Search results for: system of nonlinear equations

Authors: Der Chyan Lin

Abstract:

Since the early introduction by Ormondroyd and Den Hartog, vibration absorber (VA) has become one of the most commonly used vibration mitigation strategies. The strategy is most effective for a primary plant subjected to a single frequency excitation. For continuous systems, notable advances in vibration absorption in the multi-frequency system were made. However, the efficacy of the VA strategy for systems under multi-frequency excitation is not well understood. For example, for an N degrees-of-freedom (DOF) primary-absorber system, there are N 'peak' frequencies of large amplitude vibration per every new excitation frequency. In general, the usable range for vibration absorption can be greatly reduced as a result. Frequency modulated harmonic excitation is a commonly seen multi-frequency excitation example: f(t) = cos(ϖ(t)t) where ϖ(t)=ω(1+α sin⁡(δt)). It is known that f(t) has a series expansion given by the Bessel function of the first kind, which implies an infinity of forcing frequencies in the frequency modulated harmonic excitation. For an SDOF system of natural frequency ωₙ subjected to f(t), it can be shown that amplitude peaks emerge at ω₍ₚ,ₖ₎=(ωₙ ± 2kδ)/(α ∓ 1),k∈Z; i.e., there is an infinity of resonant frequencies ω₍ₚ,ₖ₎, k∈Z, making the use of VA strategy ineffective. In this work, we propose an absorber frequency placement strategy for SDOF vibration systems subjected to frequency-modulated excitation. An SDOF linear mass-spring system coupled to lateral absorber systems is used to demonstrate the ideas. Although the mechanical components are linear, the governing equations for the coupled system are nonlinear. We show using N identical absorbers, for N ≫ 1, that (a) there is a cluster of N+1 natural frequencies around every natural absorber frequency, and (b) the absorber frequencies can be moved away from the plant's resonance frequency (ω₀) as N increases. Moreover, we also show the bandwidth of the VA performance increases with N. The derivations of the clustering and bandwidth widening effect will be given, and the superiority of the proposed strategy will be demonstrated via numerical experiments.

Keywords: Bessel function, bandwidth, frequency modulated excitation, vibration absorber

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Authors: Shaban Aly, Ali Al-Qahtani, Houari B. Khenous

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Synchronization is an important phenomenon commonly observed in nature. A system of periodically forced complex Duffings oscillators was introduced and shown to display chaotic behavior and possess strange attractors. Such complex oscillators appear in many problems of physics and engineering, as, for example, nonlinear optics, deep-water wave theory, plasma physics and bimolecular dynamics. In this paper, we study the remarkable phenomenon of chaotic synchronization on these oscillator systems, using impulsive synchronization techniques. We derive analytical expressions for impulsive control functions and show that the dynamics of error evolution is globally stable, by constructing appropriate Lyapunov functions. This means that, for a relatively large set initial conditions, the differences between the drive and response systems vanish exponentially and synchronization is achieved. Numerical results are obtained to test the validity of the analytical expressions and illustrate the efficiency of these techniques for inducing chaos synchronization in our nonlinear oscillators.

Keywords: complex nonlinear oscillators, impulsive synchronization, chaotic systems, global exponential synchronization

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Authors: A. Zerarka, W. Djoudi

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We use some fractional transformations to obtain many types of new exact solutions of nonlinear lattice equation. These solutions include rational solutions, periodic wave solutions, and doubly periodic wave solutions.

Keywords: fractional transformations, nonlinear equation, travelling wave solutions, lattice equation

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Authors: Eugene Stepanov, Arkadi Ponossov

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Ordinary differential equations with switching nonlinearities constitute a very useful tool in many applications. The solutions of such equations can usually be calculated analytically if they cross the discontinuities transversally. Otherwise, one has trajectories that slides along the discontinuity, and the calculations become less straightforward in this case. For instance, one of the problems one faces is non-uniqueness of the sliding modes. In the presentation, it is proposed to apply the theory of hybrid dynamical systems to calculate the solutions that are ‘hidden’ in the discontinuities. Roughly, one equips the underlying switched system with an explicitly designed discrete dynamical system (‘automaton’), which governs the dynamics of the switched system. This construction ‘splits’ the dynamics, which, as it is shown in the presentation, gives uniqueness of the resulting hybrid trajectories and at the same time provides explicit formulae for them. Projecting the hybrid trajectories back onto the original continuous system explains non-uniqueness of its trajectories. The automaton is designed with the help of the attractors of the specially constructed adjoint dynamical system. Several examples are provided in the presentation, which supports the efficiency of the suggested scheme. The method can be of interest in control theory, gene regulatory networks, neural field models and other fields, where switched dynamics is a part of the analysis.

Keywords: hybrid dynamical systems, singular perturbation analysis, sliding modes, switched dynamics

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Authors: Hamid Goharnejad, Milad Sadeghpoor Moalem, Mahmood Zakeri Niri, Leili Sadeghi Khalegh Abadi

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While there are many benefits to using reservoir dams, their break leads to destructive effects. From the viewpoint of International Committee of Large Dams (ICOLD), dam break means the collapse of whole or some parts of a dam; thereby the dam will be unable to hold water. Therefore, studying dam break phenomenon and prediction of its behavior and effects reduces losses and damages of the mentioned phenomenon. One of the most common types of reservoir dams is embankment dam. Overtopping in embankment dams occurs because of flood discharge system inability in release inflows to reservoir. One of the most important issues among managers and engineers to evaluate the performance of the reservoir dam rim when sliding into the storage, creating waves is large and long. In this study, the effects of floods which caused the overtopping of the dam have been investigated. It was assumed that spillway is unable to release the inflow. To determine outflow hydrograph resulting from dam break, numerical model using Flow-3D software and empirical equations was used. Results of numerical models and their comparison with empirical equations show that numerical model and empirical equations can be used to study the flood resulting from dam break.

Keywords: embankment dam break, empirical equations, Taleghan dam, Flow-3D numerical model

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Authors: Hendradi Hardhienata, Tony Sumaryada, Sri Setyaningsih

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Current progress in the field of nonlinear optics has enabled precise surface characterization in semiconductor materials. Nonlinear optical techniques are favorable due to their nondestructive measurement and ability to work in nonvacuum and ambient conditions. The advance of the bond hyperpolarizability models opens a wide range of nanoscale surface investigation including the possibility to detect molecular orientation at the surface of silicon and zincblende semiconductors, investigation of electric field induced second harmonic fields at the semiconductor interface, detection of surface impurities, and very recently, study surface defects such as twin boundary in wurtzite semiconductors. In this work, we show using nonlinear optical techniques, e.g. nonlinear bond models how arbitrary polarization of the incoming electric field in Rotational Anisotropy Spectroscopy experiments can provide more information regarding the origin of the nonlinear sources in zincblende and wurtzite semiconductor structure. In addition, using hyperpolarizability consideration, we describe how the nonlinear susceptibility tensor describing SHG can be well modelled using only few parameter because of the symmetry of the bonds. We also show how the third harmonic intensity feature shows considerable changes when the incoming field polarization angle is changed from s-polarized to p-polarized. We also propose a method how to investigate surface reconstruction and defects in wurtzite and zincblende structure at the nanoscale level.

Keywords: surface characterization, bond model, rotational anisotropy spectroscopy, effective hyperpolarizability

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Authors: Andriy Didenko, Zanin Kavazovic

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Engineering students often have certain difficulties in mastering major theoretical concepts in mathematical courses such as differential equations. Student projects were proposed to motivate students’ learning and can be used as a tool to promote students’ interest in the material. Authors propose a student project that includes the use of Microsoft Excel. This instructional tool is often overlooked by both educators and students. An integral component of the experimental part of such a project is the exploration of an interactive spreadsheet. The aim is to assist engineering students in better understanding of Euler’s method. This method is employed to numerically solve first order differential equations. At first, students are invited to select classic equations from a list presented in a form of a drop-down menu. For each of these equations, students can select and modify certain key parameters and observe the influence of initial condition on the solution. This will give students an insight into the behavior of the method in different configurations as solutions to equations are given in numerical and graphical forms. Further, students could also create their own equations by providing functions of their own choice and a variety of initial conditions. Moreover, they can visualize and explore the impact of the length of the time step on the convergence of a sequence of numerical solutions to the exact solution of the equation. As a final stage of the project, students are encouraged to develop their own spreadsheets for other numerical methods and other types of equations. Such projects promote students’ interest in mathematical applications and further improve their mathematical and programming skills.

Keywords: student project, Euler's method, spreadsheet, engineering education

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Authors: Mei-Jie Xu, Yang Zhong

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Based on the symplectic geometry method, the theory of Hamilton system can be applied in the analysis of problem solved using the theory of elasticity and in the solution of elliptic partial differential equations. With this technique, this paper derives the theoretical solution for a thick rectangular plate with four free edges supported on a Winkler foundation by variable separation method. In this method, the governing equation of thick plate was first transformed into state equations in the Hamilton space. The theoretical solution of this problem was next obtained by applying the method of variable separation based on the Hamilton system. Compared with traditional theoretical solutions for rectangular plates, this method has the advantage of not having to assume the form of deflection functions in the solution process. Numerical examples are presented to verify the validity of the proposed solution method.

Keywords: symplectic geometry method, Winkler foundation, thick rectangular plate, variable separation method, Hamilton system

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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Authors: Davit Shahnazaryan, Diogo Gomes, Mher Safaryan

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Many symbolic computations and manipulations required in the analysis of partial differential equations (PDE) or systems of PDEs are tedious and error-prone. These computations arise when determining conservation laws, entropies or integral identities, which are essential tools for the study of PDEs. Here, we discuss a new Mathematica package for the symbolic analysis of PDEs that automate multiple tasks, saving time and effort. Methodologies: During the research, we have used concepts of linear algebra and partial differential equations. We have been working on creating algorithms based on theoretical mathematics to find results mentioned below. Major Findings: Our package provides the following functionalities; finding symmetry group of different PDE systems, generation of polynomials invariant with respect to different symmetry groups; simplification of integral quantities by integration by parts and null Lagrangian cleaning, computing general forms of expressions by integration by parts; finding equivalent forms of an integral expression that are simpler or more symmetric form; determining necessary and sufficient conditions on the coefficients for the positivity of a given symbolic expression. Conclusion: Using this package, we can simplify integral identities, find conserved and dissipated quantities of time-dependent PDE or system of PDEs. Some examples in the theory of mean-field games and semiconductor equations are discussed.

Keywords: partial differential equations, symbolic computation, conserved and dissipated quantities, mathematica

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Authors: Zahid Ullah, Atlas Khan

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This research endeavors to explore the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. These equations hold significance in understanding complex physical systems like porous media flow, with applications spanning various branches of mathematics. The focus is on unraveling and analyzing regularity results to gain insights into the smoothness of solutions for these highly degenerate equations. Elliptic equations, fundamental in expressing and understanding diverse physical phenomena through partial differential equations (PDEs), are particularly adept at modeling steady-state and equilibrium behaviors. However, within the realm of elliptic equations, the subset of extremely degenerate cases presents a level of complexity that challenges traditional analytical methods, necessitating a deeper exploration of mathematical theory. While elliptic equations are celebrated for their versatility in capturing smooth and continuous behaviors across different disciplines, the introduction of degeneracy adds a layer of intricacy. Extremely degenerate elliptic equations are characterized by coefficients approaching singular behavior, posing non-trivial challenges in establishing classical solutions. Still, the exploration of extremely degenerate cases remains uncharted territory, requiring a profound understanding of mathematical structures and their implications. The motivation behind this research lies in addressing gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations. The study of extreme degeneracy is prompted by its prevalence in real-world applications, where physical phenomena often exhibit characteristics defying conventional mathematical modeling. Whether examining porous media flow or highly anisotropic materials, comprehending the regularity of solutions becomes crucial. Through this research, the aim is to contribute not only to the theoretical foundations of mathematics but also to the practical applicability of mathematical models in diverse scientific fields.

Keywords: elliptic equations, extremely degenerate, regularity results, partial differential equations, mathematical modeling, porous media flow

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Authors: Mohammad Reza Esmaili

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After the occurrence of blackouts, the most important subject is how fast the electric service is restored. Power system restoration is an immensely complex issue and there should be a plan to be executed within the shortest time period. This plan has three main stages of black start, network reconfiguration and load restoration. In the black start stage, operators and experts may face several problems, for instance, the unsuccessful connection of the long high-voltage transmission line connected to the electrical source. In this situation, the generator may be tripped because of the unsuitable setting of its line charging mode or high absorbed reactive power. In order to solve this problem, the line charging process is defined as a nonlinear programming problem, and it is optimized by using GAMS software in this paper. The optimized process is performed on a grid that includes a 250 MW hydroelectric unit and a 400 KV transmission system. Simulations and field test results show the effectiveness of optimal planning.

Keywords: power system restoration, black start, line charging mode, nonlinear programming

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Authors: Daniel S. Brox

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Starting from earthquake fault dynamic equations, a correspondence between earthquake occurrence statistics in a seismic region before a major earthquake and eigenvalue statistics of a differential operator whose bound state eigenfunctions characterize the distribution of stress in the seismic region is derived. Modeling these eigenvalue statistics with a 2D Coulomb gas statistical physics model, previously reported deviation of seismic activation earthquake occurrence statistics from Gutenberg-Richter statistics in time intervals preceding the major earthquake is derived. It also explains how statistical physics modeling predicts a finite-dimensional nonlinear dynamic system that describes real-time velocity model evolution in the region undergoing seismic activation and how this prediction can be tested experimentally.

Keywords: seismic activation, statistical physics, geodynamics, signal processing

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Authors: Ayaz Ahmad

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In this work, we present the effect of noise on the solution of a partial differential equation (PDE) in three different setting. We shall first consider random initial condition for two nonlinear dispersive PDE the non linear Schrodinger equation and the Kortteweg –de vries equation and analyse their effect on some special solution , the soliton solutions.The second case considered a linear partial differential equation , the wave equation with random initial conditions allow to substantially decrease the computational and data storage costs of an algorithm to solve the inverse problem based on the boundary measurements of the solution of this equation. Finally, the third example considered is that of the linear transport equation with a singular drift term, when we shall show that the addition of a multiplicative noise term forbids the blow up of solutions under a very weak hypothesis for which we have finite time blow up of a solution in the deterministic case. Here we consider the problem of wave propagation, which is modelled by a nonlinear dispersive equation with noisy initial condition .As observed noise can also be introduced directly in the equations.

Keywords: drift term, finite time blow up, inverse problem, soliton solution

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Authors: A. S. Gorobtsov, A. S. Polyanina, A. E. Andreev

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The movement of points feet of the anthropomorphous robot in space occurs along some stable trajectory of a known form. A large number of modifications to the methods of control of biped robots indicate the fundamental complexity of the problem of stability of the program trajectory and, consequently, the stability of the control for the deviation for this trajectory. Existing gait generators use piecewise interpolation of program trajectories. This leads to jumps in the acceleration at the boundaries of sites. Another interpolation can be realized using differential equations with fractional derivatives. In work, the approach to synthesis of generators of program trajectories is considered. The resulting system of nonlinear differential equations describes a smooth trajectory of movement having rectilinear sites. The method is based on the theory of an asymptotic stability of invariant sets. The stability of such systems in the area of localization of oscillatory processes is investigated. The boundary of the area is a bounded closed surface. In the corresponding subspaces of the oscillatory circuits, the resulting stable limit cycles are curves having rectilinear sites. The solution of the problem is carried out by means of synthesis of a set of the continuous smooth controls with feedback. The necessary geometry of closed trajectories of movement is obtained due to the introduction of high-order nonlinearities in the control of stabilization systems. The offered method was used for the generation of trajectories of movement of point’s feet of the anthropomorphous robot. The synthesis of the robot's program movement was carried out by means of the inverse method.

Keywords: control, limits cycle, robot, stability

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Authors: Mohamed Omar

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Steel bracing members are widely used in steel structures to reduce lateral displacement and dissipate energy during earthquake motions. Concentric steel bracing provide an excellent approach for strengthening and stiffening steel buildings. Using these braces the designer can hardly adjust the stiffness together with ductility as needed because of buckling of braces in compression. In this study the use of SMA bracing and steel bracing (Mega) utilized in steel frames are investigated. The effectiveness of these two systems in rehabilitating a mid-rise eight-storey steel frames were examined using time-history nonlinear analysis utilizing Seismo-Struct software. Results show that both systems improve the strength and stiffness of the original structure but due to excellent behavior of SMA in nonlinear phase and under compressive forces this system shows much better performance than the rehabilitation system of Mega bracing.

Keywords: finite element analysis, seismic response, shapes memory alloy, steel frame, mega bracing

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Authors: Dehini Rachid, Ferdi Brahim

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The shunt active power filter (SAPF) is not destined only to improve the power factor, but also to compensate the unwanted harmonic currents produced by nonlinear loads. This paper presents a SAPF with identification and control method based on artificial neural network (ANN). To identify harmonics, many techniques are used, among them the conventional p-q theory and the relatively recent one the artificial neural network method. It is difficult to get satisfied identification and control characteristics by using a normal (ANN) due to the nonlinearity of the system (SAPF + fast nonlinear load variations). This work is an attempt to undertake a systematic study of the problem to equip the (SAPF) with the harmonics identification and DC link voltage control method based on (ANN). The latter has been applied to the (SAPF) with fast nonlinear load variations. The results of computer simulations and experiments are given, which can confirm the feasibility of the proposed active power filter.

Keywords: artificial neural networks (ANN), p-q theory, harmonics, total harmonic distortion

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Authors: Prashant G. Metri

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A numerical model is developed to study nano liquid film flow over an unsteady stretching sheet in the presence of hydromagnetic have been investigated. Similarity transformations are used to convert unsteady boundary layer equations to a system of non-linear ordinary differential equations. The resulting non-linear ordinary differential equations are solved numerically using Runge-Kutta-Fehlberg and Newton-Raphson schemes. A relationship between film thickness β and the unsteadiness parameter S is found, the effect of unsteadiness parameter S, and the hydromagnetic parameter S, on the velocity and temperature distributions are presented. The present analysis shows that the combined effect of magnetic field and viscous dissipation has a significant influence in controlling the dynamics of the considered problem. Comparison with known results for certain particular cases is in excellent agreement.

Keywords: boundary layer flow, nanoliquid, thin film, unsteady stretching sheet

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Authors: M. S. H. Chowdhury, Ishak Hashim

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In this paper, linear and non-linear stiff systems of ordinary differential equations are solved by the classical Adomian decomposition method (ADM) and the multi-stage Adomian decomposition method (MADM). The MADM is a technique adapted from the standard Adomian decomposition method (ADM) where standard ADM is converted into a hybrid numeric-analytic method called the multistage ADM (MADM). The MADM is tested for several examples. Comparisons with an explicit Runge-Kutta-type method (RK) and the classical ADM demonstrate the limitations of ADM and promising capability of the MADM for solving stiff initial value problems (IVPs).

Keywords: stiff system of ODEs, Runge-Kutta Type Method, Adomian decomposition method, Multistage ADM

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Authors: Trilok Mathur, Shivi Agarwal

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This paper deals with the solutions of fuzzy-fractional-order Riccati equations under Caputo-type fuzzy fractional derivatives. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhura difference and strongly generalized fuzzy differentiability. The Laplace-Adomian-Pade method is used for solving fractional Riccati-type initial value differential equations of fractional order. Moreover, we also displayed some examples to illustrate our methods.

Keywords: Caputo-type fuzzy fractional derivative, Fractional Riccati differential equations, Laplace-Adomian-Pade method, Mittag Leffler function

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Authors: Y. N. Reddy

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The class of differential-difference equations which have characteristics of both classes, i.e., delay/advance and singularly perturbed behaviour is known as singularly perturbed differential-difference equations. The expression ‘positive shift’ and ‘negative shift’ are also used for ‘advance’ and ‘delay’ respectively. In general, an ordinary differential equation in which the highest order derivative is multiplied by a small positive parameter and containing at least one delay/advance is known as singularly perturbed differential-difference equation. Singularly perturbed differential-difference equations arise in the modelling of various practical phenomena in bioscience, engineering, control theory, specifically in variational problems, in describing the human pupil-light reflex, in a variety of models for physiological processes or diseases and first exit time problems in the modelling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. In this paper, we envisage the use of Liouville Green Transformation to find the solution of singularly perturbed differential difference equations. First, using Taylor series, the given singularly perturbed differential difference equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. Several model examples are solved, and the results are compared with other methods. It is observed that the present method gives better approximate solutions.

Keywords: difference equations, differential equations, singular perturbations, boundary layer

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Authors: Hamid Ahmadi, Neda Azari-Dodaran

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A total of 270 nonlinear steady-state finite element (FE) analyses were performed on 54 FE models of two-planar circular hollow section (CHS) KK-joints subjected to axial loading at five different temperatures (20 ºC, 200 ºC, 400 ºC, 550 ºC, and 700 ºC). The primary goal was to investigate the effects of temperature and geometrical characteristics on the ultimate strength, modes of failure, and initial stiffness of the KK-joints. Results indicated that on an average basis, the ultimate load of a two-planar tubular KK-joint at 200 ºC, 400 ºC, 550 ºC, and 700 ºC is 90%, 75%, 45%, and 16% of the joint’s ultimate load at ambient temperature, respectively. Outcomes of the parametric study showed that replacing the yield stress at ambient temperature with the corresponding value at elevated temperature to apply the EN 1993-1-8 equations for the calculation of the joint’s ultimate load at elevated temperatures may lead to highly unconservative results that might endanger the safety of the structure. Results of the parametric study were then used to develop a set of design formulas, through nonlinear regression analyses, to calculate the ultimate load of two-planar tubular KK-joints subjected to axial loading at elevated temperatures.

Keywords: ultimate load, two-planar tubular KK-joint, axial loading, elevated temperature, parametric equation

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Authors: A. Torokhti

Abstract:

A new method of mathematical modeling of the distributed nonlinear system is developed. The system is represented by a combination of the set of spatially distributed sensors and the fusion center. Its mathematical model is obtained from the iterative procedure that converges to the model which is optimal in the sense of minimizing an associated cost function.

Keywords: mathematical modeling, non-linear system, spatially distributed sensors, fusion center

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Authors: Esra Zengin, Sinan Akkar

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Reliable and accurate prediction of nonlinear structural response requires specification of appropriate earthquake ground motions to be used in nonlinear time history analysis. The current research has mainly focused on selection and manipulation of real earthquake records that can be seen as the most critical step in the performance based seismic design and assessment of the structures. Utilizing amplitude scaled ground motions that matches with the target spectra is commonly used technique for the estimation of nonlinear structural response. Representative ground motion ensembles are selected to match target spectrum such as scenario-based spectrum derived from ground motion prediction equations, Uniform Hazard Spectrum (UHS), Conditional Mean Spectrum (CMS) or Conditional Spectrum (CS). Different sets of criteria exist among those developed methodologies to select and scale ground motions with the objective of obtaining robust estimation of the structural performance. This study presents ground motion selection and scaling procedure that considers the spectral variability at target demand with the level of ground motion dispersion. The proposed methodology provides a set of ground motions whose response spectra match target median and corresponding variance within a specified period interval. The efficient and simple algorithm is used to assemble the ground motion sets. The scaling stage is based on the minimization of the error between scaled median and the target spectra where the dispersion of the earthquake shaking is preserved along the period interval. The impact of the spectral variability on nonlinear response distribution is investigated at the level of inelastic single degree of freedom systems. In order to see the effect of different selection and scaling methodologies on fragility curve estimations, results are compared with those obtained by CMS-based scaling methodology. The variability in fragility curves due to the consideration of dispersion in ground motion selection process is also examined.

Keywords: ground motion selection, scaling, uncertainty, fragility curve

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Authors: Alireza Abbasi Moshaii, Shaghayegh Nasiri, Mehdi Tale Masouleh

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The main purpose of this study is static analysis of two three-degree of freedom parallel mechanisms: 3-RCC and 3-RRS. Geometry of these mechanisms is expressed and static equilibrium equations are derived for the whole chains. For these mechanisms due to the equal number of equations and unknowns, the solution is as same as 3-RCC mechanism. Mathematical software is used to solve the equations. In order to prove the results obtained from solving the equations of mechanisms, their CAD model has been simulated and their static is analysed in ADAMS software. Due to symmetrical geometry of the mechanisms, the force and external torque acting on the end-effecter have been considered asymmetric to prove the generality of the solution method. Finally, the results of both softwares, for both mechanisms are extracted and compared as graphs. The good achieved comparison between the results indicates the accuracy of the analysis.

Keywords: robotic, static analysis, 3-RCC, 3-RRS

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Authors: Hisham M. Soliman, Hassan Yousef

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This manuscript presents new results on design saturated power system stabilizers (PSS) to assign system poles within a desired region for achieving good dynamic performance. The regional pole placement is accomplished against model uncertainties caused by different load conditions. The design is based on a sufficient condition in the form of linear matrix inequalities (LMI) which forces the saturated nonlinear controller to lie within the linear zone. The controller effectiveness is demonstrated on a single machine infinite bus system.

Keywords: power system stabilizer, saturated control, robust control, regional pole placement, linear matrix inequality (LMI)

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Authors: H. Niranjan, S. Sivasankaran, Zailan Siri

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This study investigates mixed convection heat transfer about a thin vertical plate in the presence of magnetohydrodynamic (MHD) and heat transfer effects in the porous medium. The fluid is assumed to be steady, laminar, incompressible and in two-dimensional flow. The nonlinear coupled parabolic partial differential equations governing the flow are transformed into the non-similar boundary layer equations, which are then solved numerically using the shooting method. The effects of the conjugate heat transfer parameter, the porous medium parameter, the permeability parameter, the mixed convection parameter, the magnetic parameter, and the thermal radiation on the velocity and temperature profiles as well as on the local skin friction and local heat transfer are presented and analyzed. The validity of the methodology and analysis is checked by comparing the results obtained for some specific cases with those available in the literature. The various parameters on local skin friction, heat and mass transfer rates are presented in tabular form.

Keywords: MHD, porous medium, soret/dufour, stagnation-point

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Authors: Ali Ballouch, Nourelhouda Choukri, Zouhair Soufiani, Mohamed El Jouad, Mohamed Addou

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For several years, significant research has been developed in the areas of applications of semiconductor wide bandgap such as ZnO in optoelectronics. This oxide has the advantage of having a large exciton energy (60 meV) three times higher than that of GaN (21 meV) or ZnS (20 meV). This energy makes zinc oxide resistant for laser irradiations and very interesting for the near UV-visible optic, as well as for studying physical microcavities. A high-energy direct gap at room temperature (Eg > 1 eV) which makes it a potential candidate for emitting devices in the near UV and visible. Our work is to study the nonlinear optical properties, mainly the nonlinear third-order susceptibility of europium doped Zinc oxide thin films. The samples were prepared by chemical vapor spray method (Spray), XRD, SEM technique, THG were used for characterization. In this context, the influence of europium doping on the nonlinear optical response of the Zinc oxide was investigated. The nonlinear third-order properties depend on the physico-chemical parameters (crystallinity, strain, and surface roughness), the nature and the level of doping, temperature.

Keywords: ZnO, characterization, non-linear optical properties, optoelectronics

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Authors: Jin Liang, James H. Liu, Ti-Jun Xiao

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It is known that there exist many physical phenomena where abrupt or impulsive changes occur either in the system dynamics, for example, ad-hoc network, or in the input forces containing impacts, for example, the bombardment of space antenna by micrometeorites. There are many other examples such as ultra high-speed optical signals over communication networks, the collision of particles, inventory control, government decisions, interest changes, changes in stock price, etc. These are impulsive phenomena. Hence, as a combination of the traditional initial value problems and the short-term perturbations whose duration can be negligible in comparison with the duration of the process, the systems with impulsive conditions (i.e., impulsive systems) are more realistic models for describing the impulsive phenomenon. Such a situation is also suitable for the delay systems, which include some of the past states of the system. So far, there have been a lot of research results in the study of impulsive systems with delay both in finite and infinite dimensional spaces. In this paper, we investigate the periodicity of solutions to the nonautonomous impulsive evolution equations with infinite delay in Banach spaces, where the coefficient operators (possibly unbounded) in the linear part depend on the time, which are impulsive systems in infinite dimensional spaces and come from the optimal control theory. It was indicated that the study of periodic solutions for these impulsive evolution equations with infinite delay was challenging because the fixed point theorems requiring some compactness conditions are not applicable to them due to the impulsive condition and the infinite delay. We are happy to report that after detailed analysis, we are able to combine the techniques developed in our previous papers, and some new ideas in this paper, to attack these impulsive evolution equations and derive periodic solutions. More specifically, by virtue of the related transition operator family (evolution family), we present a Poincaré operator given by the nonautonomous impulsive evolution system with infinite delay, and then show that the operator is a condensing operator with respect to Kuratowski's measure of non-compactness in a phase space by using an Amann's lemma. Finally, we derive periodic solutions from bounded solutions in view of the Sadovskii fixed point theorem. We also present a relationship between the boundedness and the periodicity of the solutions of the nonautonomous impulsive evolution system. The new results obtained here extend some earlier results in this area for evolution equations without impulsive conditions or without infinite delay.

Keywords: impulsive, nonautonomous evolution equation, optimal control, periodic solution

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Authors: Lizhou Chen, Abdelhamid Belgaid, Assem Elsayed, Xiaoming Yang

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Compression index is essential in foundation settlement calculation. The traditional method for determining compression index is consolidation test which is expensive and time consuming. Many researchers have used regression methods to develop empirical equations for predicting compression index from soil properties. Based on a large number of compression index data collected from consolidation tests, the accuracy of some popularly empirical equations were assessed. It was found that primary compression index is significantly overestimated in some equations while it is underestimated in others. The sensitivity analyses of soil parameters including water content, liquid limit and void ratio were performed. The results indicate that the compression index obtained from void ratio is most accurate. The ANOVA (analysis of variance) demonstrates that the equations with multiple soil parameters cannot provide better predictions than the equations with single soil parameter. In other words, it is not necessary to develop the relationships between compression index and multiple soil parameters. Meanwhile, it was noted that secondary compression index is approximately 0.7-5.0% of primary compression index with an average of 2.0%. In the end, the proposed prediction equations using power regression technique were provided that can provide more accurate predictions than those from existing equations.

Keywords: compression index, clay, settlement, consolidation, secondary compression index, soil parameter

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