Search results for: equivalent nonlinear spring

Authors: Ridha Salhi, Mondher Labidi, Fethi Choubani

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Metamaterials have attracted much attention in recent years because of their electromagnetic exquisite proprieties. We will present, in this paper, the modeling of three metamaterial structures by equivalent circuit model. We begin by modeling the SRR (Split Ring Resonator), then we model the HIS (High Impedance Surfaces), and finally, we present the model of the CPW (Coplanar Wave Guide). In order to validate models, we compare the results obtained by an equivalent circuit models with numerical simulation.

Keywords: metamaterials, SRR, HIS, CPW, IDC

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Authors: E. Shahsavari, R. Ghasemi, A. Akramizadeh

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This paper presents a new method to design nonlinear feedback linearization controller for polymer electrolyte membrane fuel cells (PEMFCs). A nonlinear controller is designed based on nonlinear model to prolong the stack life of PEM fuel cells. Since it is known that large deviations between hydrogen and oxygen partial pressures can cause severe membrane damage in the fuel cell, feedback linearization is applied to the PEM fuel cell system so that the deviation can be kept as small as possible during disturbances or load variations. To obtain an accurate feedback linearization controller, tuning the linear parameters are always important. So in proposed study NSGA_II method was used to tune the designed controller in aim to decrease the controller tracking error. The simulation result showed that the proposed method tuned the controller efficiently.

Keywords: nonlinear dynamic model, polymer electrolyte membrane fuel cells, feedback linearization, optimal control, NSGA_II

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Authors: Tai-Ping Chang

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In the present study, the effects on chaotic motion of single-walled carbon nanotube (SWCNT) due to the linear and nonlinear damping are investigated. By using the Hamilton’s principle, the nonlinear governing equation of the single-walled carbon nanotube embedded in a matrix is derived. The Galerkin’s method is adopted to simplify the integro-partial differential equation into a nonlinear dimensionless governing equation for the SWCNT, which turns out to be a forced Duffing equation. The variations of the Lyapunov exponents of the SWCNT with damping and harmonic forcing amplitudes are investigated. Based on the computations of the top Lyapunov exponent, it is concluded that the chaotic motion of the SWCNT occurs when the amplitude of the periodic excitation exceeds certain value, besides, the chaotic motion of the SWCNT occurs with small linear damping and tiny nonlinear damping.

Keywords: chaotic motion, damping, Lyapunov exponents, single-walled carbon nanotube

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Authors: Kuo-Teng Tsai, You-Min Huang

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In this study, the problem of a spiral fin with a period base temperature is analyzed by using the Adomian decomposition method. The Adomian decomposition method is a useful and practice method to solve the nonlinear energy equation which are associated with the heat radiation. The period base temperature is around a mean value. The results including the temperature distribution and the heat flux from the spiral fin base can be calculated directly. The results also discussed the effects of the dimensionless variables for the temperature variations and the total energy transferred from the spiral fin base.

Keywords: spiral fin, period, adomian decomposition method, nonlinear

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Authors: Tudor Barbu

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We present a robust nonlinear parabolic partial differential equation (PDE)-based denoising scheme in this article. Our approach is based on a second-order anisotropic diffusion model that is described first. Then, a consistent and explicit numerical approximation algorithm is constructed for this continuous model by using the finite-difference method. Finally, our restoration experiments and method comparison, which prove the effectiveness of this proposed technique, are discussed in this paper.

Keywords: anisotropic diffusion, finite differences, image denoising and restoration, nonlinear PDE model, anisotropic diffusion, numerical approximation schemes

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Authors: Birinderjit Singh Kalyan, Inderpreet Kaur, Balwinder Singh Sohi

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In this paper, an equivalent model for floating gate transistor has been proposed. Using the floating gate voltage value, capacitive coupling coefficients has been found at different bias conditions. The amount of charge present on the gate has been then calculated using the transient models of hot electron programming and Fowler-Nordheim Tunnelling. The proposed model can be extended to the transient conditions as well. The SPICE equivalent model is designed and current-voltage characteristics and Transfer characteristics are comparatively analysed. The dc current-voltage characteristics, as well as dc transfer characteristics, have been plotted for an FGMOS with W/L=0.25μm/0.375μm, the inter-poly capacitance of 0.8fF for both programmed and erased states. The Comparative analysis has been made between the present model and capacitive coefficient coupling methods which were already available.

Keywords: FGMOS, floating gate transistor, capacitive coupling coefficient, SPICE model

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Authors: Hua Cao, Laurent Peyrodie, Olivier Agnani, Cecile Donze

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Multiple sclerosis (MS) is a disease, which affects the central nervous system, and causes balance problem. In clinical, this disorder is usually evaluated using static posturography. Some linear or nonlinear measures, extracted from the posturographic data (i.e. center of pressure, COP) recorded during a balance test, has been used to analyze postural control of MS patients. In this study, the trend (TREND) and the sample entropy (SampEn), two nonlinear parameters were chosen to investigate their relationships with the expanded disability status scale (EDSS) score. Forty volunteers with different EDSS scores participated in our experiments with eyes open (EO) and closed (EC). TREND and two types of SampEn (SampEn1 and SampEn2) were calculated for each combined COP’s position signal. The results have shown that TREND had a weak negative correlation to EDSS while SampEn2 had a strong positive correlation to EDSS. Compared to TREND and SampEn1, SampEn2 showed a better significant correlation to EDSS and an ability to discriminate the MS patients in the EC case. In addition, the outcome of the study suggests that the multi-dimensional nonlinear analysis could provide some information about the impact of disability progression in MS on dynamics of the COP data.

Keywords: balance, multiple sclerosis, nonlinear analysis, postural sway

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Authors: T. Sanches, K. Bousson

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As part of the development of a 4D autopilot system for unmanned aerial vehicles (UAVs), i.e. a time-dependent robust trajectory generation and control algorithm, this work addresses the problem of optimal path control based on the flight sensors data output that may be unreliable due to noise on data acquisition and/or transmission under certain circumstances. Although several filtering methods, such as the Kalman-Bucy filter or the Linear Quadratic Gaussian/Loop Transfer Recover Control (LQG/LTR), are available, the utter complexity of the control system, together with the robustness and reliability required of such a system on a UAV for airworthiness certifiable autonomous flight, required the development of a proper robust filter for a nonlinear system, as a way of further mitigate errors propagation to the control system and improve its ,performance. As such, a nonlinear algorithm based upon the LQG/LTR, is validated through computational simulation testing, is proposed on this paper.

Keywords: autonomous flight, LQG/LTR, nonlinear state estimator, robust flight control

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Authors: M. Altekin, R. F. Yükseler

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Geometrically nonlinear axisymmetric bending of a shallow spherical shell with a point support at the apex under linearly varying axisymmetric load was investigated numerically. The edge of the shell was assumed to be simply supported or clamped. The solution was obtained by the finite difference and the Newton-Raphson methods. The thickness of the shell was considered to be uniform and the material was assumed to be homogeneous and isotropic. Sensitivity analysis was made for two geometrical parameters. The accuracy of the algorithm was checked by comparing the deflection with the solution of point supported circular plates and good agreement was obtained.

Keywords: Bending, Nonlinear, Plate, Point support, Shell.

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Authors: Sonia Sonia

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This paper presents a family of iterative scheme for solving nonlinear systems of equations which have wide application in sciences and engineering. The proposed iterative family is based upon some parameters which generates many different iterative schemes. This family is completely derivative free and uses first of divided difference operator. Moreover some numerical experiments are performed and compared with existing methods. Analysis of convergence shows that the presented family has fourth-order of convergence. The dynamical behaviour of proposed family and local convergence have also been discussed. The numerical performance and convergence region comparison demonstrates that proposed family is efficient.

Keywords: convergence, divided difference operator, nonlinear system, Newton's method

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Authors: Kamel Al-Khaled

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In this paper, numerical solutions for the nonlinear coupled Korteweg-de Vries, (abbreviated as KdV) equations are calculated by Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. First, discretizing time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a $\theta-$weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method.

Keywords: Nonlinear coupled KdV equations, Soliton solutions, Sinc-collocation method, Sinc functions

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Authors: R. Loukil, M. Chtourou, T. Damak

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In this work, we use the Fault detection and isolation and the Fault tolerant control based on sliding mode observer in order to introduce the well diagnosis of a nonlinear system. The robustness of the proposed observer for the two techniques is tested through a physical example. The results in this paper show the interaction between the Fault tolerant control and the Diagnosis procedure.

Keywords: fault detection and isolation FDI, fault tolerant control FTC, sliding mode observer, nonlinear system, robustness, stability

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Authors: Sunghyun Kim, Hong-Gun Park

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In the performance-based design (PBD), by using the nonlinear dynamic analysis (NDA), the actual performance of the structure is evaluated. Unlike frame structures, in the wall structures, base shear force which is resulted from the NDA, is greatly amplified than that from the elastic analysis. This shear amplifying effect causes repeated designs which make designer difficult to apply the PBD. Therefore, in this paper, factors which affect shear amplification were studied. For the 20-story wall model, the NDA was performed. From the analysis results, the base shear amplification factor was proposed.

Keywords: performance based design, shear amplification factor, nonlinear dynamic analysis, RC shear wall

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Authors: Mohamed M. El Gendy, Ibrahim A. El Arabi, Rafeek W. Abdel-Missih, Omar A. Kandil

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Nonlinear analysis is one of the most important design and safety tools in structural engineering. Based on the finite-element method, a geometrical and material nonlinear analysis of large span reinforced concrete arches is carried out considering soil-structure interaction. The concrete section details and reinforcement distribution are taken into account. The behavior of soil is considered via Winkler's and continuum models. A computer program (NARC II) is specially developed in order to follow the structural behavior of large span reinforced concrete arches up to failure. The results obtained by the proposed model are compared with available literature for verification. This work confirmed that the geometrical and material nonlinearities, as well as soil structure interaction, have considerable influence on the structural response of reinforced concrete arches.

Keywords: nonlinear analysis, reinforced concrete arched structure, soil-structure interaction, geotechnical engineering

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Authors: M. Honarpardaz, Z. Zhang, J. Derkx, A. Trangärd, J. Larsson

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Pilot stages are one of the most common positioners and regulators in industry. In this paper, we present two novel concepts for pilot stages with low power consumption to regulate a pneumatic device. Pilot 1, first concept, is designed based on a conventional frame core electro-magnetic actuator and a leaf spring to control the air flow and pilot 2 has an axisymmetric actuator and spring made of non-oriented electrical steel. Concepts are simulated in a system modeling tool to study their dynamic behavior. Both concepts are prototyped and tested. Experimental results are comprehensively analyzed and compared. The most promising concept that consumes less than 8 mW is highlighted and presented.

Keywords: electro-magnetic actuator, multidisciplinary system, low power consumption, pilot stage

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Authors: Archil Motsonelidze, Vitaly Dvalishvili

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Existing roller compacted concrete (RCC) dams indicate that the layer-by-layer construction method gives considerable economies as compared with the conventional methods. RCC dams have also gained acceptance in the regions of high seismic activity. Earthquake resistance analysis of RCC gravity dams based on nonlinear finite element technique is presented. An elastic-plastic approach is used to describe the material of a dam while it is under static conditions (period of construction). Seismic force, as an acceleration equivalent to that produced by a real earthquake, is supposed to act when the dam is completed. The materials of the dam and foundation may be nonhomogeneous and anisotropic. The “dam-foundation” system is idealized as a plain strain problem.

Keywords: finite element method, layer-by-layer construction, RCC dams, strength analysis

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Authors: Edamana Vasudevan Krishnan

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This paper studies solitons in optical materials with the help of Mapping Method. Two types of nonlinear media have been investigated, namely, the cubic nonlinearity and the quintic nonlinearity. The soliton solutions, shock wave solutions and singular solutions have been derives with certain constraint conditions.

Keywords: solitons, integrability, metamaterials, mapping method

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Authors: Ivan Belik, Kurt Jornsten

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We construct the coauthorship network based on the scientific collaboration between the faculty members at the Norwegian School of Economics (NHH) and based on their international academic publication experience. The network structure is based on the NHH faculties’ publications recognized by the ISI Web of Science for the period 1950 – Spring, 2014. The given network covers the publication activities of the NHH faculty members (over six departments) based on the information retrieved from the ISI Web of Science in Spring, 2014. In this paper we analyse the constructed coauthorship network in different aspects of the theory of social networks analysis.

Keywords: coauthorship networks, social networks analysis, Norwegian School of Economics, ISI

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Authors: Shubham Jaiswal

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During modeling of transport phenomena in porous media, many nonlinear partial differential equations (NPDEs) encountered which greatly described the convection, diffusion and reaction process. To solve such types of nonlinear problems, a reliable and efficient technique is needed. In this article, the numerical solution of NPDEs encountered in porous media is derived. Here Jacobi collocation method is used to solve the considered problems which convert the NPDEs in systems of nonlinear algebraic equations that can be solved using Newton-Raphson method. The numerical results of some illustrative examples are reported to show the efficiency and high accuracy of the proposed approach. The comparison of the numerical results with the existing analytical results already reported in the literature and the error analysis for each example exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: nonlinear porous media equation, shifted Jacobi polynomials, operational matrix, spectral collocation method

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Authors: Ayda Nikkar, Roghayye Ahmadiasl

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In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham–Broer–Kaup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.

Keywords: homotopy perturbation method, Whitham–Broer–Kaup (WBK) equation, Modified Boussinesq, Approximate Long Wave

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Authors: Ghania Zidani, Said Drid, Larbi Chrifi-Alaoui, Abdeslam Benmakhlouf, Souad Chaouch

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In this paper, we focus on the study for path tracking control of unicycle-type Wheeled Mobile Robots (WMR), by applying the Backstepping technic. The latter is a relatively new technic for nonlinear systems. To solve the problem of constraints nonholonomics met in the path tracking of such robots, an adaptive Backstepping based nonlinear controller is developed. The stability of the controller is guaranteed, using the Lyapunov theory. Simulation results show that the proposed controller achieves the objective and ensures good path tracking.

Keywords: Backstepping control, kinematic and dynamic controllers, Lyapunov methods, nonlinear control systems, Wheeled Mobile Robot (WMR).

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Authors: Guy Joseph Eyebe, Gambo Betchewe, Alidou Mohamadou, Timoleon Crepin Kofane

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In the present study, the dynamics of nanobeam resting on fractional order softening nonlinear viscoelastic pasternack foundations is studied. The Hamilton principle is used to derive the nonlinear equation of the motion. Approximate analytical solution is obtained by applying the standard averaging method. The Melnikov method is used to investigate the chaotic behaviors of device, the critical curve separating the chaotic and non-chaotic regions are found. It is shown that appearance of chaos in the system depends strongly on the fractional order parameter.

Keywords: chaos, fractional-order, Melnikov method, nanobeam

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Authors: Slim Naifar, Sonia Bradai, Christian Viehweger, Olfa Kanoun

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Vibration provides an interesting source of energy since it is available in many indoor and outdoor applications. Nevertheless, in order to have an efficient design of the harvesting system, vibration converters have to satisfy some criterion in terms of robustness, compactness and energy outcome. In this work, an electromagnetic converter based on mechanical spring principle is proposed. The designed harvester is formed by a coil oscillating around ten ring magnets using a mechanical spring. The proposed design overcomes one of the main limitation of the moving coil by avoiding the contact between the coil wires with the mechanical spring which leads to a better robustness for the converter. In addition, the whole system can be implemented in a cavity of a screw. Different parameters in the harvester were investigated by finite element method including the magnet size, the coil winding number and diameter and the excitation frequency and amplitude. A prototype was realized and tested. Experiments were performed for 0.5 g to 1 g acceleration. The used experimental setup consists of an electrodynamic shaker as an external artificial vibration source controlled by a laser sensor to measure the applied displacement and frequency excitation. Together with the laser sensor, a controller unit, and an amplifier, the shaker is operated in a closed loop which allows controlling the vibration amplitude. The resonance frequency of the proposed designs is in the range of 24 Hz. Results indicate that the harvester can generate 612 mV and 1150 mV maximum open circuit peak to peak voltage at resonance for 0.5 g and 1 g acceleration respectively which correspond to 4.75 mW and 1.34 mW output power. Tuning the frequency to other values is also possible due to the possibility to add mass to the moving part of the or by changing the mechanical spring stiffness.

Keywords: energy harvesting, electromagnetic principle, vibration converter, moving coil

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Authors: Ahmed Nouainia, Mohamed Hajji, Taoufik Aguili

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In this paper, an electromagnetic analysis is presented for describing the influence of shielding in a rectangular waveguide. A hybridization based on the method of moments combined to the generalized equivalent circuit MoM-GEC is used to model the problem. This is validated by applying the MoM-GEC hybridization to investigate a diffraction structure. It consists of electromagnetic diffraction by an iris in a rectangular waveguide. Numerical results are shown and discussed and a comparison with FEM and Marcuvitz methods is achieved.

Keywords: method MoM-GEC, waveguide, shielding, equivalent circuit

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Authors: Seyed Saeid Tabaee, Omid Bahar

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Nowadays, using energy dissipation devices has been commonly used in structures. A high rate of energy absorption during earthquakes is the benefit of using such devices, which results in damage reduction of structural elements specifically columns. The hysteretic damping capacity of energy dissipation devices is the key point that it may adversely complicate analysis and design of such structures. This effect may be generally represented by equivalent viscous damping. The equivalent viscous damping may be obtained from the expected hysteretic behavior under the design or maximum considered displacement of a structure. In this paper, the hysteretic damping coefficient of a steel moment resisting frame (MRF), which its performance is enhanced by a buckling restrained brace (BRB) system has been evaluated. Having the foresight of damping fraction between BRB and MRF is inevitable for seismic design procedures like Direct Displacement-Based Design (DDBD) method. This paper presents an approach to calculate the damping fraction for such systems by carrying out the dynamic nonlinear time history analysis (NTHA) under harmonic loading, which is tuned to the natural frequency of the system. Two steel moment frame structures, one equipped with BRB, and the other without BRB are simultaneously studied. The extensive analysis shows that proportion of each system damping fraction may be calculated by its shear story portion. In this way, the contribution of each BRB in the floors and their general contribution in the structural performance may be clearly recognized, in advance.

Keywords: buckling restrained brace, direct displacement based design, dual systems, hysteretic damping, moment resisting frames

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Authors: A. Guezane-Lakoud, S. Bensebaa

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In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained.

Keywords: positive solution, fractional caputo derivative, Banach contraction principle, Avery and Peterson fixed point theorem

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Authors: Gemma A. Gruyal

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Plants can contain a wide variety of substances with antioxidative properties which are associated to important health benefits. These positive health effects are of great importance at a time when the environment is laden with many toxic substances. Five selected herbal plants namely, Mimosa pudica, Phyllanthus niruri, Ceiba pentandra, Eleusine polydactyla and Trema amboinensis, were chosen for the experiment to investigate their total phenolics content and antioxidant activities using ABTS radical cation decolorization power, and ferric reducing antioxidant power. The total phenolic content of each herbal plants ranges from 0.84 to 42.59 mg gallic acid equivalent/g. The antioxidant activity in the ABTS radical cation decolorization power varies from 0.005 to 0.362 mg trolox equivalent/g and the FRAP ranges from 0.30 to 28.42 mg gallic acid equivalent/g. Among the five medicinal plants, Mimosa pudica has been an excellent performer in terms of the 3 parameters measured; it is followed by Phyllanthus niruri. The five herbal plants do not have equivalent antioxidant power. The relative high values for M. pudica and P. niruri supports the medicinal value of both plants. The total phenolics, ABTS and FRAP correlate strongly with one another.

Keywords: ABTS, FRAP, Leaf extracts, phenol

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Authors: Youssef Abdelli, Rachid Nasri

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The large amplitude free vibration analysis of three-layered symmetric sandwich beams is carried out using two different approaches. The governing nonlinear partial differential equations of motion in free natural vibration are derived using Hamilton's principle. The formulation leads to two nonlinear partial differential equations that are coupled both in axial and binding deformations. In the first approach, the method of multiple scales is applied directly to the governing equation that is a nonlinear partial differential equation. In the second approach, we discretize the governing equation by using Galerkin's procedure and then apply the shooting method to the obtained ordinary differential equations. In order to check the validity of the solutions obtained by the two approaches, they are compared with the solutions obtained by two approaches; they are compared with the solutions obtained numerically by the finite difference method.

Keywords: finite difference method, large amplitude vibration, multiple scales, nonlinear vibration

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Authors: Sara Mahesar, Saleem M. Chandio, Hira Soomro

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Nonlinear system of equations in two variables is a system which contains variables of degree greater or equal to two or that comprises of the transcendental functions. Mathematical modeling of numerous physical problems occurs as a system of nonlinear equations. In applied and pure mathematics it is the main dispute to solve a system of nonlinear equations. Numerical techniques mainly used for finding the solution to problems where analytical methods are failed, which leads to the inexact solutions. To find the exact roots or solutions in case of the system of non-linear equations there does not exist any analytical technique. Various methods have been proposed to solve such systems with an improved rate of convergence and accuracy. In this paper, a new scheme is developed for solving system of non-linear equation in two variables. The iterative scheme proposed here is modified form of the conventional Newton’s Method (CN) whose order of convergence is two whereas the order of convergence of the devised technique is three. Furthermore, the detailed error and convergence analysis of the proposed method is also examined. Additionally, various numerical test problems are compared with the results of its counterpart conventional Newton’s Method (CN) which confirms the theoretic consequences of the proposed method.

Keywords: conventional Newton’s method, modified Newton’s method, order of convergence, system of nonlinear equations

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Authors: M. Zamurad Shah, M. Kemal Ozgoren, Raza Samar

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This paper presents a 3D guidance scheme for Unmanned Aerial Vehicles (UAVs). The proposed guidance scheme is based on the sliding mode approach using nonlinear sliding manifolds. Generalized 3D kinematic equations are considered here during the design process to cater for the coupling between longitudinal and lateral motions. Sliding mode based guidance scheme is then derived for the multiple-input multiple-output (MIMO) system using the proposed nonlinear manifolds. Instead of traditional sliding surfaces, nonlinear sliding surfaces are proposed here for performance and stability in all flight conditions. In the reaching phase control inputs, the bang-bang terms with signum functions are accompanied with proportional terms in order to reduce the chattering amplitudes. The Proposed 3D guidance scheme is implemented on a 6-degrees-of-freedom (6-dof) simulation of a UAV and simulation results are presented here for different 3D trajectories with and without disturbances.

Keywords: unmanned aerial vehicles, sliding mode control, 3D guidance, nonlinear sliding manifolds

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