Search results for: mechanical and plumbing systems

Authors: M. Zheng, V. S. Alagar

Abstract:

The paper discusses complexity of component-based development (CBD) of embedded systems. Although CBD has its merits, it must be augmented with methods to control the complexities that arise due to resource constraints, timeliness, and run-time deployment of components in embedded system development. Software component specification, system-level testing, and run-time reliability measurement are some ways to control the complexity.

Keywords: Components, embedded systems, complexity, softwaredevelopment, traffic controller system.

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Authors: Meei-Hoan Ho, Chee-Ming Chan

Abstract:

Soft clays are defined as cohesive soil whose water content is higher than its liquid limits. Thus, soil-cement mixing is adopted to improve the ground conditions by enhancing the strength and deformation characteristics of the soft clays. For the above mentioned reasons, a series of laboratory tests were carried out to study some fundamental mechanical properties of cement stabilized soft clay. The test specimens were prepared by varying the portion of ordinary Portland cement to the soft clay sample retrieved from the test site of RECESS (Research Centre for Soft Soil). Comparisons were made for both homogeneous and columnar system specimens by relating the effects of cement stabilized clay of for 0, 5 and 10 % cement and curing for 3, 28 and 56 days. The mechanical properties examined included one-dimensional compressibility and undrained shear strength. For the mechanical properties, both homogeneous and columnar system specimens were prepared to examine the effect of different cement contents and curing periods on the stabilized soil. The one-dimensional compressibility test was conducted using an oedometer, while a direct shear box was used for measuring the undrained shear strength. The higher the value of cement content, the greater is the enhancement of the yield stress and the decrease of compression index. The value of cement content in a specimen is a more active parameter than the curing period.

Keywords: Soft soil, Oedometer, Direct shear box, Cementstabilisedcolumn.

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Authors: J. Y. Lee, J. Kim, H. J. Chang, J. M. Kim

Abstract:

People’s tendency towards living in apartment houses is increasing in a densely populated country. However, some residents living in apartment houses are bothered by noise coming from the houses above. In order to reduce noise pollution, the communities are increasingly imposing a bylaw, including the limitation of floor impact sound, minimum thickness of floors, and floor soundproofing solutions. This research effort focused on the specific long-time deflection of resilient materials in the floor sound insulation systems of apartment houses. The experimental program consisted of testing nine floor sound insulation specimens subjected to sustained load for 45 days. Two main parameters were considered in the experimental investigation: three types of resilient materials and magnitudes of loads. The test results indicated that the structural behavior of the floor sound insulation systems under long-time load was quite different from that the systems under short-time load. The loading period increased the deflection of floor sound insulation systems and the increasing rate of the long-time deflection of the systems with ethylene vinyl acetate was smaller than that of the systems with low density ethylene polystyrene.

Keywords: Resilient materials, floor sound insulation systems, long-time deflection, sustained load, noise pollution.

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Authors: Ramli Nazir, Hossein Moayedi

Abstract:

Soil confinement systems serve as effective solutions to any erosion control project. Various confinements systems, namely triangular, circular and rectangular with the size of 50, 100, and 150 mm, and with a depth of 10 mm, were embedded in soil samples at slope angle of 60°. The observed soil mass losses for the confined soil systems were much smaller than those from unconfined system. As a result, the size of confinement and rainfall intensity have a direct effect on the soil mass loss. The triangular and rectangular confinement systems showed the lowest and highest soil loss masses, respectively. The slopes also failed much faster in the unconfined system than in the confined slope.

Keywords: Erosion control, Soil confinement, Soil erosion, Slope stability.

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Authors: Miroslav Popelka, Jakub Nožička

Abstract:

In this paper we deal with using Lego Mindstorms in simulation of robotic systems with respect to cost reduction. Lego Mindstorms kit contains broad variety of hardware components which are required to simulate, program and test the robotics systems in practice. Algorithm programming went in development environment supplied together with Lego kit as in programming language C# as well. Algorithm following the line, which we dealt with in this paper, uses theoretical findings from area of controlling circuits. PID controller has been chosen as controlling circuit whose individual components were experimentally adjusted for optimal motion of robot tracking the line. Data which are determined to process by algorithm are collected by sensors which scan the interface between black and white surfaces followed by robot. Based on discovered facts Lego Mindstorms can be considered for low-cost and capable kit to simulate real robotics systems.

Keywords: LEGO Mindstorms, PID controller, low-cost robotics systems, line follower, sensors, programming language C#, EV3 Home Edition Software.

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Authors: Onur Ayaz, Nuray Ucar, Elif Bahar, Oguzhan Ucar, Mustafa Oksuz, Aysen Onen, Mehmet Ucar, Ezgi İşmar, Ali Demir

Abstract:

In this study, single nozzle method used for electrospinning technique which composite polymer solution with cellulose nanowiskers (CNW) was treated by ultrasonic sonificator have been compared with coaxial (double) nozzle method, in terms of mechanical, thermal and morphological properties of composite nanofiber. The effect of water content in composite polymer solution on properties of nanofiber has also been examined. It has been seen that single nozzle method which polymer solution does not contain water has better results than that of coaxial method, in terms of mechanical, thermal and morphological properties of nanofiber. However, it is necessary to make an optimization study on setting condition of ultrasonic treatment to get better dispersion of CNW in composite nanofiber and to get better mechanical and thermal properties

Keywords: cellulose nanowhiskers, coaxial nozzle, composite nanofiber, electrospinning

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Authors: Dhiflaoui Hafedh, Khlifi Kaouthar, Ben Cheikh Larbi Ahmed

Abstract:

The present study deals with the characterization of CrSiN coatings obtained by PVD magnetron sputtering systems. CrSiN films were deposited with different Si contents, in order to check the effect of at.% variation on the different properties of the Cr–N system. Coatings were characterized by scanning electron microscopy (SEM) for thickness measurements, X-ray diffraction. Surface morphology and the roughness characteristics were explored using AFM, Mechanicals properties, elastic and plastic deformation resistance of thin films were investigated using nanoindentation test. We observed that the Si addition improved the hardness and the Young’s modulus of the Cr–N system. Indeed, the hardness value is 18,56 GPa for CrSiN coatings. Besides, the Young’s modulus value is 224,22 GPa for CrSiN coatings for Si content of 1.2 at.%.

Keywords: Thin film, mechanicals properties, PVD.

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Authors: Marco Ryll, Svetan Ratchev

Abstract:

This paper discusses the applicability of the Data Distribution Service (DDS) for the development of automated and modular manufacturing systems which require a flexible and robust communication infrastructure. DDS is an emergent standard for datacentric publish/subscribe middleware systems that provides an infrastructure for platform-independent many-to-many communication. It particularly addresses the needs of real-time systems that require deterministic data transfer, have low memory footprints and high robustness requirements. After an overview of the standard, several aspects of DDS are related to current challenges for the development of modern manufacturing systems with distributed architectures. Finally, an example application is presented based on a modular active fixturing system to illustrate the described aspects.

Keywords: Flexible Manufacturing, Publish/Subscribe, Plug & Produce.

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Authors: M. S. Alrubaih, M. F. M. Zain, N. L. N. Ibrahim, M.A. Alghoul, K. I. Ben Sauod

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Careful design and selection of daylighting systems can greatly help in reducing not only artificial lighting use, but also decrease cooling energy consumption and, therefore, potential for downsizing air-conditioning systems. This paper aims to evaluate the energy performance of two types of top-light daylighting systems due to the integration of daylight together with artificial lighting in an existing examinaton hall in University Kebangsaan Malaysia, based on a hot and humid climate. Computer simulation models have been created for building case study (base case) and the two types of toplight daylighting designs for building energy performance evaluation using the VisualDOE 4.0 building energy simulation program. The finding revealed that daylighting through top-light systems is a very beneficial design strategy in reducing annual lighting energy consumption and the overall total annual energy consumption.

Keywords: Academic buildings, Daylighting, Top-lighting, Energy savings, Tropical Climate

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Authors: L. Novakova-Marcincinova, J. Novak-Marcincin, M. Janak

Abstract:

The computer aided for design, analysis, control, visualization and simulation of robotized workcells is very interesting in this time. Computer Aided Robot Control (CARC) is a subsystem of the system CIM including the computer aided systems of all activities connected with visualization and working of robotized workcells. There are three basic ideas: current CAD/CAM/CAE systems for design and 3D visualization, special PC based control and simulation systems and Augmented Reality Aided Manufacturing (ARAM) systems. This paper describes example of Open Source software application that can to be utilized at planning of the robotized workcells, visualization and off-line programming the automated processes realized by authors.

Keywords: Intelligent control, augmented reality, robot.

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Authors: R. Oonsivilai, A. Oonsivilai

Abstract:

Realistic systems generally are systems with various inputs and outputs also known as Multiple Input Multiple Output (MIMO). Such systems usually prove to be complex and difficult to model and control purposes. Therefore, decomposition was used to separate individual inputs and outputs. A PID is assigned to each individual pair to regulate desired settling time. Suitable parameters of PIDs obtained from Genetic Algorithm (GA), using Mean of Squared Error (MSE) objective function.

Keywords: Gas Turbine, PID, Genetic Algorithm, Transfer function.Mean of Squared Error

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Authors: Xinhui Wang, Xiuyong Ding

Abstract:

This paper addresses the controller synthesis problem of discrete-time switched positive systems with bounded time-varying delays. Based on the switched copositive Lyapunov function approach, some necessary and sufficient conditions for the existence of state-feedback controller are presented as a set of linear programming and linear matrix inequality problems, hence easy to be verified. Another advantage is that the state-feedback law is independent on time-varying delays and initial conditions. A numerical example is provided to illustrate the effectiveness and feasibility of the developed controller.

Keywords: Switched copositive Lyapunov functions, positive linear systems, switched systems, time-varying delays, stabilization.

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Authors: M. Ektesabi

Abstract:

In this paper the problems associated with immunity of embedded systems used in Motor-Drive systems are investigated and appropriate solutions are presented. Integration of VSD motor systems (Integral Motor) while partially reducing some of these effects, adds to immunity problem of their embedded systems. Fail safe operation of an Integral Motor in arduous industrial environments is considered. In this paper an integral motor with a unique design is proposed to overcome critical issues such as heat, vibration and electromagnetic interference which are damaging to sensitive electronics without requirement of any additional cooling system. Advantages of the proposed Integral motor are compactness of combo motor and drive system with no external cabling/wiring. This motor provides a perfect shielding for least amount of radiated emission. It has an inbuilt filter for EMC compliance and has been designed to provide lower EMC noise for immunity of the internal electronics as well as the other neighbouring systems.

Keywords: Electromagnetic Interference, Immunity, IntegralMotor, Radiated & Conducted Emission, Sensitive Electronics, Variable Speed Drive

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Authors: Florian Müller, Christian Kukla, Thomas Lucyshyn, Clemens Holzer

Abstract:

In this paper, the influencing parameters of a novel purely mechanical wireless in-mould injection moulding sensor were investigated. The sensor is capable of detecting the melt front at predefined locations inside the mould. The sensor comprises a movable pin which acts as the sensor element generating structure-borne sound triggered by the passing melt front. Due to the sensor design, melt pressure is the driving force. For pressure level measurement during pin movement a pressure transducer located at the same position as the movable pin. By deriving a mathematical model for the mechanical movement, dominant process parameters could be investigated towards their impact on the melt front detection characteristic. It was found that the sensor is not affected by the investigated parameters enabling it for reliable melt front detection. In addition, it could be proved that the novel sensor is in comparable range to conventional melt front detection sensors.

Keywords: Injection Moulding, In-Mould Sensor, Structure-Borne Sound, Wireless Sensor

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Authors: Diana Gómez-Cano, J. C. Ochoa-Botero, Roberto Bernal Correa, Yhan Paul Arias

Abstract:

To obtain high mechanical performance, the fresh conditions of a mortar are decisive. Measuring the absorption of aggregates used in mortar mixes is a fundamental requirement for proper design of the mixes prior to their placement in construction sites. In this sense, absorption is a determining factor in the design of a mix because it conditions the amount of water, which in turn affects the water/cement ratio and the final porosity of the mortar. Thus, this work focuses on the mechanical behavior of recycled mortars manufactured from moisture correction using the Thermogravimetric Balancing Halogen Light (TBHL) technique in comparison with the traditional ASTM C 128 International Standard method. The advantages of using the TBHL technique are favorable in terms of reduced consumption of resources such as materials, energy and time. The results show that in contrast to the ASTM C 128 method, the TBHL alternative technique allows obtaining a higher precision in the absorption values of recycled aggregates, which is reflected not only in a more efficient process in terms of sustainability in the characterization of construction materials, but also in an effect on the mechanical performance of recycled mortars.

Keywords: Alternative raw materials, halogen light, recycled mortar, resources optimization, water absorption.

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Authors: Azadeh Maroufmashat, Sourena Sattari Khavas, Halle Bakhteeyar

Abstract:

Multi-energy systems will enhance the system reliability and power quality. This paper presents an integrated approach for the design and operation of distributed energy resources (DER) systems, based on energy hub modeling. A multi-objective optimization model is developed by considering an integrated view of electricity and natural gas network to analyze the optimal design and operating condition of DER systems, by considering two conflicting objectives, namely, minimization of total cost and the minimization of environmental impact which is assessed in terms of CO2 emissions. The mathematical model considers energy demands of the site, local climate data, and utility tariff structure, as well as technical and financial characteristics of the candidate DER technologies. To provide energy demands, energy systems including photovoltaic, and co-generation systems, boiler, central power grid are considered. As an illustrative example, a hotel in Iran demonstrates potential applications of the proposed method. The results prove that increasing the satisfaction degree of environmental objective leads to increased total cost.

Keywords: Multi objective optimization, DER systems, Energy hub, Cost, CO2 emission.

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Authors: Young Sik Kim, Tae Kwon Ha

Abstract:

Effect of Zn addition on the microstructure and mechanical properties of Mg-Zn alloys with Zn contents from 6 to 10 weight percent was investigated in this study. Through calculation of phase equilibria of Mg-Zn alloys, carried out by using FactSage® and FTLite database, solution treatment temperature was decided as temperatures from 300 to 400oC, where supersaturated solid solution can be obtained. Solid solution treatment of Mg-Zn alloys was successfully conducted at 380oC and supersaturated microstructure with all beta phase resolved into matrix was obtained. After solution treatment, hot rolling was successfully conducted by reduction of 60%. Compression and tension tests were carried out at room temperature on the samples as-cast, solution treated, hot-rolled and recrystallized after rolling. After solid solution treatment, each alloy was annealed at temperatures of 180 and 200oC for time intervals from 1 min to 48 hrs and hardness of each condition was measured by micro-Vickers method. Peak aging conditions were deduced as at the temperature of 200oC for 10 hrs. By addition of Zn by 10 weight percent, hardness and strength were enhanced.

Keywords: Mg-Zn alloy, Heat treatment, Microstructure, Mechanical properties, Hardness.

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Authors: Mohd Yussni Hashim, Mohd Nazrul Roslan, Azriszul Mohd Amin, Ahmad Mujahid Ahmad Zaidi, Saparudin Ariffin

Abstract:

Environmental awareness and depletion of the petroleum resources are among vital factors that motivate a number of researchers to explore the potential of reusing natural fiber as an alternative composite material in industries such as packaging, automotive and building constructions. Natural fibers are available in abundance, low cost, lightweight polymer composite and most importance its biodegradability features, which often called “ecofriendly" materials. However, their applications are still limited due to several factors like moisture absorption, poor wettability and large scattering in mechanical properties. Among the main challenges on natural fibers reinforced matrices composite is their inclination to entangle and form fibers agglomerates during processing due to fiber-fiber interaction. This tends to prevent better dispersion of the fibers into the matrix, resulting in poor interfacial adhesion between the hydrophobic matrix and the hydrophilic reinforced natural fiber. Therefore, to overcome this challenge, fiber treatment process is one common alternative that can be use to modify the fiber surface topology by chemically, physically or mechanically technique. Nevertheless, this paper attempt to focus on the effect of mercerization treatment on mechanical properties enhancement of natural fiber reinforced composite or so-called bio composite. It specifically discussed on mercerization parameters, and natural fiber reinforced composite mechanical properties enhancement.

Keywords: Mercerization treatment, mechanical properties, natural fiber and bio composite

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Authors: Huaiyu Zhang

Abstract:

The method of modeling is the key technology for digital mockup (DMU). Based upon the developing for mechanical product DMU, the theory, method and approach for virtual environment (VE) and virtual object (VO) were studied. This paper has expounded the design goal and architecture of DMU system, analyzed the method of DMU application, and researched the general process of physics modeling and behavior modeling.

Keywords: DMU, VR, virtual environment, virtual object, physics modeling, behavior modeling

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Authors: S. Talabgaew, V. Laemlaksakul

Abstract:

A new generation product made from bamboo strips, known as laminated bamboo, has gained importance. The objective of this research was to experiment the effect of three factors on the mechanical property of laminated bamboo. The interested factors for experimental design were (A) four bamboo species, namely Bambusa blumeana Schultes (Pai See Suk), Dendrocalamus asper Backer (Pai Tong), Dendrocalamus hamiltonii Nees (Pai Hok) and Dendrocalamus sericeus Munro (Pai Sang Mon), (B) two types of glue adhesive, polyvinyl acetate emulsion (PVAC) fortified with urea-formaldehyde (UF) and urea-formaldehyde (UF) to make parallel-oriented bamboo strips laminates and (C) glue weight per strip area, 150 g/m2 and 190 g/m2. Experimental results showed that Dendrocalamus asper Backer (Pai Tong) and Dendrocalamus sericeus Munro (Pai Sang Mon) were best used for manufacturing due to their highest MOR and MOE. The amount of glue weight 150 g/m2 yielded higher MOR and MOE than the amount of glue weight 190 g/m2. At the conclusion, the laminated bamboo manufacturers can benefit from this research in order to select right materials according to strength, cost and accessibility.

Keywords: Laminated Bamboo, Mechanical Property, 3-WayANOVA.

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Authors: A. Chidley, F. Roger, A. Traidia

Abstract:

A method is presented for using thermo-mechanical fatigue analysis as a tool in the design of automotive heat exchangers. Use of infra-red thermography to measure the real thermal history in the heat exchanger reduces the time necessary for calculating design parameters and improves prediction accuracy. Thermal shocks are the primary cause of heat exchanger damage. Thermo-mechanical simulation is based on the mean behavior of the aluminum tubes used in the heat exchanger. An energetic fatigue criterion is used to detect critical zones.

Keywords: Heat exchanger, Fatigue, Thermal shocks. I.

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Authors: Eleni Aggelogiannaki, Haralambos Sarimveis

Abstract:

In this work, a radial basis function (RBF) neural network is developed for the identification of hyperbolic distributed parameter systems (DPSs). This empirical model is based only on process input-output data and used for the estimation of the controlled variables at specific locations, without the need of online solution of partial differential equations (PDEs). The nonlinear model that is obtained is suitably transformed to a nonlinear state space formulation that also takes into account the model mismatch. A stable robust control law is implemented for the attenuation of external disturbances. The proposed identification and control methodology is applied on a long duct, a common component of thermal systems, for a flow based control of temperature distribution. The closed loop performance is significantly improved in comparison to existing control methodologies.

Keywords: Hyperbolic Distributed Parameter Systems, Radial Basis Function Neural Networks, H∞ control, Thermal systems.

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Authors: Michal Polanský, C. Ardil

Abstract:

This paper shows a new method for design of fuzzy observers for Takagi-Sugeno systems. The method is based on Linear matrix inequalities (LMIs) and it allows to insert H constraint into the design procedure. The speed of estimation can tuned be specification of a decay rate of the observer closed loop system. We discuss here also the influence of parametric uncertainties at the output control system stability.

Keywords: H norm, Linear Matrix Inequalities, Observers, Takagi-Sugeno Systems, Parallel Distributed Compensation

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Authors: S. Ariffin, K. Hasnan, R.H. Weston

Abstract:

A new generation of manufacturing machines so-called MIMCA (modular and integrated machine control architecture) capable of handling much increased complexity in manufacturing control-systems is presented. Requirement for more flexible and effective control systems for manufacturing machine systems is investigated and dimensioned-which highlights a need for improved means of coordinating and monitoring production machinery and equipment used to- transport material. The MIMCA supports simulation based on machine modeling, was conceived by the authors to address the issues. Essentially MIMCA comprises an organized unification of selected architectural frameworks and modeling methods, which include: NISTRCS, UMC and Colored Timed Petri nets (CTPN). The unification has been achieved; to support the design and construction of hierarchical and distributed machine control which realized the concurrent operation of reusable and distributed machine control components; ability to handle growing complexity; and support requirements for real- time control systems. Thus MIMCA enables mapping between 'what a machine should do' and 'how the machine does it' in a well-defined but flexible way designed to facilitate reconfiguration of machine systems.

Keywords: Machine control, architectures, Petri nets, modularity, modeling, simulation.

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Authors: Anouar Ben Khalifa, Sami Gazzah, Najoua Essoukri BenAmara

Abstract:

Multimodal biometric systems integrate the data presented by multiple biometric sources, hence offering a better performance than the systems based on a single biometric modality. Although the coupling of biometric systems can be done at different levels, the fusion at the scores level is the most common since it has been proven effective than the rest of the fusion levels. However, the scores from different modalities are generally heterogeneous. A step of normalizing the scores is needed to transform these scores into a common domain before combining them. In this paper, we study the performance of several normalization techniques with various fusion methods in a context relating to the merger of three unimodal systems based on the face, the palmprint and the fingerprint. We also propose a new adaptive normalization method that takes into account the distribution of client scores and impostor scores. Experiments conducted on a database of 100 people show that the performances of a multimodal system depend on the choice of the normalization method and the fusion technique. The proposed normalization method has given the best results.

Keywords: Multibiometrics, Fusion, Score level, Score normalization, Adaptive normalization.

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Authors: Hui Chen, Xiao Feng

Abstract:

Depressurization and pressurization streams in industrial systems constitute a work exchange network (WEN). In this paper, a novel graphical approach for targeting energy conservation potential of a WEN is proposed. Through constructing the composite work curves in the pressure-work diagram and assuming all of the mechanical energy of the depressurization streams is recovered by expanders, the maximum work target of a WEN can be determined via the proposed targeting steps. A WEN in an ammonia production process is used as a case study to illustrate the applicability of the proposed graphical approach.

Keywords: Expanders, Graphical approach, Pressure-work diagram, Work exchange network, Work target

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Authors: Xin-Lei Feng, Ting-Zhu Huang

Abstract:

According to conjugate gradient algorithm, a new consensus protocol algorithm of discrete-time multi-agent systems is presented, which can achieve finite-time consensus. Finally, a numerical example is given to illustrate our theoretical result.

Keywords: Consensus protocols; Graph theory; Multi-agent systems;Conjugate gradient algorithm; Finite-time.

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Authors: Jamal Moshtagh, Hassan Pourvali Souraki

Abstract:

In North America, Most power distribution systems employ a four-wire multi-grounded neutral (MGN) design. This paper has explained the inherent characteristics of multi-grounded three-phase four-wire distribution systems under unbalanced situations. As a result, the mechanism of voltage swell and voltage sag in MGN feeders becomes difficult to understand. The simulation tool that has been used in this paper is MATLAB under Windows software. In this paper the equivalent model of a full-scale multigrounded distribution system implemented by MATLAB is introduced. The results are expected to help utility engineers to understand the impact of MGN on distribution system operations.

Keywords: Distribution systems, multi- grounded, neutral, three-phase four-wire, ground.

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Authors: Berkay Ergene, Çağın Bolat

Abstract:

In this study, we mainly focused on a simulation study regarding composite footbed in order to contribute to shoe industry. As a footbed, e-glass fiber reinforced polyurethane was determined since polyurethane based materials are already used for footbed in shoe manufacturing frequently. Flat, elliptical and rectangular grooved shoe soles were modeled and analyzed separately as TPU, 10% glass fiber reinforced, 30% glass fiber reinforced and 50% glass fiber reinforced materials according to their properties under three point bending and compression situations to determine the relationship between model, material type and mechanical behaviours of composite model. ANSYS 14.0 APDL mechanical structural module is utilized in all simulations and analyzed stress and strain distributions for different footbed models and materials. Furthermore, materials constants like young modulus, shear modulus, Poisson ratio and density of the composites were calculated theoretically by using composite mixture rule and interpreted for mechanical aspects.

Keywords: Composite, elastic behaviour, footbed, simulation.

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Authors: Nidhal Jamia, Sami El-Borgi

Abstract:

In this paper, the problem of a mixed-Mode crack embedded in an infinite medium made of a functionally graded piezoelectric material (FGPM) with crack surfaces subjected to electro-mechanical loadings is investigated. Eringen’s non-local theory of elasticity is adopted to formulate the governing electro-elastic equations. The properties of the piezoelectric material are assumed to vary exponentially along a perpendicular plane to the crack. Using Fourier transform, three integral equations are obtained in which the unknown variables are the jumps of mechanical displacements and electric potentials across the crack surfaces. To solve the integral equations, the unknowns are directly expanded as a series of Jacobi polynomials, and the resulting equations solved using the Schmidt method. In contrast to the classical solutions based on the local theory, it is found that no mechanical stress and electric displacement singularities are present at the crack tips when nonlocal theory is employed to investigate the problem. A direct benefit is the ability to use the calculated maximum stress as a fracture criterion. The primary objective of this study is to investigate the effects of crack length, material gradient parameter describing FGPMs, and lattice parameter on the mechanical stress and electric displacement field near crack tips.

Keywords: Functionally graded piezoelectric material, mixed-mode crack, non-local theory, Schmidt method.

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