Search results for: surface displacement history

Authors: P. R. Prabhu, S. M. Kulkarni, S. S. Sharma

Abstract:

Deep cold rolling (DCR) and low plasticity burnishing (LPB) process are cold working processes, which easily produce a smooth and work-hardened surface by plastic deformation of surface irregularities. The present study focuses on the surface roughness and surface hardness aspects of AISI 4140 work material, using fractional factorial design of experiments. The assessment of the surface integrity aspects on work material was done, in order to identify the predominant factors amongst the selected parameters. They were then categorized in order of significance followed by setting the levels of the factors for minimizing surface roughness and/or maximizing surface hardness. In the present work, the influence of main process parameters (force, feed rate, number of tool passes/overruns, initial roughness of the work piece, ball material, ball diameter and lubricant used) on the surface roughness and the hardness of AISI 4140 steel were studied for both LPB and DCR process and the results are compared. It was observed that by using LPB process surface hardness has been improved by 167% and in DCR process surface hardness has been improved by 442%. It was also found that the force, ball diameter, number of tool passes and initial roughness of the workpiece are the most pronounced parameters, which has a significant effect on the work piece-s surface during deep cold rolling and low plasticity burnishing process.

Keywords: Deep cold rolling, burnishing, surface roughness, surface hardness, design of experiments, AISI4140 steel.

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Authors: Md. Anayet U. Patwari, Mohammad Ahsan Habib, Md. Tanzib Ehsan, Md Golam Ahnaf, Md. S. I. Chowdhury

Abstract:

Surface roughness is one of the key quality parameters of the finished product. During any machining operation, high temperatures are generated at the tool-chip interface impairing surface quality and dimensional accuracy of products. Cutting fluids are generally applied during machining to reduce temperature at the tool-chip interface. However, usages of cutting fluids give rise to problems such as waste disposal, pollution, high cost, and human health hazard. Researchers, now-a-days, are opting towards dry machining and other cooling techniques to minimize use of coolants during machining while keeping surface roughness of products within desirable limits. In this paper, a concept of using peltier cooling effects during aluminium milling operation has been presented and adopted with an aim to improve surface roughness of the machined surface. Experimental evidence shows that peltier cooling effect provides better surface roughness of the machined surface compared to dry machining.

Keywords: Aluminium, surface roughness, Peltier cooling effect, milling operation.

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Authors: Mara Magda Maftei

Abstract:

The article emphasizes the ideological commitment of the philosopher Emil Cioran. It presents firstly Cioran's works on the theme announced by the title, then the European context that determined the political option of Cioran and a brief analysis of his relationship with History during his French period. The anti- Semitism of Cioran was favored by his attachment to a few philosophers, but also by the European extremist and anti-Semitic context. The article seeks to demonstrate that the philosopher Cioran, known more for his pessimism and nihilism, maintained in time an obsessive relationship with History. His political philosophy is as important as his subjective philosophy, better known than the former.

Keywords: Cioran, French writings, History, Iron Guard

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Authors: Anant Kumar Singh, Sunil Jha, Pulak M. Pandey

Abstract:

A novel nanofinishing process using improved ball end magnetorheological (MR) finishing tool was developed for finishing of flat as well as 3D surfaces of ferromagnetic and non ferromagnetic workpieces. In this process a magnetically controlled ball end of smart MR polishing fluid is generated at the tip surface of the tool which is used as a finishing medium and it is guided to follow the surface to be finished through computer controlled 3-axes motion controller. The experiments were performed on ferromagnetic workpiece surface in the developed MR finishing setup to study the effect of finishing time on final surface roughness. The performance of present finishing process on final finished surface roughness was studied. The surface morphology was observed under scanning electron microscopy and atomic force microscope. The final surface finish was obtained as low as 19.7 nm from the initial surface roughness of 142.9 nm. The outcome of newly developed finishing process can be found useful in its applications in aerospace, automotive, dies and molds manufacturing industries, semiconductor and optics machining etc.

Keywords: Ball end MR finishing tool, Magnetorheological finishing, Nanofinishing

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Authors: Liu Xuedong, Liu Hanpeng, Zhou Ling

Abstract:

Study fluid flow and heat transfer characteristics of microchannel in a primary Cross-corrugated(CC) surface recuperators with corrugations and without corrugations, using CFD method. The pitch-over-height ratios P/H of Cross-corrugated (CC) surface is from 1.5 to 4.0, included angles β=75º. The study was performed using CFD software FLUENT to create unit model and simulate fluid temperature, velocity, heat transfer coefficient and other parameters. The results from these simulations were compared to experimental data. It is concluded that, when the Reynolds number is constant, if increase P/H, j/f will decrease, also the decreasing trend will become weak. Under the condition of P/H=2.2, if increase the inlet velocity j/f will decrease; in addition, the heat transfer performance in surface with corrugation will increase 10% compared to that without corrugation. The study results can provide the basis to optimize the design, select the type of heat transfer surface, the scale structure, and heat-transfer surface arrangement for recuperators.

Keywords: Cross-corrugated surface, Primary surface, Numerical simulation, Heat transfer.

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Authors: Meenakshi Goyal, Rashmi Dhawan

Abstract:

Adsorption of CS2 vapors has been studied on different types of activated carbons obtained from different source raw materials. The activated carbons have different surface areas and are associated with varying amounts of the carbon-oxygen surface groups. The adsorption of CS2 vapors is not directly related to surface area, but is considerably influenced by the presence of carbonoxygen surface groups. The adsorption decreases on increasing the amount of carbon-oxygen surface groups on oxidation and increases when these surface groups are eliminated on degassing. The adsorption is maximum in case of the 950°-degassed carbon sample which is almost completely free of any associated oxygen. The kinetic data as analysed by Empirical diffusion model and Linear driving force mass transfer model indicate that the adsorption does not involve Fickian diffusion but may be considered as a pseudo first order mass transfer process. The activation energy of adsorption and isosteric enthalpies of adsorption indicate that the adsorption does not involve interaction between CS2 and carbon-oxygen surface groups, but hydrophobic interactions between CS2 and C-C atoms in the carbon lattice.

Keywords: Adsorption, surface groups, adsorption kinetics, isosteric enthalpy of adsorption.

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

Abstract:

This paper presents the elastic buckling of homogeneous beams with a pair of piezoelectric layers surface bonded on both sides of the beams. The displacement field of beam is assumed based on the Engesser-Timoshenko beam theory. Applying the Hamilton's principle, the equilibrium equation is established. The influences of applied voltage, dimensionless geometrical parameter and piezoelectric thickness 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, Engesser-Timoshenko beam theory - Piezoelectric layer.

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Authors: Jin Y. Park, Jeong Wan Lee

Abstract:

An experimental and analytical research on shear buckling of a comparably large polymer composite I-section is presented. It is known that shear buckling load of a large span composite beam is difficult to determine experimentally. In order to sensitively detect shear buckling of the tested I-section, twenty strain rosettes and eight displacement sensors were applied and attached on the web and flange surfaces. The tested specimen was a pultruded composite beam made of vinylester resin, E-glass, carbon fibers and micro-fillers. Various coupon tests were performed before the shear buckling test to obtain fundamental material properties of the Isection. An asymmetric four-point bending loading scheme was utilized for the shear test. The loading scheme resulted in a high shear and almost zero moment condition at the center of the web panel. The shear buckling load was successfully determined after analyzing the obtained test data from strain rosettes and displacement sensors. An analytical approach was also performed to verify the experimental results and to support the discussed experimental program.

Keywords: Strain sensor, displacement sensor, shear buckling, polymer composite I-section, asymmetric loading.

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Authors: J. Mlýnek, R. Srb

Abstract:

This article is focused on the calculation of heat radiation intensity and its optimization on an aluminum mould surface. The inside of the mould is sprinkled with a special powder and its outside is heated by infra heaters located above the mould surface, up to a temperature of 250°C. By this way artificial leathers in the car industry are produced (e. g. the artificial leather on a car dashboard). A mathematical model of heat radiation of infra heaters on a mould surface is described in this paper. This model allows us to calculate a heat-intensity radiation on the mould surface for the concrete location of infra heaters above the mould surface. It is necessary to ensure approximately the same heat intensity radiation on the mould surface by finding a suitable location for the infra heaters, and in this way the same material structure and color of artificial leather. In the model we have used a genetic algorithm to optimize the radiation intensity on the mould surface. Experimental measured values for the heat radiation intensity by a sensor in the surroundings of an infra heater are used for the calculation procedures. A computational procedure was programmed in language Matlab.

Keywords: Genetic algorithm, mathematical model of heat radiation, optimization of radiation intensity, software implementation

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Authors: J. Kundrák, I. Sztankovics, K. Gyáni

Abstract:

In addition to the increase of the material removal rate or surface rate, or the improvement of the surface quality, which are the main aims of the development of manufacturing technology, a growing number of other manufacturing requirements have appeared in the machining of workpiece surfaces. Among these it is becoming increasingly dominant to generate a surface topography in finishing operations which meets more closely the needs of operational requirements.

These include the examination of the surface periodicity and/or ensuring that the twist-structure values are within the limits (or even preventing its occurrence) in specified cases such as on the sealing surfaces of rotating shafts or on the inside working surfaces of needle roller bearings. In the view of the measurement the twist has different parameters from surface roughness, which must be determined for the machining procedures. Therefore in this paper the alteration of the theoretical values of the parameters determining twist structure are studied as a function of the kinematic properties.

Keywords: Kinematic parameters, rotational turning, surface topography, twist structure

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Authors: C.W. Kan

Abstract:

This paper investigates the use of atmospheric pressure plasma for improving the surface hydrophobicity of polyurethane synthetic leather with tetramethylsilane (TMS). The atmospheric pressure plasma treatment with TMS is a single-step process to enhance the hydrophobicity of polyurethane synthetic leather. The hydrophobicity of the treated surface was examined by contact angle measurement. The physical and chemical surface changes were evaluated by scanning electron microscopy (SEM) and infrared spectroscopy (FTIR). The purpose of this paper is to provide learning materials for understanding how to use atmospheric pressure plasma in the textile finishing process to transform a hydrophilic surface to hydrophobic.

Keywords: Learning materials, atmospheric pressure plasma treatment, hydrophobic, hydrophilic, surface.

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Authors: N. Li, Y. M. Cheng

Abstract:

In this paper, the classical bearing capacity problem is re-considered from discrete element analysis. In the discrete element approach, the bearing capacity problem is considered from the elastic stage to plastic stage to rupture stage (large displacement). The bearing capacity failure mechanism of a strip footing on soil is investigated, and the influence of micro-parameters on the bearing capacity of soil is also observed. It is found that the distinct element method (DEM) gives very good visualized results, and basically coincides well with that derived by the classical methods.

Keywords: Bearing capacity, distinct element method, failure mechanism, large displacement.

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Authors: Houssam Hijazi, Laurent Cantrel, Jean-François Paul

Abstract:

Periodic DFT calculations were performed to study the chemistry of CsI particles and the possible release of volatile iodine from CsI surfaces for nuclear safety interest. The results show that water adsorbs at low temperature associatively on the (011) surface of CsI, while water desorbs at higher temperatures. On the other hand, removing iodine species from the surface requires oxidizing the surface one time for each removed iodide atom. The activation energy of removing I₂ from the surface in the presence of two OH is 1,2 eV.

Keywords: Aerosols, CsI, reactivity, DFT, water adsorption.

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Authors: M. P. Neupane, T. S. N. Sankara Narayanan, J. E. Park, Y. K. Kim, I. S. Park, K. Y. Song, T. S. Bae, M. H. Lee

Abstract:

Titanium oxide films with different morphologies have for the first time been fabricated through hydrothermal reactions between a titanium substrate and iodine powder in water or ethanol. SEM revealed that iodine supported titanium (Ti-I2) surface shows different morphologies with variable treatment conditions. The mean surface roughness (Ra) was increased in the different groups. Use of surfactant has a role to increase the roughness of the film. The surface roughness was in the range of 0.15 μm-0.42 μm. Furthermore, the electrochemical examinations showed that the Ti-I2 surface fabricated in alcoholic medium has high corrosion resistance than in aqueous medium.

Keywords: Corrosion, Hydrothermal, Surface roughness, Titanium oxide.

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Authors: Jian-Jun Shu

Abstract:

A cold, thin film of liquid impinging on an isothermal hot, horizontal surface has been investigated. An approximate solution for the velocity and temperature distributions in the flow along the horizontal surface is developed, which exploits the hydrodynamic similarity solution for thin film flow. The approximate solution may provide a valuable basis for assessing flow and heat transfer in more complex settings.

Keywords: Flux, free impinging jet, solid-surface, uniform wall temperature.

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Authors: Nagalingam Arun Prasanth, Ahmed Syed Adnan, S. H. Yeo

Abstract:

Surface topography plays a significant role in the functional performance of engineered parts. It is important to have a control on the surface geometry and understanding on the surface details to get the desired performance. Hence, in the current research contribution, a non-contact micro-texturing technique has been explored and developed. The technique involves ultrasonic excitation of a tool as a prime source of surface texturing for aluminum alloy workpieces. The specimen surface is polished first and is then immersed in a liquid bath containing 10% weight concentration of Ti6Al4V grade 5 spherical powders. A submerged slurry jet is used to recirculate the spherical powders under the ultrasonic horn which is excited at an ultrasonic frequency and amplitude of 40 kHz and 70 µm respectively. The distance between the horn and workpiece surface was remained fixed at 200 µm using a precision control stage. Texturing effects were investigated for different process timings of 1, 3 and 5 s. Thereafter, the specimens were cleaned in an ultrasonic bath for 5 mins to remove loose debris on the surface. The developed surfaces are characterized by optical and contact surface profiler. The optical microscopic images show a texture of circular spots on the workpiece surface indented by titanium spherical balls. Waviness patterns obtained from contact surface profiler supports the texturing effect produced from the proposed technique. Furthermore, water droplet tests were performed to show the efficacy of the proposed technique to develop hydrophilic surfaces and to quantify the texturing effect produced.

Keywords: Surface texturing, surface modification, topography, ultrasonic.

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Authors: John P. O’Sullivan, Thomas M. P. Ratouis, Michael J. O’Sullivan

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As the use of geothermal energy grows internationally more effort is required to monitor and protect areas with rare and important geothermal surface features. A number of approaches are presented for developing and calibrating numerical geothermal reservoir models that are capable of accurately representing geothermal surface features. The approaches are discussed in the context of cases studies of the Rotorua geothermal system and the Orakei-korako geothermal system, both of which contain important surface features. The results show that models are able to match the available field data accurately and hence can be used as valuable tools for predicting the future response of the systems to changes in use.

Keywords: Geothermal reservoir models, surface features, monitoring, TOUGH2.

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Authors: S. Lecheb, A. Chellil, H. Mechakra, A. Zeggane, H. Kebir

Abstract:

In this work, repaired crack in 6061- T6 aluminum plate with composite patches presented, firstly we determine the displacement, strain and stress, also the first six mode shape of the plate, secondly we took the same model adding central crack initiation, which is located in the center of the plate, its seize vary from 20 mm to 60 mm and we compare the first results with second. Thirdly we repair various cracks with composite patch (carbon/ epoxy) and for (2 layers, 4 layers). Finally the comparison of stress, strain, displacement and six first natural frequencies between un-cracked specimen, crack propagation and composite patch repair.

Keywords: Composite patch repair, crack growth, aluminum alloy plate, stress.

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Authors: Sisuwan Kaseamsawat, Sivapan Choo-In

Abstract:

This study aimed to evaluated the surface water quality for agriculture and consumption in the Amphawa District. The surface water quality parameters in this study included water temperature, turbidity, conductivity, salinity, pH, dissolved oxygen, BOD, nitrate, suspended solids, phosphorus, total dissolved solids (TDS), iron (Fe), copper (Cu), zinc (Zn), manganese (Mn), lead (Pb) and cadmium (Cd). The water samples were collected from small excavation, Lychee, Pomelo and Coconut orchards for 3 seasons from January to December 2011.

The surface water quality from small excavation, Lychee, pomelo and coconut orchards were met the type III of surface water quality standard. The concentration of heavy metal and did not differ significantly at 0.05 level, except dissolved oxygen.

The surface water was suitable for consumption by the usual sterile and generally improving water quality through the process before and was suitable for agriculture.

Keywords: Water Quality, Surface Water Quality.

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Authors: R. Abbasnia, F. Mohajeri Nav, S. Zahedifar, A. Tajik

Abstract:

Recent years, adaptive pushover methods have been developed for seismic analysis of structures. Herein, the accuracy of the displacement-based adaptive pushover (DAP) method, which is introduced by Antoniou and Pinho [2004], is evaluated for Irregular buildings. The results are compared to the force-based procedure. Both concrete and steel frame structures, asymmetric in plan and elevation are analyzed and also torsional effects are taking into the account. These analyses are performed using both near fault and far fault records. In order to verify the results, the Incremental Dynamic Analysis (IDA) is performed.

Keywords: Pushover Analysis, DAP, IDA, Torsion.

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Authors: Alaoua Bouaicha, Fahim Kahlouche, Abdelhamid Benouali

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Many embankment dams have suffered failures during earthquakes due to the increase of pore water pressure under seismic loading. After analyzing of the behavior of embankment dams under severe earthquakes, major advances have been attained in the understanding of the seismic action on dams. The present study concerns numerical analysis of the seismic response of earth dams. The procedure uses a nonlinear stress-strain relation incorporated into the code FLAC2D based on the finite difference method. This analysis provides the variation of the pore water pressure and horizontal displacement.

Keywords: Earthquake, numerical analysis, FLAC2D, displacement, Embankment Dam, pore water pressure.

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Authors: Nguyen Q. M. P., Chen X., Lam Y. C., Yue C. Y.

Abstract:

Polymer melt compressibility and mold surface roughness, which are generally ignored during the filling stage of the conventional injection molding, may become increasingly significant in micro injection molding where the parts become smaller. By employing the 2.5D generalized Hele-Shaw model, we presented here the effects of polymer compressibility and mold surface roughness on mold-filling in a micro-thickness cavity. To elucidate the effects of surface roughness, numerical investigations were conducted using a cavity flat plate which has two halves with different surface roughness. This allows the comparison of flow field on two different halves under identical processing conditions but with different roughness. Results show that polymer compressibility and mold surface roughness have effects on mold filling in micro injection molding. There is in shrinkage reduction as the density is increased due to polymer melt compressibility during the filling stage.

Keywords: Compressible flow, Micro-injection molding, Polymer, Surface roughness

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Authors: V. Geza, J. Vencels, G. Zageris, S. Pavlovs

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One of the most perspective methods to produce SoG-Si is refinement via metallurgical route. The most critical part of this route is refinement from boron and phosphorus. Therefore, a new approach could address this problem. We propose an approach of creating surface waves on silicon melt’s surface in order to enlarge its area and accelerate removal of boron via chemical reactions and evaporation of phosphorus. A two dimensional numerical model is created which includes coupling of electromagnetic and fluid dynamic simulations with free surface dynamics. First results show behaviour similar to experimental results from literature.

Keywords: Numerical modelling, silicon refinement, surface waves, VOF method.

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Authors: Louis Denis Kevin Catherine, Raja Aziz Raja Ma’arof, Azrina Arshad, Sangeeth Suresh

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Machining parameters are very important in determining the surface quality of any material. In the past decade, some new engineering materials were developed for the manufacturing industry which created a need to conduct an investigation on the impact of the said parameters on their surface roughness. Polyurethane (PU) block is widely used in the automotive industry to manufacture parts such as checking fixtures that are used to verify the dimensional accuracy of automotive parts. In this paper, the design of experiment (DOE) was used to investigate on the effect of the milling parameters on the PU block. Furthermore, an analysis of the machined surface chemical composition was done using scanning electron microscope (SEM). It was found that the surface roughness of the PU block is severely affected when PU undergoes a flood machining process instead of a dry condition. In addition the stepover and the silicon content were found to be the most significant parameters that influence the surface quality of the PU block.

Keywords: Polyurethane (PU), design of experiment (DOE), scanning electron microscope (SEM), surface roughness.

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Authors: Balgaisha Mukanova, Tolkyn Mirgalikyzy

Abstract:

Theory of interpretation of electromagnetic fields studied in the electrical prospecting with direct current is mainly developed for the case of a horizontal surface observation. However in practice we often have to work in difficult terrain surface. Conducting interpretation without the influence of topography can cause non-existent anomalies on sections. This raises the problem of studying the impact of different shapes of ground surface relief on the results of electrical prospecting's research. This research examines the numerical solutions of the direct problem of electrical prospecting for two-dimensional and three-dimensional media, taking into account the terrain. The problem is solved using the method of integral equations. The density of secondary currents on the relief surface is obtained.

Keywords: Ground surface relief, method of integral equations, numerical method.

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Authors: Aichun Feng, Zhi-Min Chen, Jing Tang Xing

Abstract:

A two-dimensional linear wave-body interaction problem can be solved using a desingularized integral method by placing free surface Rankine sources over calm water surface and satisfying boundary conditions at prescribed collocation points on the calm water surface. A new free-surface Rankine source distribution scheme, determined by the intersection points of free surface and body surface, is developed to reduce numerical computation cost. Associated with this, a new treatment is given to the intersection point. The present scheme results are in good agreement with traditional numerical results and measurements.

Keywords: Source point distribution, panel method, Rankine source, desingularized algorithm.

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Authors: Chang S. Woo, Hyun S. Park, Wan D. Kim

Abstract:

Fatigue life prediction and evaluation are the key technologies to assure the safety and reliability of automotive rubber components. The objective of this study is to develop the fatigue analysis process for vulcanized rubber components, which is applicable to predict fatigue life at initial product design step. Fatigue life prediction methodology of vulcanized natural rubber was proposed by incorporating the finite element analysis and fatigue damage parameter of maximum strain appearing at the critical location determined from fatigue test. In order to develop an appropriate fatigue damage parameter of the rubber material, a series of displacement controlled fatigue test was conducted using threedimensional dumbbell specimen with different levels of mean displacement. It was shown that the maximum strain was a proper damage parameter, taking the mean displacement effects into account. Nonlinear finite element analyses of three-dimensional dumbbell specimens were performed based on a hyper-elastic material model determined from the uni-axial tension, equi-biaxial tension and planar test. Fatigue analysis procedure employed in this study could be used approximately for the fatigue design.

Keywords: Rubber, Material test, Finite element analysis, Strain, Fatigue test, Fatigue life prediction.

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Authors: Ali M. Jawarneh

Abstract:

Beam and diffuse radiation data are extracted analytically from previous measured data on a horizontal surface in Zarqa city. Moreover, radiation data on a tilted surfaces with different slopes have been derived and analyzed. These data are consisting of of beam contribution, diffuse contribution, and ground reflected contribution radiation. Hourly radiation data for horizontal surface possess the highest radiation values on June, and then the values decay as the slope increases and the sharp decreasing happened for vertical surface. The beam radiation on a horizontal surface owns the highest values comparing to diffuse radiation for all days of June. The total daily radiation on the tilted surface decreases with slopes. The beam radiation data also decays with slopes especially for vertical surface. Diffuse radiation slightly decreases with slopes with sharp decreases for vertical surface. The groundreflected radiation grows with slopes especially for vertical surface. It-s clear that in June the highest harvesting of solar energy occurred for horizontal surface, then the harvesting decreases as the slope increases.

Keywords: Beam and Diffuse Radiation, Zarqa City

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Authors: M. J. Kao, S.F. Chang, C.C. Chen, C.G. Kuo

Abstract:

This paper aims to fabricated high quality anodic aluminum oxide (AAO) film by anodization method. AAO pore size, pore density, and film thickness can be controlled in 10~500 nm, 108~1011 pore．cm-2, and 1~100 μm. AAO volume and surface area can be computed based on structural parameters such as thickness, pore size, pore density, and sample size. Base on the thetorical calculation, AAO has 100 μm thickness with 15 nm, 60 nm, and 500 nm pore diameters AAO surface areas are 1225.2 cm2, 3204.4 cm2, and 549.7 cm2, respectively. The large unit surface area which is useful for adsorption application. When AAO adsorbed pH indictor of bromphenol blue presented a sensitive pH detection of solution change. This testing method can further be used for the precise measurement of biotechnology, convenience measurement of industrial engineering.

Keywords: AAO, Pore, Surface area, Adsorption, Indicator

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Authors: Marwan Abukhaled, Ibrahim Sadek

Abstract:

This paper presents the vibrations suppression of a thermoelastic beam subject to sudden heat input by a distributed piezoelectric actuators. An optimization problem is formulated as the minimization of a quadratic functional in terms of displacement and velocity at a given time and with the least control effort. The solution method is based on a combination of modal expansion and variational approaches. The modal expansion approach is used to convert the optimal control of distributed parameter system into the optimal control of lumped parameter system. By utilizing the variational approach, an explicit optimal control law is derived and the determination of the corresponding displacement and velocity is reduced to solving a set of ordinary differential equations.

Keywords: Optimal control, Thermoelastic beam, variational approach, modal expansion approach

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