Search results for: cubic bi-ideal

Authors: S. H. Yahaya, J. M. Ali, T.A. Abdullah

Abstract:

The exploration of this paper will focus on the Cshaped transition curve. This curve is designed by using the concept of circle to circle where one circle lies inside other. The degree of smoothness employed is curvature continuity. The function used in designing the C-curve is Bézier-like cubic function. This function has a low degree, flexible for the interactive design of curves and surfaces and has a shape parameter. The shape parameter is used to control the C-shape curve. Once the C-shaped curve design is completed, this curve will be applied to design spur gear tooth. After the tooth design procedure is finished, the design will be analyzed by using Finite Element Analysis (FEA). This analysis is used to find out the applicability of the tooth design and the gear material that chosen. In this research, Cast Iron 4.5 % Carbon, ASTM A-48 is selected as a gear material.

Keywords: Bézier-like cubic function, Curvature continuity, Cshapedtransition curve, Spur gear tooth.

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Authors: Mamta Agrawal, Neeru Adlakha, K.R. Pardasani

Abstract:

An attempt has been made to develop a seminumerical model to study temperature variations in dermal layers of human limbs. The model has been developed for two dimensional steady state case. The human limb has been assumed to have elliptical cross section. The dermal region has been divided into three natural layers namely epidermis, dermis and subdermal tissues. The model incorporates the effect of important physiological parameters like blood mass flow rate, metabolic heat generation, and thermal conductivity of the tissues. The outer surface of the limb is exposed to the environment and it is assumed that heat loss takes place at the outer surface by conduction, convection, radiation, and evaporation. The temperature of inner core of the limb also varies at the lower atmospheric temperature. Appropriate boundary conditions have been framed based on the physical conditions of the problem. Cubic splines approach has been employed along radial direction and Fourier series along angular direction to obtain the solution. The numerical results have been computed for different values of eccentricity resembling with the elliptic cross section of the human limbs. The numerical results have been used to obtain the temperature profile and to study the relationships among the various physiological parameters.

Keywords: Blood Mass Flow Rate, Metabolic Heat Generation, Fourier Series, Cubic splines and Thermal Conductivity.

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Authors: Florian Gschösser, Walter Purrer

Abstract:

The paper shows examples for the (environmental) optimization of production processes for asphalt mixtures applied for typical road pavements in Austria and Switzerland. The conducted “from-cradle-to-gate” LCA firstly analyzes the production one cubic meter of asphalt and secondly all material production processes for exemplary highway pavements applied in Austria and Switzerland. It is shown that environmental impacts can be reduced by the application of reclaimed asphalt pavement (RAP) and by the optimization of specific production characteristics, e.g. the reduction of the initial moisture of the mineral aggregate and the reduction of the mixing temperature by the application of low-viscosity and foam bitumen. The results of the LCA study demonstrate reduction potentials per cubic meter asphalt of up to 57 % (Global Warming Potential–GWP) and 77 % (Ozone depletion–ODP). The analysis per square meter of asphalt pavement determined environmental potentials of up to 40 % (GWP) and 56 % (ODP).

Keywords: Asphalt mixtures, environmental potentials, life cycle assessment, material production.

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Authors: Lewis E. Hibell, Honghai Liu, David J. Brown

Abstract:

This paper presents the use of a newly created network structure known as a Self-Delaying Dynamic Network (SDN) to create a high resolution image from a set of time stepped input frames. These SDNs are non-recurrent temporal neural networks which can process time sampled data. SDNs can store input data for a lifecycle and feature dynamic logic based connections between layers. Several low resolution images and one high resolution image of a scene were presented to the SDN during training by a Genetic Algorithm. The SDN was trained to process the input frames in order to recreate the high resolution image. The trained SDN was then used to enhance a number of unseen noisy image sets. The quality of high resolution images produced by the SDN is compared to that of high resolution images generated using Bi-Cubic interpolation. The SDN produced images are superior in several ways to the images produced using Bi-Cubic interpolation.

Keywords: Image Enhancement, Neural Networks, Multi-Frame.

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Authors: Amir Azizi, Amir Yazid b. Ali, Loh Wei Ping, Mohsen Mohammadzadeh

Abstract:

Uncertainties of a serial production line affect on the production throughput. The uncertainties cannot be prevented in a real production line. However the uncertain conditions can be controlled by a robust prediction model. Thus, a hybrid model including autoregressive integrated moving average (ARIMA) and multiple polynomial regression, is proposed to model the nonlinear relationship of production uncertainties with throughput. The uncertainties under consideration of this study are demand, breaktime, scrap, and lead-time. The nonlinear relationship of production uncertainties with throughput are examined in the form of quadratic and cubic regression models, where the adjusted R-squared for quadratic and cubic regressions was 98.3% and 98.2%. We optimized the multiple quadratic regression (MQR) by considering the time series trend of the uncertainties using ARIMA model. Finally the hybrid model of ARIMA and MQR is formulated by better adjusted R-squared, which is 98.9%.

Keywords: ARIMA, multiple polynomial regression, production throughput, uncertainties

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Authors: Wenzhe Li, Xiaoyu Ying, Grace Ding

Abstract:

Architecture plane form is an important consideration in the design of green buildings due to its significant impact on energy performance. The most effective method to consider energy performance in the early design stages is parametric modelling. This paper presents a methodology to program plane forms using MATLAB language, generating 16 kinds of plane forms by changing four designed parameters. DesignBuilder (an energy consumption simulation software) was proposed to simulate the energy consumption of the generated planes. A regression mathematical model was established to study the relationship between the plane forms and their energy consumption. The main finding of the study suggested that there was a cubic function relationship between the depth-ratio of U-shaped buildings and energy consumption, and there is also a cubic function relationship between the width-ratio and energy consumption. In the design, the depth-ratio of U-shaped buildings should not be less than 2.5, and the width-ratio should not be less than 2.

Keywords: Graphic parameterization, green building design, mathematical model, U-shaped buildings.

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Authors: R. Bharanidaran, B. T. Ramesh

Abstract:

High precision in motion is required to manipulate the micro objects in precision industries for micro assembly, cell manipulation etc. Precision manipulation is achieved based on the appropriate mechanism design of micro devices such as microgrippers. Design of a compliant based mechanism is the better option to achieve a highly precised and controlled motion. This research article highlights the method of designing a compliant based three fingered microgripper suitable for holding asymmetric objects. Topological optimization technique, a systematic method is implemented in this research work to arrive a topologically optimized design of the mechanism needed to perform the required micro motion of the gripper. Optimization technique has a drawback of generating senseless regions such as node to node connectivity and staircase effect at the boundaries. Hence, it is required to have post processing of the design to make it manufacturable. To reduce the effect of post processing stage and to preserve the edges of the image, a cubic spline interpolation technique is introduced in the MATLAB program. Structural performance of the topologically developed mechanism design is tested using finite element method (FEM) software. Further the microgripper structure is examined to find its fatigue life and vibration characteristics.

Keywords: Compliant mechanism, Cubic spline interpolation, FEM, Topology optimization.

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Authors: Joseph C. Chen, Venkata Karthik Jakka

Abstract:

The main objective of this research is to optimize tensile strength and dimensional accuracy in injection molding processes using Taguchi Parameter Design. An L16 orthogonal array (OA) is used in Taguchi experimental design with five control factors at four levels each and with non-controllable factor vibration. A total of 32 experiments were designed to obtain the optimal parameter setting for the process. The optimal parameters identified for the shrinkage are shot volume, 1.7 cubic inch (A4); mold term temperature, 130 ºF (B1); hold pressure, 3200 Psi (C4); injection speed, 0.61 inch3/sec (D2); and hold time of 14 seconds (E2). The optimal parameters identified for the tensile strength are shot volume, 1.7 cubic inch (A4); mold temperature, 160 ºF (B4); hold pressure, 3100 Psi (C3); injection speed, 0.69 inch3/sec (D4); and hold time of 14 seconds (E2). The Taguchi-based optimization framework was systematically and successfully implemented to obtain an adjusted optimal setting in this research. The mean shrinkage of the confirmation runs is 0.0031%, and the tensile strength value was found to be 3148.1 psi. Both outcomes are far better results from the baseline, and defects have been further reduced in injection molding processes.

Keywords: Injection molding processes, Taguchi Parameter Design, tensile strength, shrinkage test, high-density polyethylene, HDPE.

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Authors: Mikhail Semenov , Svetlana Kolupaeva, Tatiana Kovalevskaya, Olga Daneyko

Abstract:

An investigation of the process of deformation hardening and evolution of deformation defect medium in dispersion-hardened materials with face centered cubic matrices and nanoparticles was done. Mathematical model including balance equation for the deformation defects was used.

Keywords: deformation defects, dispersion-hardened materials, mathematical modeling, plastic deformation

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Authors: M. Zarebnia, M. Hoshyar, M. Sedaghati

Abstract:

In this paper, a numerical solution based on nonpolynomial cubic spline functions is used for finding the solution of boundary value problems which arise from the problems of calculus of variations. This approximation reduce the problems to an explicit system of algebraic equations. Some numerical examples are also given to illustrate the accuracy and applicability of the presented method.

Keywords: Calculus of variation; Non-polynomial spline functions; Numerical method

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Authors: Gokhan Soydan, Musa Demirci, Nazli Yildiz Ikikardes, Ismail Naci Cangul

Abstract:

In this work, we consider the rational points on elliptic curves over finite fields Fp where p ≡ 5 (mod 6). We obtain results on the number of points on an elliptic curve y2 ≡ x3 + a3(mod p), where p ≡ 5 (mod 6) is prime. We give some results concerning the sum of the abscissae of these points. A similar case where p ≡ 1 (mod 6) is considered in [5]. The main difference between two cases is that when p ≡ 5 (mod 6), all elements of Fp are cubic residues.

Keywords: Elliptic curves over finite fields, rational points.

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Authors: S. Mousavian, F. Mousavian, V. Nikkhah Rashidabad

Abstract:

Cubic equations of state like Redlich–Kwong (RK)  EOS have been proved to be very reliable tools in the prediction of  phase behavior. Despite their good performance in compositional  calculations, they usually suffer from weaknesses in the predictions  of saturated liquid density. In this research, RK equation was  modified. The result of this study show that modified equation has  good agreement with experimental data.

 

Keywords: Equation of state, modification, ammonia, genetic algorithm.

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Authors: Sang Wook Park, Jun Su Park, Byung Kwan Oh, Yousok Kim, Hyo Seon Park

Abstract:

This study suggests the estimation method of stress distribution for the beam structures based on TLS (Terrestrial Laser Scanning). The main components of method are the creation of the lattices of raw data from TLS to satisfy the suitable condition and application of CSSI (Cubic Smoothing Spline Interpolation) for estimating stress distribution. Estimation of stress distribution for the structural member or the whole structure is one of the important factors for safety evaluation of the structure. Existing sensors which include ESG (Electric strain gauge) and LVDT (Linear Variable Differential Transformer) can be categorized as contact type sensor which should be installed on the structural members and also there are various limitations such as the need of separate space where the network cables are installed and the difficulty of access for sensor installation in real buildings. To overcome these problems inherent in the contact type sensors, TLS system of LiDAR (light detection and ranging), which can measure the displacement of a target in a long range without the influence of surrounding environment and also get the whole shape of the structure, has been applied to the field of structural health monitoring. The important characteristic of TLS measuring is a formation of point clouds which has many points including the local coordinate. Point clouds are not linear distribution but dispersed shape. Thus, to analyze point clouds, the interpolation is needed vitally. Through formation of averaged lattices and CSSI for the raw data, the method which can estimate the displacement of simple beam was developed. Also, the developed method can be extended to calculate the strain and finally applicable to estimate a stress distribution of a structural member. To verify the validity of the method, the loading test on a simple beam was conducted and TLS measured it. Through a comparison of the estimated stress and reference stress, the validity of the method is confirmed.

Keywords: Structural health monitoring, terrestrial laser scanning, estimation of stress distribution, coordinate transformation, cubic smoothing spline interpolation.

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Authors: Kanda Wongwailikhit

Abstract:

Copper (I) oxide microparticles with the morphology of cubic and hollow sphere were synthesized with the assistance of surfactant as the shape controller. Both particles were then subjected to study the catalytic activity and observed the results of shape effects of catalysts on rate of catalytic reaction. The decolorizing reaction of crystal violet and sodium hydroxide was chosen and measured the decreasing of reactant with respect to times using spectrophotometer. The result revealed that morphology of crystal had no effect on the catalytic activity for crystal violet reaction but contributed to total surface area predominantly.

Keywords: Copper (I) oxide, Catalytic activity, Crystal violet.

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Authors: Panos Kotsas

Abstract:

This paper presents the application of a signal intensity independent registration criterion for non-rigid body registration of medical images. The criterion is defined as the weighted ratio image of two images. The ratio is computed on a voxel per voxel basis and weighting is performed by setting the ratios between signal and background voxels to a standard high value. The mean squared value of the weighted ratio is computed over the union of the signal areas of the two images and it is minimized using the Chebyshev polynomial approximation. The geometric transformation model adopted is a local cubic B-splines based model.

Keywords: Medical image, non-rigid, registration.

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Authors: Nitima Aschariyaphotha, Pratan Sakkaplangkul, Anirut Luadsong

Abstract:

The study of the Andaman Sea can be studied by using the oceanic model; therefore the grid covering the study area should be generated. This research aims to generate grid covering the Andaman Sea, situated between longitudes 90◦E to 101◦E and latitudes 1◦N to 18◦N. A horizontal grid is an orthogonal curvilinear with 87 × 217 grid points. The methods used in this study are cubic spline and bilinear interpolations. The boundary grid points are generated by spline interpolation while the interior grid points have to be specified by bilinear interpolation method. A vertical grid is sigma coordinate with 15 layers of water column.

Keywords: Sigma Coordinate, Curvilinear Coordinate, AndamanSea.

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Authors: Anurag Gaur, Neha Sharma

Abstract:

In this work, we have synthesized BaTiO₃ via sol gel method by sintering at different temperatures (600, 700, 800, 900, 1000⁰C) and studied their structural, optical and ferroelectric properties through X-ray diffraction (XRD), UV-Vis spectrophotometer and PE Loop Tracer. X-ray diffraction patterns of barium titanate samples show that the peaks of the diffractogram are successfully indexed with the tetragonal and cubic structure of BaTiO₃. The Optical band gap calculated through UV Visible spectrophotometer varies from 4.37 to 3.80 eV for the samples sintered at 600 to 1000⁰C, respectively. The particle size calculated through transmission electron microscopy varies from 20 to 40 nm for the samples sintered at 600 to 1000⁰C, respectively. Moreover, it has been observed that the ferroelectricity increases as we increase the sintering temperature.

Keywords: Nanostructures, Ferroelectricity, Sol-gel method.

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Authors: Adil Al-Rammahi

Abstract:

Electronic mail is very important in present time. Many researchers work for designing, improving, securing, fasting, goodness and others fields in electronic mail. This paper introduced new algorithm to use Cantor sets and cubic spline interpolating function in the electronic mail design. Cantor sets used as the area (or domain) of the mail, while spline function used for designing formula. The roots of spline function versus Cantor sets used as the controller admin. The roots calculated by the numerical Newton – Raphson's method. The result of this algorithm was promised.

Keywords: Cantor sets, spline, electronic mail design, Newton – Raphson's method.

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Authors: N. Z. Baderisham, H. A. Hamid, N. Osman

Abstract:

The powders of Ba(Ce_1-xZr_x)_0.90Y_0.1O_3-δ (BCZY) with 0.2 ≤ x ≤ 0.6 have been prepared by a modified sol-gel method. Triethylenetetramine (TETA) was employed as chelating agent. Phase formation of calcined powders at 1100^oC and sintered pellets at 1400^oC of BCZY were examined by an X-ray diffractrometer (XRD). XRD results showed the calcined powder and sintered pellet formed a single perovskite phase over the entire range of x values. As the amount of zirconium substitution (x values) increase, the main peaks are shifted to the higher 2theta values which suggest a complete substitution of zirconium into cerium sites. All the obtained calcined powders and sintered pellets possess cubic structure (Pm-3m) at all x values.

Keywords: Structure, phase formation, modified sol-gel, cerate-zirconate electrolye, XRD.

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Authors: Josef Brychta, Jiri Kratochvil, Marek Pagac

Abstract:

The group of progressive cutting materials can include non-traditional, emerging and less-used materials that can be an efficient use of cutting their lead to a quantum leap in the field of machining. This is essentially a “superhard” materials (STM) based on polycrystalline diamond (PCD) and polycrystalline cubic boron nitride (PCBN) cutting performance ceramics and development is constantly "perfecting" fine coated cemented carbides. The latter cutting materials are broken down by two parameters, toughness and hardness. A variation of alloying elements is always possible to improve only one of each parameter. Reducing the size of the core on the other hand doing achieves "contradictory" properties, namely to increase both hardness and toughness.

Keywords: Grained cutting materials difficult to machine materials, optimum utilization.

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Authors: N. Kazantseva, P. Krakhmalev, I. Yadroitsev, A. Fefelov, N. Vinogradova, I. Ezhov, T. Kurennykh

Abstract:

Martensitic texture-phase transition in Selective Laser Melting (SLM) Ti-6Al-4V (ELI) alloys was found. Electron Backscatter Diffraction (EBSD) analysis showed the initial cubic beta < 100 > (001) BCC texture. Such kind of texture is observed in BCC metals with flat rolling texture when axis is in the direction of rolling and the texture plane coincides with the plane of rolling. It was found that the texture of the parent BCC beta-phase determined the texture of low-temperature HCP alpha-phase limited the choice of its orientation variants. The {10-12} < -1011 > twinning system in titanium alloys after SLM was determined. Analysis of the oxygen contamination in SLM alloys was done. Comparison of the obtained results with the conventional titanium alloys is also provided.

Keywords: Additive technology, texture, Ti-6Al-4V, twins, oxygen content.

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Authors: R. O. Ocaya, J. J. Terblans

Abstract:

The laws of Newtonian mechanics allow ab-initio molecular dynamics to model and simulate particle trajectories in material science by defining a differentiable potential function. This paper discusses some considerations for the coding of ab-initio programs for simulation on a standalone computer and illustrates the approach by C language codes in the context of embedded metallic atoms in the face-centred cubic structure. The algorithms use velocity-time integration to determine particle parameter evolution for up to several thousands of particles in a thermodynamical ensemble. Such functions are reusable and can be placed in a redistributable header library file. While there are both commercial and free packages available, their heuristic nature prevents dissection. In addition, developing own codes has the obvious advantage of teaching techniques applicable to new problems.

Keywords: C-language, molecular dynamics, simulation, embedded atom method.

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Authors: S. Chuenchooklin

Abstract:

This research was conducted in the Pua Watershed whereas located in the Upper Nan River Basin in Nan province, Thailand. Nan River basin originated in Nan province that comprises of many tributary streams to produce as inflow to the Sirikit dam provided huge reservoir with the storage capacity of 9510 million cubic meters. The common problems of most watersheds were found i.e. shortage water supply for consumption and agriculture utilizations, deteriorate of water quality, flood and landslide including debris flow, and unstable of riverbank. The Pua Watershed is one of several small river basins that flow through the Nan River Basin. The watershed includes 404 km2 representing the Pua District, the Upper Nan Basin, or the whole Nan River Basin, of 61.5%, 18.2% or 1.2% respectively. The Pua River is a main stream producing all year streamflow supplying the Pua District and an inflow to the Upper Nan Basin. Its length approximately 56.3 kilometers with an average slope of the channel by 1.9% measured. A diversion weir namely Pua weir bound the plain and mountainous areas with a very steep slope of the riverbed to 2.9% and drainage area of 149 km2 as upstream watershed while a mild slope of the riverbed to 0.2% found in a river reach of 20.3 km downstream of this weir, which considered as a gauged basin. However, the major branch streams of the Pua River are ungauged catchments namely: Nam Kwang and Nam Koon with the drainage area of 86 and 35 km2 respectively. These upstream watersheds produce runoff through the 3-streams downstream of Pua weir, Jao weir, and Kang weir, with an averaged annual runoff of 578 million cubic meters. They were analyzed using both statistical data at Pua weir and simulated data resulted from the hydrologic modeling system (HEC–HMS) which applied for the remaining ungauged basins. Since the Kwang and Koon catchments were limited with lack of hydrological data included streamflow and rainfall. Therefore, the mathematical modeling: HEC-HMS with the Snyder-s hydrograph synthesized and transposed methods were applied for those areas using calibrated hydrological parameters from the upstream of Pua weir with continuously daily recorded of streamflow and rainfall data during 2008-2011. The results showed that the simulated daily streamflow and sum up as annual runoff in 2008, 2010, and 2011 were fitted with observed annual runoff at Pua weir using the simple linear regression with the satisfied correlation R2 of 0.64, 062, and 0.59, respectively. The sensitivity of simulation results were come from difficulty using calibrated parameters i.e. lag-time, coefficient of peak flow, initial losses, uniform loss rates, and missing some daily observed data. These calibrated parameters were used to apply for the other 2-ungauged catchments and downstream catchments simulated.

Keywords: Streamflow, hydrological model, ungauged catchments.

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Authors: A.R.Nezamabadi, M.Mansouri Gavari, S.Mansouri, M.Mansouri Gavari

Abstract:

This article considers the positional buckling of composite thick plates under thermal loading . For this purpose , the complex finite strip method is used . In analysis of complex finite strip, harmonic complex function in longitudinal direction , cubic functions in transversal direction and parabola distribution of transverse shear strain in thickness of thick plate based on higherorder shear deformation theory are used . In given examples , the effect of angles of stratification , number of layers , dimensions ratio and length – to – thick ratio across critical temperature are considered.

Keywords: Thermal buckling , Thick plate , Complex finite strip , Higher – order shear deformation theory.

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Authors: Stella A. Arnaouti, Demos C. Angelides, Theodoros N. Chatzigogos, Witold M. Pytel

Abstract:

The Želazny Most tailing pond is one of the largest facilities worldwide for waste disposal from the copper mines located in South-West Poland. A potential failure of the dam would allow more than 10 million cubic meters of contaminated slurry to flow to the valley, causing immense environmental problems to the surrounding area. Thus, the determination of the strength properties of the dam's soils and their variability is of utmost importance. An extensive site investigation consisting of more than 480 cone penetration tests (CPTs) with or without pore water pressure measurements were conducted within a period of 13 years to study the mechanical properties of the tailings body. The present work investigates the point variability of the soil strength parameters (effective friction angle

Keywords: Soil strength variability, friction angle spatial variability, Želazny Most tailing dam.

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Authors: Ivan Yatchev, Ewen Ritchie

Abstract:

Comparison of two approaches for the simulation of the dynamic behaviour of a permanent magnet linear actuator is presented. These are full coupled model, where the electromagnetic field, electric circuit and mechanical motion problems are solved simultaneously, and decoupled model, where first a set of static magnetic filed analysis is carried out and then the electric circuit and mechanical motion equations are solved employing bi-cubic spline approximations of the field analysis results. The results show that the proposed decoupled model is of satisfactory accuracy and gives more flexibility when the actuator response is required to be estimated for different external conditions, e.g. external circuit parameters or mechanical loads.

Keywords: Coupled problems, dynamic models, finite elementanalysis, linear actuators, permanent magnets.

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Authors: A. Pourahmad, Sh. Gharipour

Abstract:

The present work describes the preparation and characterization of nanosized SiO₂@PbS core-shell particles by using a simple wet chemical route. This method utilizes silica spheres formation followed by successive ionic layer adsorption and reaction method assisted lead sulphide shell layer formation. The final product was characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), UV–vis spectroscopic, infrared spectroscopy (IR) and transmission electron microscopy (TEM) experiments. The morphological studies revealed the uniformity in size distribution with core size of 250 nm and shell thickness of 18 nm. The electron microscopic images also indicate the irregular morphology of lead sulphide shell layer. The structural studies indicate the face-centered cubic system of PbS shell with no other trace for impurities in the crystal structure.

Keywords: Core-shell, nanostructure, semiconductor, optical property, XRD.

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Authors: Somayeh Tourani, Alireza Behvandi

Abstract:

The peng-Robinson (PR), a cubic equation of state (EoS), is extended to polymers by using a single set of energy (A1, A2, A3) and co-volume (b) parameters per polymer fitted to experimental volume data. Excellent results for the volumetric behavior of the 11 polymer up to 2000 bar pressure are obtained. The EoS is applied to the correlation and prediction of Henry constants in polymer solutions comprising three polymer and many nonpolar and polar solvents, including supercritical gases. The correlation achieved with two adjustable parameter is satisfactory compared with the experimental data. As a result, the present work provides a simple and useful model for the prediction of Henry's constant for polymer containing systems including those containing polar, nonpolar and supercritical fluids.

Keywords: Equation of state, Henry's constant, Peng-Robinson, polymer solution.

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Authors: M. Abdulkawi, Z. K. Eshkuvatov, N. M. A. Nik Long

Abstract:

This manuscript presents a method for the numerical solution of the Cauchy type singular integral equations of the first kind, over a finite segment which is bounded at the end points of the finite segment. The Chebyshev polynomials of the second kind with the corresponding weight function have been used to approximate the density function. The force function is approximated by using the Chebyshev polynomials of the first kind. It is shown that the numerical solution of characteristic singular integral equation is identical with the exact solution, when the force function is a cubic function. Moreover, it also shown that this numerical method gives exact solution for other singular integral equations with degenerate kernels.

Keywords: Singular integral equations, Cauchy kernel, Chebyshev polynomials, interpolation.

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Authors: Atul Krishna Banik

Abstract:

Nonlinear response behaviour of a cracked RC beam under harmonic excitation is analysed to investigate various instability phenomena like, bifurcation, jump phenomena etc. The nonlinearity of the system arises due to opening and closing of the cracks in the RC beam and is modelled as a cubic polynomial. In order to trace different branches at the bifurcation point on the response curve (amplitude versus frequency of excitation plot), an arc length continuation technique along with the incremental harmonic balance (IHBC) method is employed. The stability of the solution is investigated by the Floquet theory using Hsu-s scheme. The periodic solutions obtained by the IHBC method are compared with these obtained by the numerical integration of the equation of motion. Characteristics of solutions fold bifurcation, jump phenomena and from stable to unstable zones are identified.

Keywords: Incremental harmonic balance, arc-length continuation, bifurcation, jump phenomena.

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