Showing papers in "Mathematical Problems in Engineering in 2006"
TL;DR: In this paper, the authors present an overview of thermomechanical behavior of shape memory alloys, discussing the main constitutive models for their mathematical description, and five phenomenological theories are presented.
Abstract: The remarkable properties of shape memory alloys have facilitated their applications in many areas of technology. The purpose of this paper is to present an overview of thermomechanical behavior of these alloys, discussing the main constitutive models for their mathematical description. Metallurgical features and engineering applications are addressed as an introduction. Afterwards, five phenomenological theories are presented. In general, these models capture the general thermomechanical behavior of shape memory alloys, characterized by pseudoelasticity, shape memory effect, phase transformation phenomenon due to temperature variation, and internal subloops due to incomplete phase transformations.
181 citations
TL;DR: In this paper, a method for solving the nonlinear second-order Fredholm integro-differential equations is presented, based on a compactly supported linear semiorthogonal B-spline wavelets.
Abstract: A method for solving the nonlinear second-order Fredholm integro-differential equations is presented. The approach is based on a compactly supported linear semiorthogonal B-spline wavelets. The operational matrices of derivative for B-spline scaling functions and wavelets are presented and utilized to reduce the solution of Fredholm integro-differential to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.
87 citations
TL;DR: In this paper, a linearized implicit finite difference method to obtain numerical solution of the one-dimensional regularized long-wave (RLW) equation is presented, and the performance and accuracy of the method are illustrated by solving three test examples of the problem: a single solitary wave, two positive solitary waves, and an undular bore.
Abstract: A linearized implicit finite difference method to obtain numerical solution of the one-dimensional regularized long-wave (RLW) equation is presented. The performance and the accuracy of the method are illustrated by solving three test examples of the problem: a single solitary wave, two positive solitary waves interaction, and an undular bore. The obtained results are presented and compared with earlier work.
67 citations
TL;DR: In this paper, a numerical method is presented for finding the solution of some variational problems, which is done using Adomian decomposition method which is a powerful tool for solving large amount of problems.
Abstract: In this paper, a numerical method is presented for finding the solution of some variational problems. The main objective is to find the solution of an ordinary differential equation which arises from the variational problem. This work is done using Adomian decomposition method which is a powerful tool for solving large amount of problems. In this approach, the solution is found in the form of a convergent power series with easily computed components. To show the efficiency of the method, numerical results are presented.
59 citations
TL;DR: In this article, the algebraic form for R=Pr ⊆(X,Y) with dependence between X and Y is derived when the joint distribution is bivariate exponential.
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
58 citations
TL;DR: In this paper, the dynamic treatment of one-dimensional generalized thermoelastic problem of heat conduction is made for a layered thin plate which is exposed to a uniform thermal shock taking into account variable temperature and thermal conductivity.
Abstract: The dynamic treatment of one-dimensional generalized thermoelastic problem of heat conduction is made for a layered thin plate which is exposed to a uniform thermal shock taking into account variable thermal conductivity. The basic equations are transformed by Laplace transform and solved by a direct method. The solution was applied for a plate of sandwich structure, which is thermally shocked, and is traction-free in the outer sides. The inverses of Laplace transforms are obtained numerically. The temperature, the stress, and the displacement distributions are represented graphically.
54 citations
TL;DR: In this paper, the problems of stability and stabilizability for linear discrete-time systems with varying time delay are considered, and sufficient conditions for checking the stability of this class of systems are developed.
Abstract: This paper deals with the class of linear discrete-time systems with varying time delay. The problems of stability and stabilizability for this class of systems are considered. Given an upper bound and a lower bound on the time-varying delay, sufficient conditions for checking the stability of this class of systems are developed. A control design algorithm is also provided. All the results developed in this paper are in the LMI formalism which makes their solvability easier using existing tools. A numerical example is provided to show the effectiveness of the established results.
53 citations
TL;DR: In this paper, the authors proposed a new necessary and sufficient condition in terms of a strict linear matrix inequality (LMI) for a nominal continuous descriptor system to be admissible (stable, regular, and impulse-free) based on this, the statefeedback admissibility problem is solved and the solution is extended to the case of uncertain descriptor systems.
Abstract: This paper deals with the problems of robust stability and stabilization for uncertain continuous descriptor systems. We propose a new necessary and sufficient condition in terms of a strict linear matrix inequality (LMI) for a nominal continuous descriptor system to be admissible (stable, regular, and impulse-free). Based on this, the state-feedback admissibility problem is solved and the solution is extended to the case of uncertain descriptor systems. Finally, numerical examples are given to illustrate the results.
41 citations
TL;DR: In this article, a Galerkin projection method is proposed for the construction of nonlinear modes that are accurate out to large amplitude of vibration. But the Galerkins method is not suitable for modeling large-scale nonlinear structural systems.
Abstract: Recent progress in the area of nonlinear modal analysis for structural systems is reported. Systematic methods are developed for generating minimally sized reduced-order models that accurately describe the vibrations of large-scale nonlinear engineering structures. The general approach makes use of nonlinear normal modes that are defined in terms of invariant manifolds in the phase space of the system model. An efficient Galerkin projection method is developed, which allows for the construction of nonlinear modes that are accurate out to large amplitudes of vibration. This approach is successfully extended to the generation of nonlinear modes for systems that are internally resonant and for systems subject to external excitation. The effectiveness of the Galerkin-based construction of the nonlinear normal modes is also demonstrated for a realistic model of a rotating beam.
40 citations
TL;DR: In this article, the homotopy perturbation method was used to obtain an analytical solution for nonlinear Poisson-Boltzmann equation by using homogeneous perturbations.
Abstract: This paper obtains an explicit analytical solution for nonlinear Poisson-Boltzmann equation by the homotopy perturbation method, which does not require a small parameter in the equation under study, so it can be applied to both the weakly and strongly nonlinear problems. The obtained results show the evidence of the usefulness of the homotopy perturbation method for obtaining approximate analytical solutions for nonlinear equations.
36 citations
TL;DR: In this article, the influence of an inserted endoscope and magnetohydrodynamic (MHD) power-law fluid on peristaltic motion was analyzed for flow through tubes.
Abstract: To understand the influence of an inserted endoscope and magnetohydrodynamic (MHD) power-law fluid on peristaltic motion, an attempt has been made for flow through tubes. The magnetic field of uniform strength is applied in the transverse direction to the flow. The analysis has been performed under long wavelength at low-Reynolds number assumption. The velocity fields and axial pressure gradient have been evaluated analytically. Numerical results are also presented and discussed.
TL;DR: In this paper, a nonlinear oscillator with an attached pendulum, excited by movement of its point of suspension, was analyzed and the derived differential equations of motion showed that the system is strongly nonlinear and the motions of both subsystems, the pendulum and the oscillator, are strongly coupled by inertial terms, leading to the so-called autoparametric vibrations.
Abstract: Vibrations of a nonlinear oscillator with an attached pendulum, excited by movement of its point of suspension, have been analysed in the paper. The derived differential equations of motion show that the system is strongly nonlinear and the motions of both subsystems, the pendulum and the oscillator, are strongly coupled by inertial terms, leading to the so-called autoparametric vibrations. It has been found that the motion of the oscillator, forced by an external harmonic force, has been dynamically eliminated by the pendulum oscillations. Influence of a nonlinear spring on the vibration absorption near the main parametric resonance region has been carried out analytically, whereas the transition from regular to chaotic vibrations has been presented by using numerical methods. A transmission force on the foundation for regular and chaotic vibrations is presented as well.
TL;DR: Using Laplace transformation and perturbation techniques, ananalytical solution is obtained for unsteady Stokes' second-grade fluid problem as mentioned in this paper, where expressions for steady and transient solutions depend strongly upon the material parameter of second grade fluid.
Abstract: Using Laplace transformation and perturbation techniques,
analytical solution is obtained for unsteady Stokes' second
problem Expressions for steady and transient solutions are
explicitly determined These solutions depend strongly upon the
material parameter of second-grade fluid It is shown that phase
velocity decreases by increasing material parameter of
second-grade fluid
TL;DR: In this article, the authors considered the transversal oscillations of two-layer straight bar, which is under the action of the lengthwise random forces, and derived partial fractional differential equation of the beam vibrations.
Abstract: We considered the problem on transversal oscillations of two-layer straight bar, which is under the action of the lengthwise random forces. It is assumed that the layers of the bar were made of nonhomogenous continuously creeping material and the corresponding modulus of elasticity and creeping fractional order derivative of constitutive relation of each layer are continuous functions of the length coordinate and thickness coordinates. Partial fractional differential equation and particular solutions for the case of natural vibrations of the beam of creeping material of a fractional derivative order constitutive relation in the case of the influence of rotation inertia are derived. For the case of natural creeping vibrations, eigenfunction and time function, for different examples of boundary conditions, are determined. By using the derived partial fractional differential equation of the beam vibrations, the almost sure stochastic stability of the beam dynamic shapes, corresponding to the nth shape of the beam elastic form, forced by a bounded axially noise excitation, is investigated. By the use of S. T. Ariaratnam's idea, as well as of the averaging method, the top Lyapunov exponent is evaluated asymptotically when the intensity of excitation process is small.
TL;DR: In this article, the peristaltic transport of an incompressible viscous fluid in an asymmetric compliant channel is studied and the effect of wave amplitude ratio, width of the channel, phase difference, wall elastance, wall tension, and wall damping on mean-velocity and reversal flow is investigated.
Abstract: Peristaltic transport of an incompressible viscous fluid in an asymmetric compliant channel is studied. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phases. The fluid-solid interaction problem is investigated by considering equations of motion of both the fluid and the deformable boundaries. The driving mechanism of the muscle is represented by assuming the channel walls to be compliant. The phenomenon of the “mean flow reversal” is discussed. The effect of wave amplitude ratio, width of the channel, phase difference, wall elastance, wall tension, and wall damping on mean-velocity and reversal flow has been investigated. The results reveal that the reversal flow occurs near the boundaries which is not possible in the elastic symmetric channel case.
TL;DR: In this paper, the effects of radiation on the boundary layer flow and heat transfer of an electrically conducting micropolar fluid over a continuously moving stretching surface embedded in a non-Darcian porous medium with a uniform magnetic field were studied.
Abstract: We have studied the effects of radiation on the boundary layer flow and heat transfer of an electrically conducting micropolar fluid over a continuously moving stretching surface embedded in a non-Darcian porous medium with a uniform magnetic field. The transformed coupled nonlinear ordinary differential equations are solved numerically. The velocity, the angular velocity, and the temperature are shown graphically. The numerical values of the skin friction coefficient, the wall couple stress, and the wall heat transfer rate are computed and discussed for various values of parameters.
TL;DR: In this paper, a numerical study of transient natural convection in a square cavity with partly thermally active side walls is introduced, and the results are obtained for various values of amplitude, period, and Grashof numbers.
Abstract: A numerical study of transient natural convection in a square cavity with partly thermally active side walls is introduced. The thermally active regions of the side walls are periodic in time. Top and bottom of the cavity are adiabatic. Nine different positions of the thermally active zones are considered. The governing equations are solved using control volume method with power-law scheme. The results are obtained for various values of amplitude, period, and Grashof numbers ranging from 104–106 and different thermally active situations. It is found that the average heat transfer increases by increasing amplitude for P=1,5, and decreasing for P=3. The average Nusselt number behaves nonlinearly as a function of period.
TL;DR: In this paper, the exact distribution of the quotient |X/Y| is derived when X and Y are independent Gumbel and Laplace random variables, and tabulations of the associated percentage points and a computer program for generating them are also given.
Abstract: The Gumbel and the Laplace distributions are perhaps two of the most applied distributions in engineering. Motivated by engineering issues, the exact distribution of the quotient |X/Y| is derived when X and Y are independent Gumbel and Laplace random variables. Tabulations of the associated percentage points and a computer program for generating them are also given.
TL;DR: In this paper, the effect of an oscillatory motion of a viscoelastic fluid over an infinite stretching sheet through porous media in the presence of magnetic field with applied suction has been studied.
Abstract: The effect of an oscillatory motion of a viscoelastic fluid over an infinite stretching sheet through porous media in the presence of magnetic field with applied suction has been studied. The surface absorbs the fluid in a porous medium in the presence of magnetic field and the velocity oscillates depending on the stretching rate (b). Analytical expressions for the velocity and the coefficient of skin friction have been studied, first by the perturbation method and then by power series method. The effect of viscoelastic parameter k1, porous parameter k2, magnetic parameter Mn, and the vertical distance x in the presence of suction/blowing on the velocity and the flow characteristics are discussed. The velocity of the viscoelastic fluid is found to decrease in the presence of magnetic field and porous media, as compared to the study of viscous fluid. It is also found that the effect of unsteadiness in the wall velocity and skin friction are found to be appreciable in the presence of suction/blowing parameter.
TL;DR: An estimation is analytically obtained for the synchronous state in a generic N-node network relating free-running frequencies, node gains, and propagation delays.
Abstract: Fully connected phase-locked networks are built with all nodes exchanging phase and frequency signals. The nodes are phase-locked loops (PLLs) with slightly different free-running frequencies. The synchronous state emerges from a dynamic process with the phase interactions generating a common frequency steady state. In this work, an estimation is analytically obtained for the synchronous state in a generic N-node network. Numerical experiments complete the analysis of the fully connected network relating free-running frequencies, node gains, and propagation delays.
Abstract: This paper develops the procedure for the analysis of the production systems with quality control devices The evaluation of the production system requires an expression for the system performance measures as functions of the machine and buffer parameters This paper presents a method for evaluating these functions and illustrates their practical utility using a case study at a production plant
TL;DR: In this paper, the effect of service level constraint on the economic production quantity (EPQ) model with random defective rate was studied and an equation was proposed for calculating the intangible backorder cost for the situation when the required service level is not attainable.
Abstract: We study the effect of service level constraint on the economic production quantity (EPQ) model with random defective rate. We first prove that the expected overall cost for imperfect quality EPQ model with backlogging permitted is less than or equal to that of the same model without backlogging. Secondly, the relationship between “imputed backorder cost” and maximal shortage level is derived for decision-making on whether the required service level is achievable. Then an equation is proposed for calculating the intangible backorder cost for the situation when the required service level is not attainable. By including this intangible backorder cost in the mathematical analysis, one can derive a new optimal lot-size policy that minimizes expected total costs as well as satisfies the service level constraint. Numerical example is provided to demonstrate its practical usage.
TL;DR: In this paper, the applicability and the accuracy of linearization method in several problems of general nonlinear integral equations are assessed, and it is shown that the accuracy can be substantially improved by employing variable steps which adjust themselves to the solution.
Abstract: The objective of this paper is to assess both the applicability and the accuracy of linearization method in several problems of general nonlinear integral equations. This method provides piecewise linear integral equations which can be easily integrated. It is shown that the accuracy of linearization method can be substantially improved by employing variable steps which adjust themselves to the solution. This approach can reveal that, under this method, the nonlinear integral equations can be transformed into the linear integral equations which may be integrated using classical methods. Numerical examples are used to illustrate the preciseness and effectiveness of the proposed method.
TL;DR: In this paper, an analysis of chaotic behavior regions of oscillators with varying hysteresis is presented in various parametric planes, and a substantial influence of a hysteretic dissipation value on the form and location of these regions and also restraining and generating effects of the hystregating dissipation on chaos occurrence are shown.
Abstract: In the present work, hysteresis is simulated by means of internal
variables. Analytical models of different types of hysteresis
loops enable reproduction of major and minor loops and provide
good agreement with experimental data. Using an effective
algorithm based on the analysis of wandering trajectories, an
evolution of chaotic behavior regions of oscillators with
hysteresis is presented in various parametric planes. A
substantial influence of a hysteretic dissipation value on the
form and location of these regions and also restraining and
generating effects of the hysteretic dissipation on chaos
occurrence are shown. It was demonstrated that for fixed
parameters, which govern the shape of a hysteresis loop, the
extent of pinch of this loop could be controlled by means of the
amplitude and frequency of external periodic excitation.
TL;DR: In this paper, the authors studied bifurcations from sliding homoclinic solutions to bounded solutions on discontinuous planar systems under periodic perturbations and derived sufficient conditions for such perturbation problems.
Abstract: We study bifurcations from sliding homoclinic solutions to bounded solutions on ℝ for certain discontinuous planar systems under periodic perturbations. Sufficient conditions are derived for such perturbation problems.
TL;DR: In this paper, a technique for analysis of asymptotic stability for a subclass of differential inclusions is presented, which is based on the Lyapunov-type theorems.
Abstract: We present a technique for analysis of asymptotic stability for a
class of differential inclusions. This technique is based on the
Lyapunov-type theorems. The construction of the Lyapunov functions
for differential inclusions is reduced to an auxiliary problem of mathematical
programming, namely, to the problem of searching saddle points of
a suitable function. The computational approach to the auxiliary
problem contains a gradient-type algorithm for saddle-point problems. We also extend our main results to systems
described by difference inclusions. The obtained numerical schemes
are applied to some illustrative examples.
TL;DR: In this paper, a nonlinear two-degree-of-freedom system with linear oscillators and a vibro-impact oscillator was considered, where the linear oscillator is an approximation of some continuous elastic system, and the vibro impact oscillator acts as an absorber of the linear system vibrations.
Abstract: The nonlinear two-degree-of-freedom system under consideration consists of the linear oscillator with a relatively big mass, which is an approximation of some continuous elastic system, and of the vibro-impact oscillator with a relatively small mass, which is an absorber of the linear system vibrations. Analysis of nonlinear normal vibration modes shows that a stable localized vibration mode, which provides the vibration regime appropriate for the elastic vibration absorption, exists in a large region of the system parameters. In this regime, amplitudes of vibrations of the linear system are small, simultaneously vibrations of the absorber are significant.
TL;DR: In this paper, analytical methods for selecting lean buffering in serial production lines are developed under the assumption that the machines obey the Bernoulli reliability model, both closed-form expressions and recursive approaches are investigated.
Abstract: Lean buffering is the smallest buffer capacity necessary to ensure the desired production rate of a manufacturing system. In this paper, analytical methods for selecting lean buffering in serial production lines are developed under the assumption that the machines obey the Bernoulli reliability model. Both closed-form expressions and recursive approaches are investigated. The cases of identical and nonidentical machines are analyzed. Results obtained can be useful for production line designers and production managers to maintain the required production rate with the smallest possible inventories.
TL;DR: In this paper, sufficient conditions of asymptotic stability for discrete-time linear systems subject to actuator saturations with an output feedback law were derived in terms of LMIs.
Abstract: This paper presents sufficient conditions of asymptotic stability
for discrete-time linear systems subject to actuator saturations
with an output feedback law. The derived stability results are
given in terms of LMIs. A new proof is presented to
obtain previous conditions of asymptotic stability. A numerical
example is used to illustrate this technique by using a linear
optimization problem subject to LMI constraints.
TL;DR: A multiserver queueing model with the semi-Markovian arrival process and exponential service time distribution is considered, where the customer, which sees several free servers upon arrival, is served simultaneously by all these servers.
Abstract: We consider a multiserver queueing model with the semi-Markovian arrival process and exponential service time distribution. Novel customers admission discipline is under study. The customer, which sees several free servers upon arrival, is served simultaneously by all these servers. Such situation occurs, for example, in modeling wireless communication network with broadcasting. Systems with infinite buffer and with losses are investigated. Stationary distributions of a queue, waiting and sojourn times, and the main performance measures are calculated.