in addition to the static
one by applying the principle of superposition.
Application New Approach with Two Networks Slow and Fast on the Asynchronous Machine
In this paper, we propose a new modular approach called neuroglial consisting of two neural networks slow and fast which emulates a biological reality recently discovered. The implementation is based on complex multi-time scale systems; validation is performed on the model of the asynchronous machine. We applied the geometric approach based on the Gerschgorin circles for the decoupling of fast and slow variables, and the method of singular perturbations for the development of reductions models.
This new architecture allows for smaller networks with less complexity and better performance in terms of mean square error and convergence than the single network model.
Free Vibration Analysis of Non-Uniform Euler Beams on Elastic Foundation via Homotopy Perturbation Method
In this study Homotopy Perturbation Method (HPM) is employed to investigate free vibration of an Euler beam with variable stiffness resting on an elastic foundation. HPM is an easy-to-use and very efficient technique for the solution of linear or nonlinear problems. HPM produces analytical approximate expression which is continuous in the solution domain. This work shows that HPM is a promising method for free vibration analysis of nonuniform Euler beams on elastic foundation. Several case problems have been solved by using the technique and solutions have been compared with those available in the literature.
A Numerical Approach for Static and Dynamic Analysis of Deformable Journal Bearings
This paper presents a numerical approach for the static
and dynamic analysis of hydrodynamic radial journal bearings. In the
first part, the effect of shaft and housing deformability on pressure
distribution within oil film is investigated. An iterative algorithm that
couples Reynolds equation with a plane finite elements (FE)
structural model is solved. Viscosity-to-pressure dependency (Vogel-
Barus equation) is also included. The deformed lubrication gap and
the overall stress state are obtained. Numerical results are presented
with reference to a typical journal bearing configuration at two
different inlet oil temperatures. Obtained results show the great
influence of bearing components structural deformation on oil
pressure distribution, compared with results for ideally rigid
components. In the second part, a numerical approach based on
perturbation method is used to compute stiffness and damping
matrices, which characterize the journal bearing dynamic behavior.
Ion- Acoustic Solitary Waves in a Self- Gravitating Dusty Plasma Having Two-Temperature Electrons
Nonlinear propagation of ion-acoustic waves in a selfgravitating
dusty plasma consisting of warm positive ions,
isothermal two-temperature electrons and negatively charged dust
particles having charge fluctuations is studied using the reductive
perturbation method. It is shown that the nonlinear propagation of
ion-acoustic waves in such plasma can be described by an uncoupled
third order partial differential equation which is a modified form of
the usual Korteweg-deVries (KdV) equation. From this nonlinear
equation, a new type of solution for the ion-acoustic wave is
obtained. The effects of two-temperature electrons, gravity and dust
charge fluctuations on the ion-acoustic solitary waves are discussed
with possible applications.
Quantum Ion Acoustic Solitary and Shock Waves in Dissipative Warm Plasma with Fermi Electron and Positron
Ion-acoustic solitary and shock waves in dense
quantum plasmas whose constituents are electrons, positrons, and
positive ions are investigated. We assume that ion velocity is weakly
relativistic and also the effects of kinematic viscosity among the
plasma constituents is considered. By using the reductive
perturbation method, the Korteweg–deVries–Burger (KdV-B)
equation is derived.
Application of Homotopy Perturbation Method to Solve Steady Flow of Walter B Fluid A Vertical Channel In Porous Media
In this article, a simulation method called the Homotopy Perturbation Method (HPM) is employed in the steady flow of a Walter's B' fluid in a vertical channel with porous wall. We employed Homotopy Perturbation Method to derive solution of a nonlinear form of equation obtained from exerting similarity transforming to the ordinary differential equation gained from continuity and momentum equations of this kind of flow. The results obtained from the Homotopy Perturbation Method are then compared with those from the Runge–Kutta method in order to verify the accuracy of the proposed method. The results show that the Homotopy Perturbation Method can achieve good results in predicting the solution of such problems. Ultimately we use this solution to obtain the other terms of velocities and physical discussion about it.
Block Homotopy Perturbation Method for Solving Fuzzy Linear Systems
In this paper, we present an efficient numerical algorithm, namely block homotopy perturbation method, for solving fuzzy linear systems based on homotopy perturbation method. Some numerical examples are given to show the efficiency of the algorithm.
Application of He’s Parameter-Expansion Method to a Coupled Van Der Pol oscillators with Two Kinds of Time-delay Coupling
In this paper, the dynamics of a system of two van der Pol oscillators with delayed position and velocity is studied. We provide an approximate solution for this system using parameterexpansion method. Also, we obtain approximate values for frequencies of the system. The parameter-expansion method is more efficient than the perturbation method for this system because the method is independent of perturbation parameter assumption.
HPM Solution of Momentum Equation for Darcy-Brinkman Model in a Parallel Plates Channel Subjected to Lorentz Force
In this paper an analytical solution is presented for fully developed flow in a parallel plates channel under the action of Lorentz force, by use of Homotopy Perturbation Method (HPM). The analytical results are compared with exact solution and an excellent agreement has been observed between them for both Couette and Poiseuille flows. Moreover, the effects of key parameters have been studied on the dimensionless velocity profile.
Dust Acoustic Shock Waves in Coupled Dusty Plasmas with Kappa-Distributed Ions
We have considered an unmagnetized dusty plasma system consisting of ions obeying superthermal distribution and strongly coupled negatively charged dust. We have used reductive perturbation method and derived the Kordeweg-de Vries-Burgers (KdV-Burgers) equation. The behavior of the shock waves in the plasma has been investigated.
Analytical Solutions of Kortweg-de Vries(KdV) Equation
The objective of this paper is to present a
comparative study of Homotopy Perturbation Method (HPM),
Variational Iteration Method (VIM) and Homotopy Analysis
Method (HAM) for the semi analytical solution of Kortweg-de
Vries (KdV) type equation called KdV. The study have been
highlighted the efficiency and capability of aforementioned methods
in solving these nonlinear problems which has been arisen from a
number of important physical phenomenon.
On the Solution of Fully Fuzzy Linear Systems
A linear system is called a fully fuzzy linear system (FFLS) if quantities in this system are all fuzzy numbers. For the FFLS, we investigate its solution and develop a new approximate method for solving the FFLS. Observing the numerical results, we find that our method is accurate than the iterative Jacobi and Gauss- Seidel methods on approximating the solution of FFLS.
Analytical solution of Gas Flow Through a Micro-Nano Porous Media by Homotopy Perturbation method
In this paper, we have applied the homotopy perturbation
method (HPM) for obtaining the analytical solution of unsteady
flow of gas through a porous medium and we have also compared the
findings of this research with some other analytical results. Results
showed a very good agreement between results of HPM and the
numerical solutions of the problem rather than other analytical solutions
which have previously been applied. The results of homotopy
perturbation method are of high accuracy and the method is very
effective and succinct.
A Comparison Study of a Symmetry Solution of Magneto-Elastico-Viscous Fluid along a Semi- Infinite Plate with Homotopy Perturbation Method and4th Order Runge–Kutta Method
The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4th order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compared with each other, showing excellent agreement. The effects of the magnetic parameter and Prandtl number on velocity field, shear stress, temperature and heat transfer are discussed as well.
Solving Inhomogeneous Wave Equation Cauchy Problems using Homotopy Perturbation Method
In this paper, He-s homotopy perturbation method (HPM) is applied to spatial one and three spatial dimensional inhomogeneous wave equation Cauchy problems for obtaining exact solutions. HPM is used for analytic handling of these equations. The results reveal that the HPM is a very effective, convenient and quite accurate to such types of partial differential equations (PDEs).
Constructing Approximate and Exact Solutions for Boussinesq Equations using Homotopy Perturbation Padé Technique
Based on the homotopy perturbation method (HPM)
and Padé approximants (PA), approximate and exact solutions are
obtained for cubic Boussinesq and modified Boussinesq equations.
The obtained solutions contain solitary waves, rational solutions.
HPM is used for analytic treatment to those equations and PA for
increasing the convergence region of the HPM analytical solution.
The results reveal that the HPM with the enhancement of PA is a
very effective, convenient and quite accurate to such types of partial
Group Similarity Transformation of a Time Dependent Chemical Convective Process
The time dependent progress of a chemical reaction over a flat horizontal plate is here considered. The problem is solved through the group similarity transformation method which reduces the number of independent by one and leads to a set of nonlinear ordinary differential equation. The problem shows a singularity at the chemical reaction order n=1 and is analytically solved through the perturbation method. The behavior of the process is then numerically investigated for n≠1 and different Schmidt numbers. Graphical results for the velocity and concentration of chemicals based on the analytical and numerical solutions are presented and discussed.
A Wind Farm Reduced Order Model Using Integral Manifold Theory
Due to the increasing penetration of wind energy, it is
necessary to possess design tools that are able to simulate the impact
of these installations in utility grids. In order to provide a net
contribution to this issue a detailed wind park model has been
developed and is briefly presented. However, the computational costs
associated with the performance of such a detailed model in
describing the behavior of a wind park composed by a considerable
number of units may render its practical application very difficult. To
overcome this problem integral manifolds theory has been applied to
reduce the order of the detailed wind park model, and therefore
create the conditions for the development of a dynamic equivalent
which is able to retain the relevant dynamics with respect to the
existing a.c. system. In this paper integral manifold method has been
introduced for order reduction. Simulation results of the proposed
method represents that integral manifold method results fit the
detailed model results with a higher precision than singular