Showing papers in "Mathematical Problems in Engineering in 2005"
TL;DR: The peristaltic transport of Johnson-Segalman fluid by means of an infinite train of sinusoidal waves traveling along the walls of a two-dimensional flexible channel is investigated in this paper.
Abstract: The peristaltic transport of Johnson-Segalman fluid by means of an infinite train of sinusoidal waves traveling along the walls of a two-dimensional flexible channel is investigated. The fluid is electrically conducted by a transverse magnetic field. A perturbation solution is obtained for the case in which amplitude ratio is small. Numerical results are reported for various values of the physical parameters of interest.
145 citations
TL;DR: In this paper, it was shown that the distribution of uptime and downtime has the coefficients of variation less than 1 if the breakdown and repair rates are increasing functions of time, where the breakdown rate increases with the time of day.
Abstract: It was reported in the literature that the coefficients of variation of uptime and downtime of manufacturing equipment are often less than 1. This technical paper is intended to provide an analytical explanation of this phenomenon. Specifically, it shows that the distributions of uptime and downtime have the coefficients of variation less than 1 if the breakdown and repair rates are increasing functions of time.
63 citations
TL;DR: This study compares the performance of sequential quadratic programming methods and generalized reduced gradient methods with the genetic algorithms which gained popularity in recent years due to advantages in speed and robustness.
Abstract: Constrained nonlinear programming problems often arise in many
engineering applications. The most well-known optimization methods
for solving these problems are sequential quadratic programming
methods and generalized reduced gradient methods. This study
compares the performance of these methods with the genetic
algorithms which gained popularity in recent years due to advantages
in speed and robustness. We present a comparative study that is performed
on fifteen test problems selected from the literature.
60 citations
TL;DR: In this article, the authors derived explicit expressions for R when the joint distribution is bivariate beta and used them to estimate the reliability of stress-strength models with dependence between X and Y.
Abstract: In the area of stress-strength models there has been a large amount of work as regards estimation of the reliability R=Pr(X<Y). The algebraic form for R=Pr(X<Y) has been worked out for the vast majority of the well-known distributions when X and Y are independent random variables belonging to the same univariate family. In this paper, we consider forms of R when (X,Y) follows a bivariate distribution with dependence between X and Y. In particular, we derive explicit expressions for R when the joint distribution is bivariate beta. The calculations involve the use of special functions.
57 citations
TL;DR: In this article, the use of modified equivalent partial differential equation (MEPDE) as a means of estimating the order of accuracy of a given finite difference technique for convection-diffusion transport problems is emphasized.
Abstract: The numerical solution of convection-diffusion transport problems
arises in many important applications in science and engineering. These problems occur in many applications such as in the transport of air and ground water pollutants, oil reservoir flow, in the modeling of semiconductors, and so forth. This paper describes
several finite difference schemes for solving the one-dimensional convection-diffusion equation with constant coefficients. In this research the use of modified equivalent partial differential equation (MEPDE) as a means of estimating the order of accuracy of a given finite difference technique is emphasized. This approach can unify the deduction of arbitrary techniques for the numerical solution of convection-diffusion equation. It is
also used to develop new methods of high accuracy. This approach allows simple comparison of the errors associated with the partial differential equation. Various difference approximations are derived for the one-dimensional constant coefficient convection-diffusion equation. The results of a numerical experiment are provided, to verify the efficiency of the designed new algorithms. The paper ends with a concluding remark.
54 citations
TL;DR: In this paper, both time and space-splitted Burgers' equations are solved numerically, and cubic B-spline collocation method is applied to the time-splitting Burgers equation.
Abstract: Both time- and space-splitted Burgers' equations are solved
numerically. Cubic B-spline collocation method is applied to the
time-splitted Burgers' equation. Quadratic B-spline collocation
method is used to get numerical solution of the space-splitted
Burgers' equation. The results of both schemes are compared for
some test problems.
50 citations
TL;DR: A closed-form expression that shows the mathematical relationships between the system parameters, and that can be used to gain basic insight into system behavior at the initial design stage, is derived.
Abstract: We derive a simple formula for the throughput (jobs produced per unit time) of a serial production line with workstations that are subject to random failures. The derivation is based on equations developed for a line flow model that takes into account the impact of finite buffers between workstations. The formula applies in the special case of a
line with identical workstations and buffers of equal size. It is a closed-form expression that shows the mathematical relationships between the system parameters, and that can be used to gain basic insight into system behavior at the initial design stage.
49 citations
TL;DR: In this article, exactly supported linear semiorthogonal B-spline wavelets together with their dual wavelets are developed to approximate the solutions of nonlinear Fredholm-Hammerstein integral equations.
Abstract: Compactly supported linear semiorthogonal B-spline wavelets
together with their dual wavelets are developed to approximate the solutions of nonlinear Fredholm-Hammerstein integral equations. Properties of these wavelets are first presented; these properties are then utilized to reduce the computation of integral equations
to some algebraic equations. The method is computationally attractive, and applications are demonstrated through an illustrative example.
48 citations
TL;DR: In this article, the authors proposed necessary and sufficient conditions in order to render a multiple-input multiple-output linear discrete-time invariant system passive by means of a static-state feedback and using the properties of the relative degree and zero dynamics of the system.
Abstract: Some important features and implications of dissipativity and passivity properties in the discrete-time setting are collected in this paper. These properties are mainly referred to as the stability analysis (feedback stability systems and study of the zero dynamics), the relative degree, the feedback passivity
property, and the preservation of passivity under feedback and parallel interconnections. Frequency-domain characteristics are exploited to show some of these properties. The main contribution is the proposal of necessary and sufficient conditions in order to render a multiple-input multiple-output linear discrete-time invariant system passive by means of a static-state feedback and using the properties of the relative degree and zero dynamics of the system. A discrete-time model for the DC-to-DC buck converter is used as an example to illustrate the passivation scheme proposed. In addition, dissipativity frequency-domain properties
are related to some feedback stability criteria.
32 citations
TL;DR: In this article, the realization problem for positive single-input single-output (SISO) discrete-time systems with one time delay is formulated and solved, and necessary and sufficient conditions for the solvability of the problem are established.
Abstract: The realization problem for positive single-input single-output
discrete-time systems with one time
delay is formulated and solved. Necessary and sufficient
conditions for the solvability of the realization problem are
established. A procedure for computation of a minimal positive
realization of a proper rational function is presented and
illustrated by an example.
30 citations
TL;DR: In this article, coupled partial differential equations governing the moisture and heat transfer can be solved using numerical techniques, and in this paper we discuss the nature of the solutions using the physical properties of Pinus radiata.
Abstract: Luikov's theory of heat and mass transfer provides a framework to
model drying porous materials. Coupled partial differential equations governing the moisture and heat transfer can be solved using numerical techniques, and in this paper we solve them analytically in a setting suitable for industrial drying situations. We discuss the nature of the solutions using the physical properties of Pinus radiata. It is shown that the temperature gradients play a significant role in deciding the moisture profiles within the material when thickness is large and that models based only on moisture potential gradients may not be sufficient to explain the drying phenomena in moist porous materials.
TL;DR: In this paper, a single-term Walsh series is developed to approximate the solution of nonlinear Volterra-Hammerstein integral equations, and properties of the Walsh series are used to reduce the computation of integral equations.
Abstract: Single-term Walsh series are developed to approximate the
solutions of nonlinear Volterra-Hammerstein integral
equations. Properties of single-term Walsh series are presented
and are utilized to reduce the computation of integral
equations to some algebraic equations. The method is
computationally attractive, and applications are demonstrated
through illustrative examples.
TL;DR: In this paper, the existence, uniqueness, and continuous dependence of solutions with respect to initial values of set differential equations with causal operators were investigated for a set differential equation with causal operator.
Abstract: We obtain some basic results on existence, uniqueness, and
continuous dependence of solutions with respect to initial values
for set differential equations with causal operators.
TL;DR: In this paper, the generalized classical method (GCM) is used for solving linear and nonlinear differential equations. And the solution of the nonlinear transient regimes in the physical processes can be written as functional series with unknown coefficients.
Abstract: This paper presents the use of the generalized classical method (GCM) for solving linear and nonlinear differential equations. This method is based on the differential transformation (DT) technique. In the GCM, the solution of the nonlinear transient regimes in the physical processes can be written as a functional series with unknown coefficients. The series can be chosen to satisfy the initial and boundary conditions which represent the properties of the physical process. The unknown coefficients of the series are determined from the differential transformation of the nonlinear differential equation of the system. Therefore, the approximate solution of the nonlinear differential equation can be obtained as a closed-form series.
TL;DR: In this article, a power series expansion technique was used to solve the three-dimensional homogeneous and finite body of a certain shape using wave polynomials and their derivatives in Cartesian, spherical, and cylindrical coordinate systems.
Abstract: We demonstrate a specific power series expansion technique to
solve the three-dimensional homogeneous and
inhomogeneous wave equations. As solving functions, so-called wave
polynomials are used. The presented method is useful for a finite
body of certain shape. Recurrent formulas to improve efficiency
are obtained for the wave polynomials and their derivatives in a
Cartesian, spherical, and cylindrical coordinate system. Formulas
for a particular solution of the inhomogeneous wave equation are
derived. The accuracy of the method is discussed and some typical
examples are shown.
TL;DR: In this article, the exact and approximate spectrum assignment properties associated with realizable output-feedback pole-placement type controllers for single-input single-output linear time-invariant time-delay systems with commensurate point delays are investigated.
Abstract: This paper investigates the exact and approximate spectrum assignment properties associated with realizable output-feedback pole-placement type controllers for single-input single-output linear time-invariant time-delay systems with commensurate point delays. The controller synthesis problem is discussed through the solvability of a set of coupled diophantine equations of polynomials. An extra complexity is incorporated to the above design to cancel extra unsuitable dynamics being generated when solving the above diophantine equations. Thus, the complete controller tracks any arbitrary prefixed (either finite or delay-dependent) closed-loop spectrum. However, if the controller is simplified by deleting the above mentioned extra complexity, then the robust stability and approximated spectrum assignment are still achievable for a certain sufficiently small amount of delayed dynamics. Finally, the approximate spectrum assignment and robust stability problems are revisited under plant disturbances if the nominal controller is main-tained. In the current approach, the finite spectrum assignment is only considered as a particular case to the designer's choice of a (delay-dependent) arbitrary spectrum assignment objective.
TL;DR: A graph-theoretic decomposition is used to cluster the states, inputs, and outputs, and to identify an appropriate bordered block diagonal structure for the gain matrix, and the resulting control law can be easily implemented in a multiprocessor environment with a minimum of communication.
Abstract: We propose a new output control design for large, sparse dynamic
systems. A graph-theoretic decomposition is used to cluster the states, inputs, and outputs,
and to identify an appropriate bordered block diagonal structure for the gain matrix. The resulting control law can be easily implemented in a multiprocessor environment with a minimum of communication. A large-scale problem is considered to demonstrate the validity of the proposed approach.
TL;DR: In this article, a study of parametric vibrations of functionally graded plates subjected to in-plane time-dependent forces is presented, taking into account a coupling of inplane and transverse motions.
Abstract: Functionally graded materials have gained considerable attention
in the high-temperature applications A study of parametric
vibrations of functionally graded plates subjected to in-plane
time-dependent forces is presented Moderately large deflection
equations taking into account a coupling of in-plane and
transverse motions are used Material properties are graded in the
thickness direction of the plate according to volume fraction
power law distribution An oscillating temperature causes
generation of in-plane time-dependent forces destabilizing the
plane state of the plate equilibrium The asymptotic stability and
almost-sure asymptotic stability criteria involving a damping
coefficient and loading parameters are derived using Liapunov's
direct method Effects of power law exponent on the stability
domains are studied
TL;DR: In this article, the authors derived a constitutive relationship for the stress tensor of an anisotropic rod-like assembly of granular particles where not only the transverse isotropy (denoted by a unit vector n, also called the fiber direction) is included, but also the dependence of the tensor T on the density gradient, a measure of particle distribution, is studied.
Abstract: We will derive a constitutive relationship for the stress tensor of an anisotropic rod-like assembly of granular particles where not only the transverse isotropy (denoted by a unit vector n, also called the fiber direction) is included, but also the dependence of the stress tensor T on the density gradient, a measure of particle distribution, is studied. The granular media is assumed to behave as a continuum, and the effects of the interstitial fluid are ignored. No thermodynamical considerations are included, and using representation theorems, it is shown that in certain limiting cases, constitutive relations similar to those of the Leslie-Ericksen liquid crystal type can be obtained. It is also shown that in this granular model, one can observe the normal stress effects as well as the yield condition, if proper structures are imposed on the material coefficients.
TL;DR: This paper pointed out and corrected several errors that appeared in a recently published paper on transient flows of second-grade fluids and pointed out several errors in the paper's analysis. But these errors were not addressed in this paper.
Abstract: We point out and correct several errors that appear in a recently
published paper on transient flows of second-grade fluids
TL;DR: In this article, the minimization control problem of quadratic functionals for the class of affine nonlinear systems with the hypothesis of nilpotent associated Lie algebra is analyzed.
Abstract: The minimization control problem of quadratic functionals for the class of affine nonlinear systems with the hypothesis of nilpotent associated Lie algebra is analyzed. The optimal control corresponding to the first-, second-, and third-order nilpotent operators is determined. In this paper, we have considered the minimum fuel problem for the multi-input nilpotent control and for a scalar input bilinear system for such systems. For the multi-input system, usually an analytic closed-form solution for the optimal control ui∗(t) is not possible and it is necessary to use numerical integration for the set of m nonlinear coupled second-order differential equations. The optimal control of bilinear systems is obtained by considering the Lie algebra generated by the system matrices. It should be noted that we have obtained an open-loop control depending on the initial value of the state x0.
TL;DR: In this paper, a two-unit cold standby system attended by two repairmen and subjected to a priority rule is considered, and a stochastic process endowed with state probability functions satisfying coupled Hokstad-type differential equations is proposed to describe the random behavior of the twin system.
Abstract: We consider a two-unit cold standby system attended by two repairmen and subjected to a priority rule. In order to describe the random behavior of the twin system, we employ a stochastic process endowed with state probability functions satisfying coupled Hokstad-type differential equations. An explicit evaluation of the exact solution is in general quite intricate. Therefore, we propose a numerical solution of the equations. Finally, particular but important repair time distributions are involved to analyze the long-run availability of the T-system. Numerical results are illustrated by adequate computer-plotted graphs.
TL;DR: In this article, all nontrivial conservation laws for a class of (2+1) nonlinear evolution partial differential equations which are related to the soil water equations were obtained.
Abstract: We obtain all nontrivial conservation laws for a class of (2+1) nonlinear evolution partial differential equations which are related to the soil water equations. It is also pointed out that nontrivial conservation laws exist for certain classes of
equations which admit point symmetries. Moreover, we associate symmetries with conservation laws for special classes of these equations.
TL;DR: In this paper, a novel method for solving mixed boundary value problem is presented, and a computational efficiency of the proposed method is illustrated using a few mechanical examples, which is shown to be computationally efficient.
Abstract: A novel method for solving mixed boundary value problem is
presented. A computational efficiency of the proposed method is
illustrated using a few mechanical examples.
TL;DR: In this article, a delay term is added to the Volterra kernel to describe effects of particular constitutive laws, and the existence and uniqueness results are established by using an Euler implicit numerical scheme; then convergence with its order is established.
Abstract: Mechanical models are governed either by partial differential equations with boundary conditions and initial conditions (e.g., in the frame of continuum mechanics) or by ordinary differential equations (e.g., after discretization via Galerkin procedure or directly from the model description) with the initial conditions. In order to study dynamical behavior of mechanical systems with a finite number of degrees of freedom including nonsmooth terms (e.g., friction), we consider here problems governed by differential inclusions. To describe effects of particular constitutive laws, we add a delay term. In contrast to previous papers, we introduce delay via a Volterra kernel. We provide existence and uniqueness results by using an Euler implicit numerical scheme; then convergence with its order is established. A few numerical examples are given.
TL;DR: In this paper, a general reliability analysis of a standby standby system attended by a single repairman is presented, based on a refined methodology of queuing theory, which provides an explicit result for the survival function of the duplex system.
Abstract: We present a general reliability analysis of a renewable multiple
cold standby system attended by a single repairman. Our analysis
is based on a refined methodology of queuing theory. The
particular case of deterministic failures provides an explicit
exact result for the survival function of the duplex system.
TL;DR: In this article, a Jacobian elliptic function is used to approximate the potential of an oscillation system such that the asymptotic solution can be expressed in terms of Jacobian ellipses.
Abstract: The effect of negative damping to an oscillatory system is to force the amplitude to increase gradually and the motion will be out of the potential well of the oscillatory system eventually. In order to deduce the escape time from the potential well of
quadratic or cubic nonlinear oscillator, the multiple scales method is firstly used to obtain the asymptotic solutions of strongly nonlinear oscillators with slowly varying parameters, and secondly the character of modulus of Jacobian elliptic function is applied to derive the equations governing the escape time. The approximate potential method, instead of Taylor series expansion, is used to approximate the potential of an oscillation system such that the asymptotic solution can be expressed in terms of Jacobian elliptic function.
Numerical examples verify the efficiency of the present method.
TL;DR: In this article, two robust control schemes are developed for the speed control of a variable reluctance motor (VRM) in a closed loop system, and simulations show that the proposed controllers work well and are robust to changes in the parameters of the motor.
Abstract: This paper investigates the control problem of variable
reluctance motors (VRMs). VRMs are highly nonlinear motors; a
model that takes magnetic saturation into account is adopted
in this work. Two robust control schemes are developed for the
speed control of a variable reluctance motor. The first
control scheme guarantees the uniform ultimate boundedness of
the closed loop system. The second control scheme guarantees
the exponential stability of the closed loop system.
Simulation results of the proposed controllers are presented
to illustrate the theoretical developments. The simulations
indicate that the proposed controllers work well, and they are
robust to changes in the parameters of the motor and to
changes in the load.
TL;DR: In this article, various models, based on a filtered Poisson process, are used to forecast the next peak value of the flow, given that another peak was observed not too long ago.
Abstract: Various models, based on a filtered Poisson process, are used for the flow of a river. The aim is to forecast the next peak value of the flow, given that another peak was observed not too long ago. The most realistic model is the one when the time between the successive peaks does not have an exponential distribution, as is often assumed. An application to the Delaware River, in the USA, is presented.
TL;DR: In this paper, an antiplane problem of a stress deformation condition of a piecewise wedge consisting of two heterogeneous wedges with different opening angles and containing on the line of their attachment a system of arbitrary finite number of collinear cracks is investigated.
Abstract: An antiplane problem of a stress deformation condition of a piecewise wedge consisting of two heterogeneous wedges with different opening angles and containing on the line of their attachment a system of arbitrary finite number of collinear cracks is investigated. With the help of Mellin's integral transformation the problem is brought to the solution of the singular integral equation relating to the density of the displacement dislocation on the cracks, which then is reduced to a system of singular integral equations with kernels being represented in the form of sums of Cauchy kernels and regular kernels. This system of equations is solved by the known numerical method. Stress intensity factors (SIF) are calculated and the behavior of characteristic geometric and physical parameters is revealed. Besides, the density of the displacement dislocation on the cracks, their evaluation, and J -integrals are calculated.