Search results for: mechanical quadrature methods

Authors: M. Soltan Rezaee, M. R. Ghazavi, A. Najafi, W.-H. Liao

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Generally, different rods in shaft systems can be misaligned based on the mechanical system usages. These rods can be linked together via U-coupling easily. The system is self-stimulated and may cause instabilities due to the inherent behavior of the coupling. In this study, each rod includes an elastic shaft with an angular stiffness and structural damping. Moreover, the mass of shafts is considered via attached solid disks. The impact of the system architecture and shaft mass on the instability of such mechanism are studied. Stability charts are plotted via a method based on Floquet theory. Eventually, the unstable points have been found and analyzed in detail. The results show that stabilizing the driveline is feasible by changing the system characteristics which include shaft mass and architecture.

Keywords: Coupling, mechanical systems, oscillations, rotating shafts.

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Authors: S. Tunmee, P. Wongpanya, I. Toda, X. L. Zhou, Y. Nakaya, N. Konkhunthot, S. Arakawa, H. Saitoh

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The hydrogenated amorphous carbon films (α-C:H) were deposited on p-type Si (100) substrates at different thicknesses by radio frequency plasma enhanced chemical vapor deposition technique (rf-PECVD). Raman spectra display asymmetric diamond-like carbon (DLC) peaks, representative of the α-C:H films. The decrease of intensity ID/IG ratios revealed the sp3 content arise at different thicknesses of the α-C:H films. In terms of mechanical properties, the high hardness and elastic modulus values showed the elastic and plastic deformation behaviors related to sp3 content in amorphous carbon films. Electrochemical properties showed that the α-C:H films exhibited excellent corrosion resistance in air-saturated 3.5 wt.% NaCl solution for pH 2 at room temperature. Thickness increasing affected the small sp2 clusters in matrix, restricting the velocity transfer and exchange of electrons. The deposited α-C:H films exhibited excellent mechanical properties and corrosion resistance.

Keywords: Thickness, Mechanical properties, Electrochemical corrosion properties, α-C:H film.

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Authors: D. Falliano, D. De Domenico, G. Ricciardi, E. Gugliandolo

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This paper is focused on the mechanical characterization of foamed concrete specimens with protein-based foaming agent. Unlike classic foamed concrete, a peculiar property of the analyzed foamed concrete is the extrudability, which is achieved via a specific additive in the concrete mix that significantly improves the cohesion and viscosity of the fresh cementitious paste. A broad experimental campaign was conducted to evaluate the compressive strength and the indirect tensile strength of the specimens. The study has comprised three different cement types, two water/cement ratios, three curing conditions and three target dry densities. The variability of the strength values upon the above mentioned factors is discussed.

Keywords: Cement type, curing conditions, density, extrudable concrete, foamed concrete, mechanical characterization.

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Authors: M. Karami Khorramabadi, A. R. Nezamabadi

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This paper studies mechanical buckling of functionally graded beams subjected to axial compressive load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. Applying the Hamilton's principle, the equilibrium equation is established. The influences of dimensionless geometrical parameter, functionally graded index and foundation coefficient on the critical buckling load of beam are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: Mechanical Buckling, Functionally graded beam- Engesser-Timoshenko beam theory

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Authors: M. T. Z. Butt, T. Ahmad, N. A. Siddiqui

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Commercially SA 516 Grade 70 is frequently used for the manufacturing of pressure vessels, boilers and storage tanks etc. in fabrication industry. Heat input is the major parameter during welding that may bring significant changes in the microstructure as well as the mechanical properties. Different welding technique has different heat input rate per unit surface area. Materials with large thickness are dealt with different combination of welding techniques to achieve required mechanical properties. In the present research two schemes: Scheme 1: SMAW (Shielded Metal Arc Welding) & GTAW (Gas Tungsten Arc Welding) and Scheme 2: SMAW & SAW (Submerged Arc Welding) of hybrid welding techniques have been studied. The purpose of these schemes was to study hybrid welding effect on the microstructure and mechanical properties of the weldment, heat affected zone and base metal area. It is significant to note that the thickness of base plate was 12 mm, also welding conditions and parameters were set according to ASME Section IX. It was observed that two different hybrid welding techniques performed on two different plates demonstrated that the mechanical properties of both schemes are more or less similar. It means that the heat input, welding techniques and varying welding operating conditions & temperatures did not make any detrimental effect on the mechanical properties. Hence, the hybrid welding techniques mentioned in the present study are favorable to implicate for the industry using the plate thickness around 12 mm thick.

Keywords: Grade 70, GTAW, hybrid welding, SAW, SMAW.

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Authors: Guojia Ma, Guoqiang Lin, Shuili Gong, Gang Sun, Dawang Wang

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A diamond-like carbon (DLC) based solid-lubricant film was designed and DLC films were successfully prepared using a microwave plasma enhanced magnetron sputtering deposition technology. Post-test characterizations including Raman spectrometry, X-ray diffraction, nano-indentation test, adhesion test, friction coefficient test were performed to study the influence of substrate bias voltage on the mechanical properties of the W- and S-doped DLC films. The results indicated that the W- and S-doped DLC films also had the typical structure of DLC films and a better mechanical performance achieved by the application of a substrate bias of -200V.

Keywords: Adhesive Strength, Coefficient of Friction, Substrate Bias, W- and S-doped DLC film

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Authors: Sameru Sharma, Sanjay Sharma, Derick Engles

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Multiple-input multiple-output (MIMO) systems are widely in use to improve quality, reliability of wireless transmission and increase the spectral efficiency. However in MIMO systems, multiple copies of data are received after experiencing various channel effects. The limitations on account of complexity due to number of antennas in case of conventional decoding techniques have been looked into. Accordingly we propose a modified sphere decoder (MSD-1) algorithm with lower complexity and give rise to system with high spectral efficiency. With the aim to increase signal diversity we apply rotated quadrature amplitude modulation (QAM) constellation in multi dimensional space. Finally, we propose a new architecture involving space time trellis code (STTC) concatenated with space time block code (STBC) using MSD-1 at the receiver for improving system performance. The system gains have been verified with channel state information (CSI) errors.

Keywords: Channel State Information , Diversity, Multi-Antenna, Rotated Constellation, Space Time Codes.

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Authors: K. Krizova, R. Hela, S. Keprdova

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This paper introduces selected composition of conventional concretes and their resulting mechanical properties at different ages of concrete. With respect to utilization of mineral admixtures, fly ash and ground limestone agents were included in addition to pure Portland binder. The proposal of concrete composition remained constant in basic concrete components such as cement and representation of individual contents of aggregate fractions; weight dosing of admixtures and water dose were only modified. Water dose was chosen in order to achieve identical consistence by settlement for all proposals of concrete composition. Mechanical properties monitored include compression strength, static and dynamic modulus of concrete elasticity, at ages of 7, 28, 90, and 180 days.

Keywords: Cement, mineral admixtures, microstructure of concrete, mechanical properties.

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Authors: Olatunde I. Sekunowo, Stephen I. Durowaye, Oluwashina P. Gbenebor

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Copper being one of the major intrinsic residual impurities in steel possesses the tendency to induce severe microstructural distortions if not controlled within certain limits. Hence, this paper investigates the effect of this element on the mechanical properties of construction steel with a view to ascertain its safe limits for effective control. The experiment entails collection of statistically scheduled samples of hot rolled profiles with varied copper concentrations in the range of 0.12-0.39 wt. %. From these samples were prepared standard test specimens subjected to tensile, impact, hardness and microstructural analyses. Results show a rather huge compromise in mechanical properties as the specimens demonstrated 54.3%, 74.2% and 64.9% reduction in tensile strength, impact energy and hardness respectively as copper content increases from 0.12 wt. % to 0.39 wt. %. The steel’s abysmal performance is due to the severe distortion of the microstructure occasioned by the development of incoherent complex compounds which weaken the pearlite reinforcing phase. It is concluded that the presence of copper above 0.22 wt. % is deleterious to construction steel performance.

Keywords: Construction steel, mechanical properties, processing method, trace elements.

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Authors: Alireza BozorgianÏî Navid Majdi Nasab, Hassan Mirzazadeh

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In this paper, the effect of modified clay on the mechanical efficiency of epoxy resin is examined. Studies by X ray diffraction and microscopic transient electron method show that modified clay distribution in polymer area is intercalated kind. Examination the results of mechanical tests shows that existence of modified clay in epoxy area increases pressure yield strength, tension module and nano composite fracture toughness in relate of pure epoxy. By microscopic examinations it is recognized too that the action of toughness growth of this kind of nano composite is due to crack deflection, formation of new surfaces and fracture of clay piles.

Keywords: Nano clay, Epoxy, Toughness, Composite

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Authors: Shengfeng Li, Rujing Wang

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In this paper, we present two new one-step iterative methods based on Thiele-s continued fraction for solving nonlinear equations. By applying the truncated Thiele-s continued fraction twice, the iterative methods are obtained respectively. Analysis of convergence shows that the new methods are fourth-order convergent. Numerical tests verifying the theory are given and based on the methods, two new one-step iterations are developed.

Keywords: Iterative method, Fixed-point iteration, Thiele's continued fraction, Order of convergence.

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Authors: Merve Ozer, Tolga Gokkurt, Yasemen Gokkurt, Ezgi Bozbey

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In this study, research has been conducted on the recovery of automotive textile waste, which has heavy use in the automotive sector and consists of PET/PP content, through the upcycling technique of post-product and post-consumer usage. The aim is to investigate the formulation and production methods that will enable the substitution of original PP raw materials, used in the production of plastic edge bands, with PP/PET alloys. The lamination structure of the mentioned waste makes it impossible to separate the incompatible PP and PET phases, thereby hindering the production of high-quality raw materials or products through recycling. In this study, a comprehensive process was examined through a two-step production process using different types of block and maleic-grafted copolymers to achieve compatibility between these two incompatible phases. The obtained plastic raw materials, referred to as PP/PET blends, were examined in detail, with a focus on their mechanical, thermal, and morphological properties, to discuss their substitutability for the original raw materials.

Keywords: Twin screw extruders, mechanical recycling, melt blending, plastic blends, polyethylene, polypropylene, recycling of plastics.

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Authors: A. Khourgami, M. Rafiee, H. Jafari, Z. Bitarafan

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To study the effect of suitable methods for propagation of True Potato Seed (TPS) progenies, transplant and selection of the best progenies, a factorial experiment base on a randomized complete block design was carried out in the research field of Sahneh region, Kermanshah, Iran during 2009-2010. Five selective progenies from CIP (International Potato Center) including CIP.994013, CIP.994002, CIP.994014, CIP.888006, and CIP.994001 and two transplant preparation methods (Paper pot preparation for mechanical cultivation and preparation in transplant trays for manual cultivation) were studied in three replications. Results showed that different progenies had no significant effect on plant height (cm) and tuber yield (t ha-1), whereas had a significant effect on number of tubers per unit area (m2). There was significant difference between transplant preparation methods for plant height and tuber yield. The interaction effect of progenies and transplant preparation method was not significant for these traits. CIP.888006 progeny and paper pot preparation method produced the highest tuber yields. Also CIP.994002 and CIP.994014 progenies considered as the best progenies under paper pot preparation method due to high yields.

Keywords: Potato, Solanum tuberosum, TPS progenies, Transplant preparation method

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Authors: Michael Tupý, Dagmar Měřínská, Alice Tesaříková-Svobodová, Christian Carrot, Caroline Pillon, Vít Petránek

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The mechanical properties of blends consisting of plasticized poly(vinyl butyral) (PVB) and plasticized poly(vinyl chloride) (PVC) are studied, in order to evaluate the possibility of using recycled PVB waste derived from windshields. PVC was plasticized with 38% of diisononyl phthalate (DINP), while PVB was plasticized with 28% of triethylene glycol, bis(2-ethylhexanoate) (3GO). The optimal process conditions for the PVB/PVC blend in 1:1 ratio were determined. Entropy was used in order to theoretically predict the blends miscibility. The PVB content of each blend composition used was ranging from zero to 100%. Tensile strength and strain were tested. In addition, a comparison between recycled and original PVB, used as constituents of the blend, was performed.

Keywords: Poly(vinyl butyral), poly(vinyl chloride), windshield, polymer waste, mechanical properties.

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Authors: A. Buasri, N. Chaiyut, K. Borvornchettanuwat, N. Chantanachai, K. Thonglor

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Inorganic nanoparticles filled polymer composites have extended their multiple functionalities to various applications, including mechanical reinforcement, gas barrier, dimensional stability, heat distortion temperature, flame-retardant, and thermal conductivity. Sodium stearate-modified calcium carbonate (CaCO3) nanoparticles were prepared using surface modification method. The results showed that sodium stearate attached to the surface of CaCO3 nanoparticles with the chemical bond. The effect of modified CaCO3 nanoparticles on thermal properties of polypropylene (PP) was studied by means of differential scanning calorimetry (DSC) and Thermogravimetric analysis (TGA). It was found that CaCO3 significantly affected the crystallization temperature and crystallization degree of PP. Effect of the modified CaCO3 content on mechanical properties of PP/CaCO3 nanocomposites was also studied. The results showed that the modified CaCO3 can effectively improve the mechanical properties of PP. In comparison with PP, the impact strength of PP/CaCO3 nanocomposites increased by about 65% and the hardness increased by about 5%.

Keywords: Polypropylene Nanocomposites, Modified Calcium Carbonate, Sodium Stearate, Surface Treatment

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Authors: Israa Al-Neami, Ali J. Al-Askery, Martin Johnston, Charalampos Tsimenidis

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In this paper, we focus on the design of a multi-line copper wire (MLCW) communication system. First, we construct our proposed MLCW channel and verify its characteristics based on the Kolmogorov-Smirnov test. In addition, we apply Middleton class A impulsive noise (IN) to the copper channel for further investigation. Second, the MIMO G.fast system is adopted utilizing the proposed MLCW channel model and is compared to a single line G-fast system. Second, the performance of the coded system is obtained utilizing concatenated interleaved Reed-Solomon (RS) code with four-dimensional trellis-coded modulation (4D TCM), and compared to the single line G-fast system. Simulations are obtained for high quadrature amplitude modulation (QAM) constellations that are commonly used with G-fast communications, the results demonstrate that the bit error rate (BER) performance of the coded MLCW system shows an improvement compared to the single line G-fast systems.

Keywords: G.fast, Middleton Class A impulsive noise, mitigation techniques, copper channel Model.

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Authors: Jalil Rashidinia, Reza Jalilian

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In this paper we use quintic non-polynomial spline functions to develop numerical methods for approximation to the solution of a system of fourth-order boundaryvalue problems associated with obstacle, unilateral and contact problems. The convergence analysis of the methods has been discussed and shown that the given approximations are better than collocation and finite difference methods. Numerical examples are presented to illustrate the applications of these methods, and to compare the computed results with other known methods.

Keywords: Quintic non-polynomial spline, Boundary formula, Convergence, Obstacle problems.

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Authors: M. Li, V. D. Thi, M. Khelifa, M. El Ganaoui

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This study presents an overview of the work carried out by the use of wood waste as coarse aggregate in mortar. The paper describes experimental and numerical investigations carried on pervious concrete made of wood chips and also sheds lights on the mechanical properties of this new product. The properties of pervious wood-concrete such as strength, elastic modulus, and failure modes are compared and evaluated. The characterization procedure of the mechanical properties of wood waste ash are presented and discussed. The numerical and tested load–deflection response results are compared. It was observed that the numerical results are in good agreement with the experimental results.

Keywords: Wood waste ash, characterization, mechanical properties, finite element analysis, flexural behavior, bending tests.

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Authors: Olesia Mikhailova, Pavel Rovnaník

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In the present work, metakaolin-based geopolymer including different polymer admixtures was studied. Different types of commercial polymer admixtures VINNAPAS^® and polyethylene glycol of different relative molecular weight were used as polymer admixtures. The main objective of this work is to investigate the influence of different types of admixtures on the properties of metakaolin-based geopolymer mortars considering their different dosage. Mechanical properties, such as flexural and compressive strength were experimentally determined. Also, study of the microstructure of selected specimens by using a scanning electron microscope was performed. The results showed that the specimen with addition of 1.5% of VINNAPAS^® 7016 F and 10% of polyethylene glycol 400 achieved maximum mechanical properties.

Keywords: Metakaolin, geopolymer, polymer admixtures, mechanical properties, microstructure.

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Authors: A. Pashayev, C. Ardil, R. Sadiqov

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Various methods of geofield parameters restoration (by algebraic polynoms; filters; rational fractions; interpolation splines; geostatistical methods – kriging; search methods of nearest points – inverse distance, minimum curvature, local – polynomial interpolation; neural networks) have been analyzed and some possible mistakes arising during geofield surface modeling have been presented.

Keywords: interpolation methods, geofield parameters, neural networks.

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Authors: Oladeinde Mobolaji Humphrey, Akpobi John

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A mathematical model for the hydrodynamic lubrication of parabolic slider bearings with couple stress lubricants is presented. A numerical solution for the mathematical model using finite element scheme is obtained using three nodes isoparametric quadratic elements. Stiffness integrals obtained from the weak form of the governing equations were solved using Gauss Quadrature to obtain a finite number of stiffness matrices. The global system of equations was obtained for the bearing and solved using Gauss Seidel iterative scheme. The converged pressure solution was used to obtain the load capacity of the bearing. Parametric studies were carried out and it was shown that the effect of couple stresses and profile parameter are to increase the load carrying capacity of the parabolic slider bearing. Numerical experiments reveal that the magnitude of the profile parameter at which maximum load is obtained increases with decrease in couple stress parameter. The results are presented in graphical form.

Keywords: Finite element, numerical, parabolic slider.

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Authors: Amir Atrian, Javad Jafari Fesharaki, Gh. Hossein Majzoobi, Mahsa Sheidaee

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The analytical solution of functionally graded piezoelectric hollow cylinder which is under radial electric potential and non-axisymmetric thermo-mechanical loads, are presented in this paper. Using complex Fourier series and estimation of power law for variations of material characterizations through the thickness, the electro thermo mechanical behavior of the FGPM cylinder is obtained. The stress and displacement distributions and the effect of electric potential field on the cylinder behavior are also presented and some applicable results are offered at the end of the paper.

Keywords: Analytical, FGM, Fourier series, Non-axisymmetric, Piezoelectric, Thermo-elasticity

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Authors: Salma Siddika, Fayeka Mansura, Mahbub Hasan

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The term hybrid composite refers to the composite containing more than one type of fiber material as reinforcing fillers. It has become attractive structural material due to the ability of providing better combination of properties with respect to single fiber containing composite. The eco-friendly nature as well as processing advantage, light weight and low cost have enhanced the attraction and interest of natural fiber reinforced composite. The objective of present research is to study the mechanical properties of jute-coir fiber reinforced hybrid polypropylene (PP) composite according to filler loading variation. In the present work composites were manufactured by using hot press machine at four levels of fiber loading (5, 10, 15 and 20 wt %). Jute and coir fibers were utilized at a ratio of (1:1) during composite manufacturing. Tensile, flexural, impact and hardness tests were conducted for mechanical characterization. Tensile test of composite showed a decreasing trend of tensile strength and increasing trend of the Young-s modulus with increasing fiber content. During flexural, impact and hardness tests, the flexural strength, flexural modulus, impact strength and hardness were found to be increased with increasing fiber loading. Based on the fiber loading used in this study, 20% fiber reinforced composite resulted the best set of mechanical properties.

Keywords: Mechanical Properties; Coir, Jute, Polypropylene, Hybrid Composite.

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Authors: Jipeng Yan, Xingchen Yang, Xiaowei Zhou, Mengxing Tang, Honghai Liu

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Shear elastic modulus of skeletal muscles can be obtained by shear wave elastography (SWE) and has been linearly related to muscle force. However, SWE is currently implemented using array probes. Price and volumes of these probes and their driving equipment prevent SWE from being used in wearable human-machine interfaces (HMI). Moreover, beamforming processing for array probes reduces the real-time performance. To achieve SWE by wearable HMIs, a customized three-element probe is adopted in this work, with one element for acoustic radiation force generation and the others for shear wave tracking. In-phase quadrature demodulation and 2D autocorrelation are adopted to estimate velocities of tissues on the sound beams of the latter two elements. Shear wave speeds are calculated by phase shift between the tissue velocities. Three agar phantoms with different elasticities were made by changing the weights of agar. Values of the shear elastic modulus of the phantoms were measured as 8.98, 23.06 and 36.74 kPa at a depth of 7.5 mm respectively. This work verifies the feasibility of measuring shear elastic modulus by wearable devices.

Keywords: Shear elastic modulus, skeletal muscle, ultrasound, wearable human-machine interface.

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Authors: Eung Ryeol Seo, Hee Tae Lim, Eunsuk Bang, Soon Cheol Kweon, Jeoung-Kyo Jeoung, Ji-Hoon Choic

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The object of this study is to investigate the effect of pulsator on washing performance quantitatively for front-loading washer. The front-loading washer with pulsator shows washing performance improvement of 18% and the particle-based body simulation technique has been applied to figure out the relation between washing performance and mechanical forces exerted on textile during washing process. As a result, the mechanical forces, such as collision force and strain force, acting on the textile have turned out to be about twice numerically. The washing performance improvement due to additional pulsate system has been utilized for customers to save 50% of washing time.

Keywords: Front-loading washer, mechanical force, fabric movement, pulsator, time saving.

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Authors: Meriem Benzarti, Mohamed Ben Tkaya, Cyril Pailler Mattei, Hassan Zahouani

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Hair is a non homogenous complex material which can be associated with a polymer. It is made up 95% of Keratin. Hair has a great social significance for human beings. In the High Middle Ages, for example, long hairs have been reserved for kings and nobles. Most common interest in hair is focused on hair growth, hair types and hair care, but hair is also an important biomaterial which can vary depending on ethnic origin or on age, hair colour for example can be a sign of ethnic ancestry or age (dark hair for Asiatic, blond hair for Caucasian and white hair for old people in general). In this context, different approaches have been conducted to determine the differences in mechanical properties and characterize the fracture topography at the surface of hair depending on its type and its age. A tensile testing machine was especially designed to achieve tensile tests on hair. This device is composed of a microdisplacement system and a force sensor whose peak load is limited to 3N. The curves and the values extracted from each experiment, allow us to compare the evolution of the mechanical properties from one hair to another. Observations with a Scanning Electron Microscope (SEM) and with an interferometer were made on different hairs. Thus, it is possible to access the cuticle state and the fracture topography for each category.

Keywords: Hair, relaxation test, SEM, interferometer, mechanical properties.

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Authors: Kaziyev G. Z., Nabiyeva G. S., Kalizhanova A.U.

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We consider herein a concise view of discreet programming models and methods. There has been conducted the models and methods analysis. On the basis of discreet programming models there has been elaborated and offered a new class of problems, i.e. block-symmetry models and methods of applied tasks statements and solutions.

Keywords: Discreet programming, block-symmetry, analysis methods, information systems development.

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Authors: A. Ehsani, A. Karimizadeh, H. Fallahi, A. Jalali

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In an electric power system, spinning reserve requirements can be determined by using deterministic and/or probabilistic measures. Although deterministic methods are usual in many systems, application of probabilistic methods becomes increasingly important in the new environment of the electric power utility industry. This is because of the increased uncertainty associated with competition. In this paper 1) a new probabilistic method is presented which considers the reliability of transmission system in a simplified manner and 2) deterministic and probabilistic methods are compared. The studied methods are applied to the Roy Billinton Test System (RBTS).

Keywords: Reliability, Spinning Reserve, Risk, Transmission, Unit Commitment.

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Authors: Ganiyu Amuda Yusuf, Sarajul Fikri Mohamed

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The procurement and cost management approach adopted for mechanical and electrical (M&E) services in Malaysian construction industry have been criticized for its inefficiency. The study examined early cost estimating practices adopted for mechanical and electrical services (M&E) in Malaysia so as to understand the level of compliance of the current techniques with best practices. The methodology adopted for the study is a review of bidding documents used on both completed and on – going building projects awarded between 2008 – 2010 under 9th Malaysian Plan. The analysis revealed that, M&E services cost cannot be reliably estimated at pre-contract stage; the bidding techniques adopted for M&E services failed to provide uniform basis for contractors to submit tender; detailed measurement of items were not made which could complicate post contract cost control and financial management. The paper concluded that, there is need to follow a structured approach in determining the pre-contract cost estimate for M&E services which will serve as a virile tool for post contract cost control.

Keywords: Cost Management, Mechanical and Electrical Services, Procurement, Standard Method of Measurement

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Authors: Xiang Liu, Ciprian Coman

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The wrinkling of a thin elastic bi-annular plate with piecewise-constant mechanical properties, subjected to radial stretching, is considered. The critical wrinkling stretching loading and the corresponding wrinkling patterns are extensively investigated, together with the roles played by both the geometrical and mechanical parameters.

Keywords: bi-annular plate, wrinkling pattern, critical stretching loading.

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