Search results for: nonlinear stretching sheet
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1281

Search results for: nonlinear stretching sheet

1251 Numerical Simulation for the Formability Prediction of the Laser Welded Blanks (TWB)

Authors: Hossein Mamusi, Abolfazl Masoumi, Ramezanali Mahdavinezhad

Abstract:

Tailor-welded Blanks (TWBs) are tailor made for different complex component designs by welding multiple metal sheets with different thicknesses, shapes, coatings or strengths prior to forming. In this study the Hemispherical Die Stretching (HDS) test (out-of-plane stretching) of TWBs were simulated via ABAQUS/Explicit to obtain the Forming Limit Diagrams (FLDs) of Stainless steel (AISI 304) laser welded blanks with different thicknesses. Two criteria were used to detect the start of necking to determine the FLD for TWBs and parent sheet metals. These two criteria are the second derivatives of the major and thickness strains that are given from the strain history of simulation. In the other word, in these criteria necking starts when the second derivative of thickness or major strain reaches its maximum. With having the time of onset necking, one can measure the major and minor strains at the critical area and determine the forming limit curve.

Keywords: TWB, Forming Limit Diagram, Necking criteria, ABAQUS/Explicit

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1250 Simulation of the Effect of Sea Water Using Ground Tank to the Flexural Capacity of GFRP Sheet Reinforced Concrete Beams

Authors: Rudy Djamaluddin, Arbain Tata, Rita Irmawaty

Abstract:

The study conducted a simulation of the effect of sea water to the bonding capacity of GFRP sheet on the concrete beams using a simulation tank. Fiber reinforced polymer (FRP) has been developed and applied in many fields civil engineering structures on the new structures and also for strengthening of the deteriorated structures. The FRP has advantages such as its corrosion resistance as well as high tensile strength to weight ratio. Compared to the other FRP materials, Glass composed FRP (GFRP) is relatively cheaper. GFRP sheet is applied externally by bonding it on the concrete surface. The studies regarding the application of GFRP sheet have been conducted such as strengthening system, bonding behavior of GFRP sheet including the application as reinforcement in new structures. For application to the structures with direct contact to sea environment, a study regarding the effect of sea water to the bonding capacity of GFRP sheet is important to be clarified. To achieve the objective of the study, a series of concrete beams strengthened with GFRP sheet on extreme tension surface were prepared. The beams then were stored on the sea water tank for six months. Results indicated the bonding capacity decreased after six month exposed to the sea water.

Keywords: GFRP sheet, sea water, concrete beams, bonding.

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1249 Cost Effective Real-Time Image Processing Based Optical Mark Reader

Authors: Amit Kumar, Himanshu Singal, Arnav Bhavsar

Abstract:

In this modern era of automation, most of the academic exams and competitive exams are Multiple Choice Questions (MCQ). The responses of these MCQ based exams are recorded in the Optical Mark Reader (OMR) sheet. Evaluation of the OMR sheet requires separate specialized machines for scanning and marking. The sheets used by these machines are special and costs more than a normal sheet. Available process is non-economical and dependent on paper thickness, scanning quality, paper orientation, special hardware and customized software. This study tries to tackle the problem of evaluating the OMR sheet without any special hardware and making the whole process economical. We propose an image processing based algorithm which can be used to read and evaluate the scanned OMR sheets with no special hardware required. It will eliminate the use of special OMR sheet. Responses recorded in normal sheet is enough for evaluation. The proposed system takes care of color, brightness, rotation, little imperfections in the OMR sheet images.

Keywords: OMR, image processing, hough circle transform, interpolation, detection, Binary Thresholding.

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1248 A New Nonlinear PID Controller and its Parameter Design

Authors: Yongping Ren, Zongli Li, Fan Zhang

Abstract:

A new nonlinear PID controller and its stability analysis are presented in this paper. A nonlinear function is deduced from the similarities between the control effort and the electric-field effect of a capacitor. The conventional linear PID controller can be modified into a nonlinear one by this function. To analyze the stability of the nonlinear PID controlled system, an idea of energy equivalence is adapted to avoid the conservativeness which is usually arisen from some traditional theorems and Criterions. The energy equivalence is naturally related with the conceptions of Passivity and T-Passivity. As a result, an engineering guideline for the parameter design of the nonlinear PID controller is obtained. An inverted pendulum system is tested to verify the nonlinear PID control scheme.

Keywords: Nonlinear PID controller, stability, gain equivalence, dissipative, T-Passivity.

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1247 Forming Limit Analysis of DP600-800 Steels

Authors: M. C. Cardoso, L. P. Moreira

Abstract:

In this work, the plastic behaviour of cold-rolled zinc coated dual-phase steel sheets DP600 and DP800 grades is firstly investigated with the help of uniaxial, hydraulic bulge and Forming Limit Curve (FLC) tests. The uniaxial tensile tests were performed in three angular orientations with respect to the rolling direction to evaluate the strain-hardening and plastic anisotropy. True stressstrain curves at large strains were determined from hydraulic bulge testing and fitted to a work-hardening equation. The limit strains are defined at both localized necking and fracture conditions according to Nakajima’s hemispherical punch procedure. Also, an elasto-plastic localization model is proposed in order to predict strain and stress based forming limit curves. The investigated dual-phase sheets showed a good formability in the biaxial stretching and drawing FLC regions. For both DP600 and DP800 sheets, the corresponding numerical predictions overestimated and underestimated the experimental limit strains in the biaxial stretching and drawing FLC regions, respectively. This can be attributed to the restricted failure necking condition adopted in the numerical model, which is not suitable to describe the tensile and shear fracture mechanisms in advanced high strength steels under equibiaxial and biaxial stretching conditions.

Keywords: Advanced high strength steels, forming limit curve, numerical modeling, sheet metal forming.

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1246 Classification of Buckling Behavior on Uniaxial Compression using A5052-O Sheets

Authors: S. Onoda, S. Yoshihara, B. J. MacDonald, Y. Okude

Abstract:

Aluminum alloy sheets have several advantages such as the lightweight, high-specific strength and recycling efficiency. Therefore, aluminum alloy sheets in sheet forming have been used in various areas as automotive components and so forth. During the process of sheet forming, wrinkling which is caused by compression stress might occur and the formability of sheets was affected by occurrence of wrinkling. A few studies of uniaxial compressive test by using square tubes, pipes and sheets were carried out to clarify the each wrinkling behavior. However, on uniaxial compressive test, deformation behavior of the sheets hasn-t be cleared. Then, it is necessary to clarify the relationship between the buckling behavior and the forming conditions. In this study, the effect of dimension of the sheet in the buckling behavior on compression test of aluminum alloy sheet was cleared by experiment and FEA. As the results, the buckling deformation was classified by three modes in terms of the distribution of equivalent plastic strain.

Keywords: Sheet forming, Compression test, Aluminum alloy sheet, Buckling behavior

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1245 Interface Analysis of Annealed Al/Cu Cladded Sheet

Authors: Joon Ho Kim, Tae Kwon Ha

Abstract:

Effect of aging treatment on microstructural aspects of interfacial layers of the Cu/Al clad sheet produced by differential speed rolling (DSR) process were studied by electron back scattered diffraction (EBSD). Clad sheet of Al/Cu has been fabricated by using DSR, which caused severe shear deformation between Al and Cu plate to easily bond to each other. Rolling was carried out at 100oC with speed ratio of 2, in which the total thickness reduction was 45%. Interface layers of clad sheet were analyzed by EBSD after subsequent annealing at 400oC for 30 to 120min. With increasing annealing time, thickness of interface layer and fraction of high angle grain boundary were increased and average grain size was decreased.

Keywords: Aluminum/Copper clad sheet, differential speed rolling, interface layer, microstructure, annealing, electron back scattered diffraction.

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1244 Experimental Study and Analysis of Parabolic trough Collector with Various Reflectors

Authors: Avadhesh Yadav, Manoj Kumar, Balram

Abstract:

A solar powered air heating system using parabolic trough collector was experimentally investigated. In this experimental setup, the reflected solar radiations were focused on absorber tube which was placed at focal length of the parabolic trough. In this setup, air was used as working fluid which collects the heat from absorber tube. To enhance the performance of parabolic trough, collector with different type of reflectors were used. It was observed For Aluminum sheet maximum temperature is 52.3ºC, which 24.22% more than steel sheet as reflector and 8.5% more than Aluminum foil as reflector, also efficiency by using Aluminum sheet as reflector compared to steel sheet as reflector is 61.18% more. Efficiency by using Aluminum sheet as reflector compared to Aluminum foil as reflector is 18.98% more.

Keywords: Parabolic trough collector, Reflectors, Air flow rates.

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1243 Determination of Measurement Uncertainty in Extracting of Forming Limit Diagrams

Authors: M. Mahboubkhah, H. Fayazfar

Abstract:

In this research, Forming Limit Diagrams for supertension sheet metals which are using in automobile industry have been obtained. The exerted strains to sheet metals have been measured with four different methods and the errors of each method have also been represented. These methods have been compared with together and the most efficient and economic way of extracting of the exerted strains to sheet metals has been introduced. In this paper total error and uncertainty of FLD extraction procedures have been derived. Determination of the measurement uncertainty in extracting of FLD has a great importance in design and analysis of the sheet metal forming process.

Keywords: Forming Limit Diagram, Major and Minor Strain, Measurement Uncertainty.

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1242 Implicit Eulerian Fluid-Structure Interaction Method for the Modeling of Highly Deformable Elastic Membranes

Authors: Aymen Laadhari, Gábor Székely

Abstract:

This paper is concerned with the development of a fully implicit and purely Eulerian fluid-structure interaction method tailored for the modeling of the large deformations of elastic membranes in a surrounding Newtonian fluid. We consider a simplified model for the mechanical properties of the membrane, in which the surface strain energy depends on the membrane stretching. The fully Eulerian description is based on the advection of a modified surface tension tensor, and the deformations of the membrane are tracked using a level set strategy. The resulting nonlinear problem is solved by a Newton-Raphson method, featuring a quadratic convergence behavior. A monolithic solver is implemented, and we report several numerical experiments aimed at model validation and illustrating the accuracy of the presented method. We show that stability is maintained for significantly larger time steps.

Keywords: Fluid-membrane interaction, stretching, Eulerian, finite element method, Newton, implicit.

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1241 The effect of the Thickness of Electrical sheet on Overvoltage in the Asynchronous Motors Fed by PWM- converters

Authors: Belassel Mohand-Tahar

Abstract:

This work is devoted to the calculation of the undulatory parameters and the study of the influence thickness of electrical sheet on overvoltage compared to the carcass and between whorls (sections) of the asynchronous motors supplied with PWM converters.

Keywords: Asynchronous Motors, , PWM, Undulatory Process, Undulatory Parameters, Undulatory Voltage, electrical sheet.

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1240 MHD Stagnation Point Flow towards a Shrinking Sheet with Suction in an Upper-Convected Maxwell (UCM) Fluid

Authors: K. Jafar, R. Nazar, A. Ishak, I. Pop

Abstract:

The present analysis considers the steady stagnation point flow and heat transfer towards a permeable shrinking sheet in an upper-convected Maxwell (UCM) electrically conducting fluid, with a constant magnetic field applied in the transverse direction to flow and a local heat generation within the boundary layer, with a heat generation rate proportional to (T-T\infty)p Using a similarity transformation, the governing system of partial differential equations is first transformed into a system of ordinary differential equations, which is then solved numerically using a finite-difference scheme known as the Keller-box method. Numerical results are obtained for the flow and thermal fields for various values of the stretching/shrinking parameter λ, the magnetic parameter M, the elastic parameter K, the Prandtl number Pr, the suction parameter s, the heat generation parameter Q, and the exponent p. The results indicate the existence of dual solutions for the shrinking sheet up to a critical value λc whose value depends on the value of M, K, and s. In the presence of internal heat absorption (Q<0)  the surface heat transfer rate decreases with increasing p but increases with parameters Q and s when the sheet is either stretched or shrunk.

Keywords: Magnetohydrodynamic (MHD), boundary layer flow, UCM fluid, stagnation point, shrinking sheet.

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1239 Design of Nonlinear Observer by Using Chebyshev Interpolation based on Formal Linearization

Authors: Kazuo Komatsu, Hitoshi Takata

Abstract:

This paper discusses a design of nonlinear observer by a formal linearization method using an application of Chebyshev Interpolation in order to facilitate processes for synthesizing a nonlinear observer and to improve the precision of linearization. A dynamic nonlinear system is linearized with respect to a linearization function, and a measurement equation is transformed into an augmented linear one by the formal linearization method which is based on Chebyshev interpolation. To the linearized system, a linear estimation theory is applied and a nonlinear observer is derived. To show effectiveness of the observer design, numerical experiments are illustrated and they indicate that the design shows remarkable performances for nonlinear systems.

Keywords: nonlinear system, nonlinear observer, formal linearization, Chebyshev interpolation.

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1238 An Automatic Feature Extraction Technique for 2D Punch Shapes

Authors: Awais Ahmad Khan, Emad Abouel Nasr, H. M. A. Hussein, Abdulrahman Al-Ahmari

Abstract:

Sheet-metal parts have been widely applied in electronics, communication and mechanical industries in recent decades; but the advancement in sheet-metal part design and manufacturing is still behind in comparison with the increasing importance of sheet-metal parts in modern industry. This paper presents a methodology for automatic extraction of some common 2D internal sheet metal features. The features used in this study are taken from Unipunch ™ catalogue. The extraction process starts with the data extraction from STEP file using an object oriented approach and with the application of suitable algorithms and rules, all features contained in the catalogue are automatically extracted. Since the extracted features include geometry and engineering information, they will be effective for downstream application such as feature rebuilding and process planning.

Keywords: Feature Extraction, Internal Features, Punch Shapes, Sheet metal, STEP.

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1237 Bearing Capacity of Sheet Hanger Connection to the Trapezoidal Metal Sheet

Authors: Kateřina Jurdová

Abstract:

Hanging to the trapezoidal sheet by decking hanger is a very widespread solution used in civil engineering to lead the distribution of energy, sanitary, air distribution system etc. under the roof or floor structure. The trapezoidal decking hanger is usually a part of the whole installation system for specific distribution medium. The leading companies offer installation systems for each specific distribution e.g. pipe rings, sprinkler systems, installation channels etc. Every specific part is connected to the base connector which is decking hanger. The own connection has three main components: decking hanger, threaded bar with nuts and web of trapezoidal sheet. The aim of this contribution is determinate the failure mechanism of each component in connection. Load bearing capacity of most components in connection could be calculated by formulas in European codes. This contribution is focused on problematic of bearing resistance of threaded bar in web of trapezoidal sheet. This issue is studied by experimental research and numerical modelling. This contribution presented the initial results of experiment which is compared with numerical model of specimen.

Keywords: Decking hanger, concentrated load, connection, load bearing capacity, trapezoidal metal sheet.

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1236 A NonLinear Observer of an Electrical Transformer: A Bond Graph Approach

Authors: Gilberto Gonzalez-A , Israel Nuñez

Abstract:

A bond graph model of an electrical transformer including the nonlinear saturation is presented. A nonlinear observer for the transformer based on multivariable circle criterion in the physical domain is proposed. In order to show the saturation and hysteresis effects on the electrical transformer, simulation results are obtained. Finally, the paper describes that convergence of the estimates to the true states is achieved.

Keywords: Bond graph, nonlinear observer, electrical transformer, nonlinear saturation.

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1235 Design and Instrumentation of a Benchmark Multivariable Nonlinear Control Laboratory

Authors: S. H. Teh, S. Malawaraarachci, W. P. Chan, A. Nassirharand

Abstract:

The purpose of this paper is to present the design and instrumentation of a new benchmark multivariable nonlinear control laboratory. The mathematical model of this system may be used to test the applicability and performance of various nonlinear control procedures. The system is a two degree-of-freedom robotic arm with soft and hard (discontinuous) nonlinear terms. Two novel mechanisms are designed to allow the implementation of adjustable Coulomb friction and backlash.

Keywords: Nonlinear control, describing functions, AdjustableCoulomb friction, Adjustable backlash.

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1234 Design and Construction of the Semi-Automatic Sliced Ginger Machine

Authors: J. Chatthong, W. Boonchouytan, R. Burapa

Abstract:

The purpose of study was to design and construction the semi-automatic sliced ginger machine for reduce production times in sheet and slice ginger procedure furthermore, reduced amount of labor of slides and cutting method. Take consider into clean and safety of workers and consumers. The principle of machines, used 1 horsepower motor, rotation speed of sliced blade 967 rpm, the diameter of sliced dish 310 mm, consists of 2 blades for sheet cutting ginger and the power from motor which transfer to rotate the sliced blade roller, rotation speed 440 rpm. The slice cutter roller was sliced ginger from sheet ginger to line ginger. The conveyer could adjustment level of motors, used to the beginning area that sheet ginger was transference to the roller for sheet and sliced cutting in next process. The cover of sliced cutting had channel for 1 tuber of ginger. The semi-automatic sliced ginger machine could produced sheet ginger 81.8 kg/h (6.2 times of labor) and line ginger 17.9 kg/h (2.5 times of labor) compare with, labor work could produced sheet ginger 13.2 kg/h and line ginger 7.1 kg/h, and when timekeeper, the total times of semi auto machine 30.86 kg/h and labor 4.6 kg/h, there for the semi auto machine was 6.7 times of labor. The semiautomatic sliced ginger machine convenient, easy for use and maintain, in addition to reduce fatigue of body and seriousness from works; must be used high skill, and protection accident in slicing procedure. Beside, machine could used with other vegetables for example potato, carrot .etc

Keywords: Sliced Machine, Sliced Ginger, Line Ginger

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1233 The Influence of Surface Roughness of Drawbead on Non-Symmetry Deep Drawing Cold Rolled Steel Sheet

Authors: A. Watanapa, S. Torsakul

Abstract:

This study was aimed to explain the influence of surface roughness of the drawbead on non-symmetry deep drawing cold rolled steel sheet to improve the drawability of cold rolled steel sheet. The variables used in this study included semi-circle drawbead with 3 levels of surface roughness which are 6.127 mm Ra, 0.963 mm Ra and 0.152 mm Ra and cold rolled steel sheet according to 3 grades of the JIS standards which are SPCC, SPCE and SPCD with the thickness of 1.0 mm and the blankholder force which is 50% of the drawing force and the depth of 50 mm. According to the test results, when there was the increase in the surface roughness of drawbead, there would be the increase in deep drawing force, especially the SPCC cold rolled steel sheet. This is similar to the increase in the equivalent strain and the wall thickness distribution when the surface roughness of the drawbead increased. It could be concluded that the surface roughness of drawbead has an influence on deep drawing cold rolled steel sheet, especially the drawing force, the equivalent strain and the wall thickness distribution.

Keywords: Drawbead, Deep Drawing, Drawing Force, Equivalent Strain, Surface roughness

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1232 A Detailed Experimental Study of the Springback Anisotropy of Three Metals using the Stretching-Bending Process

Authors: A. Soualem

Abstract:

Springback is a significant problem in the sheet metal forming process. When the tools are released after the stage of forming, the product springs out, because of the action of the internal stresses. In many cases the deviation of form is too large and the compensation of the springback is necessary. The precise prediction of the springback of product is increasingly significant for the design of the tools and for compensation because of the higher ratio of the yield stress to the elastic modulus. The main object in this paper was to study the effect of the anisotropy on the springback for three directions of rolling: 0°, 45° and 90°. At the same time, we highlighted the influence of three different metallic materials: Aluminum, Steel and Galvanized steel. The original of our purpose consist on tests which are ensured by adapting a U-type stretching-bending device on a tensile testing machine, where we studied and quantified the variation of the springback according to the direction of rolling. We also showed the role of lubrication in the reduction of the springback. Moreover, in this work, we have studied important characteristics in deep drawing process which is a springback. We have presented defaults that are showed in this process and many parameters influenced a springback. Finally, our results works lead us to understand the influence of grains orientation with different metallic materials on the springback and drawing some conclusions how to concept deep drawing tools. In addition, the conducted work represents a fundamental contribution in the discussion the industry application.

Keywords: Deep-Drawing, Grains orientation, Laminate Tool, Springback.

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1231 Flow and Heat Transfer over a Shrinking Sheet: A Stability Analysis

Authors: Anuar Ishak

Abstract:

The characteristics of fluid flow and heat transfer over a permeable shrinking sheet is studied. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the suction parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: Dual solutions, heat transfer, shrinking sheet, stability analysis.

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1230 Heat and Mass Transfer over an Unsteady Stretching Surface Embedded in a Porous Medium in the Presence of Variable Chemical Reaction

Authors: T. G. Emam

Abstract:

The effect of variable chemical reaction on heat and mass transfer characteristics over unsteady stretching surface embedded in a porus medium is studied. The governing time dependent boundary layer equations are transformed into ordinary differential equations containing chemical reaction parameter, unsteadiness parameter, Prandtl number and Schmidt number. These equations have been transformed into a system of first order differential equations. MATHEMATICA has been used to solve this system after obtaining the missed initial conditions. The velocity gradient, temperature, and concentration profiles are computed and discussed in details for various values of the different parameters.

Keywords: Heat and mass transfer, stretching surface, chemical reaction, porus medium.

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1229 Finite Element Simulation of Multi-Stage Deep Drawing Processes and Comparison with Experimental Results

Authors: A. Pourkamali Anaraki, M. Shahabizadeh, B. Babaee

Abstract:

The plastic forming process of sheet plate takes an important place in forming metals. The traditional techniques of tool design for sheet forming operations used in industry are experimental and expensive methods. Prediction of the forming results, determination of the punching force, blank holder forces and the thickness distribution of the sheet metal will decrease the production cost and time of the material to be formed. In this paper, multi-stage deep drawing simulation of an Industrial Part has been presented with finite element method. The entire production steps with additional operations such as intermediate annealing and springback has been simulated by ABAQUS software under axisymmetric conditions. The simulation results such as sheet thickness distribution, Punch force and residual stresses have been extracted in any stages and sheet thickness distribution was compared with experimental results. It was found through comparison of results, the FE model have proven to be in close agreement with those of experiment.

Keywords: Deep drawing, Finite element method, Simulation.

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1228 Robust Adaptive Observer Design for Lipschitz Class of Nonlinear Systems

Authors: M. Pourgholi, V.J.Majd

Abstract:

This paper addresses parameter and state estimation problem in the presence of the perturbation of observer gain bounded input disturbances for the Lipschitz systems that are linear in unknown parameters and nonlinear in states. A new nonlinear adaptive resilient observer is designed, and its stability conditions based on Lyapunov technique are derived. The gain for this observer is derived systematically using linear matrix inequality approach. A numerical example is provided in which the nonlinear terms depend on unmeasured states. The simulation results are presented to show the effectiveness of the proposed method.

Keywords: Adaptive observer, linear matrix inequality, nonlinear systems, nonlinear observer, resilient observer, robust estimation.

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1227 On the outlier Detection in Nonlinear Regression

Authors: Hossein Riazoshams, Midi Habshah, Jr., Mohamad Bakri Adam

Abstract:

The detection of outliers is very essential because of their responsibility for producing huge interpretative problem in linear as well as in nonlinear regression analysis. Much work has been accomplished on the identification of outlier in linear regression, but not in nonlinear regression. In this article we propose several outlier detection techniques for nonlinear regression. The main idea is to use the linear approximation of a nonlinear model and consider the gradient as the design matrix. Subsequently, the detection techniques are formulated. Six detection measures are developed that combined with three estimation techniques such as the Least-Squares, M and MM-estimators. The study shows that among the six measures, only the studentized residual and Cook Distance which combined with the MM estimator, consistently capable of identifying the correct outliers.

Keywords: Nonlinear Regression, outliers, Gradient, LeastSquare, M-estimate, MM-estimate.

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1226 Solitons in Nonlinear Optical Lattices

Authors: Tapas Kumar Sinha, Joseph Mathew

Abstract:

Based on the Lagrangian for the Gross –Pitaevskii equation as derived by H. Sakaguchi and B.A Malomed [5] we have derived a double well model for the nonlinear optical lattice. This model explains the various features of nonlinear optical lattices. Further, from this model we obtain and simulate the probability for tunneling from one well to another which agrees with experimental results [4].

Keywords: Double well model, nonlinear optical lattice, Solitons, tunneling.

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1225 Fabrication of Al/Cu Clad Sheet by Shear Extrusion

Authors: Joon Ho Kim, Duck Su Kim, Tae Kwon Ha

Abstract:

Aluminum/Copper clad sheet has been fabricated using asymmetric extrusion method, which caused severe shear deformation between Al and Cu plate to easily bond to each other. Interfacial microstructure and mechanical properties of Al/Cu clad were studied by scanning electron microscope equipped with energy dispersive X-ray detector, micro-hardness, and tension tests. The asymmetric extrusion bonding was very effective to provide a good interface for atoms diffusion during subsequent annealing. The strength of bonding was higher with the increasing extrusion ratio.

Keywords: Aluminum/Copper clad sheet, Asymmetric extrusion, Interfacial microstructure, Annealing, Tensile test.

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1224 On a New Nonlinear Sum-difference Inequality with Application

Authors: Kelong Zheng, Shouming Zhong

Abstract:

A new nonlinear sum-difference inequality in two variables which generalize some existing results and can be used as handy tools in the analysis of certain partial difference equation is discussed. An example to show boundedness of solutions of a difference value problem is also given.

Keywords: Sum-Difference inequality, Nonlinear, Boundedness.

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1223 Chaotic Oscillations of Diaphragm Supported by Nonlinear Springs with Hysteresis

Authors: M. Sasajima, T. Yamaguchi, Y. Koike, A. Hara

Abstract:

This paper describes vibration analysis using the finite element method for a small earphone, especially for the diaphragm shape with a low-rigidity. The viscoelastic diaphragm is supported by multiple nonlinear concentrated springs with linear hysteresis damping. The restoring forces of the nonlinear springs have cubic nonlinearity. The finite elements for the nonlinear springs with hysteresis are expressed and are connected to the diaphragm that is modeled by linear solid finite elements in consideration of a complex modulus of elasticity. Further, the discretized equations in physical coordinates are transformed into the nonlinear ordinary coupled equations using normal coordinates corresponding to the linear natural modes. We computed the nonlinear stationary and non-stationary responses due to the internal resonance between modes with large amplitude in the nonlinear springs and elastic modes in the diaphragm. The non-stationary motions are confirmed as the chaos due to the maximum Lyapunov exponents with a positive number. From the time histories of the deformation distribution in the chaotic vibration, we identified nonlinear modal couplings.

Keywords: Nonlinear Vibration, Finite Element Method, Chaos , Small Earphone.

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1222 An Optimization of the New Die Design of Sheet Hydroforming by Taguchi Method

Authors: M. Hosseinzadeh, S. A. Zamani, A. Taheri

Abstract:

During the last few years, several sheet hydroforming processes have been introduced. Despite the advantages of these methods, they have some limitations. Of the processes, the two main ones are the standard hydroforming and hydromechanical deep drawing. A new sheet hydroforming die set was proposed that has the advantages of both processes and eliminates their limitations. In this method, a polyurethane plate was used as a part of the die-set to control the blank holder force. This paper outlines the Taguchi optimization methodology, which is applied to optimize the effective parameters in forming cylindrical cups by the new die set of sheet hydroforming process. The process parameters evaluated in this research are polyurethane hardness, polyurethane thickness, forming pressure path and polyurethane hole diameter. The design of experiments based upon L9 orthogonal arrays by Taguchi was used and analysis of variance (ANOVA) was employed to analyze the effect of these parameters on the forming pressure. The analysis of the results showed that the optimal combination for low forming pressure is harder polyurethane, bigger diameter of polyurethane hole and thinner polyurethane. Finally, the confirmation test was derived based on the optimal combination of parameters and it was shown that the Taguchi method is suitable to examine the optimization process.

Keywords: Sheet Hydroforming, Optimization, Taguchi Method

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