Search results for: discrete element method

Authors: Min Sun, Zhenyu Liu

Abstract:

In this paper, a new descent-projection method with a new search direction for monotone structured variational inequalities is proposed. The method is simple, which needs only projections and some function evaluations, so its computational load is very tiny. Under mild conditions on the problem-s data, the method is proved to converges globally. Some preliminary computational results are also reported to illustrate the efficiency of the method.

Keywords: variational inequalities, monotone function, global convergence.

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Authors: M. M. Fercan, A. S. Kipcak, O. Dere Ozdemir, M. B. Piskin, E. Moroydor Derun

Abstract:

Coffee is a widely consumed beverage with many components such as caffeine, flavonoids, phenolic compounds, and minerals. Coffee consumption continues to increase due to its physiological effects, its pleasant taste, and aroma. Robusta and Arabica are two basic types of coffee beans. The coffee bean used for Turkish coffee is Arabica. There are many elements in the structure of coffee and have various effect on human health such as Sodium (Na), Boron (B), Magnesium (Mg) and Iron (Fe). In this study, the amounts of Mg, Na, Fe, and B contents in Turkish coffee are determined and effect of sugar addition is investigated for conscious consumption. The analysis of the contents of coffees was determined by using inductively coupled plasma optical emission spectrometry (ICP-OES). From the results of the experiments the Mg, Na, Fe and B contents of Turkish coffee after sugar addition were found as 19.83, 1.04, 0.02, 0.21 ppm, while without using sugar these concentrations were found 21.46, 0.81, 0.008 and 0.16 ppm. In addition, element contents were calculated for 1, 3 and 5 cups of coffee in order to investigate the health effects.

Keywords: Health effect, ICP-OES, sugar, Turkish coffee.

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Authors: S. A. A. Korori, H. Valipour K., S. Shabestani, A. shirvany, M. Matinizadeh

Abstract:

Tehran, one of the heavily-populated capitals, is severely suffering from increasing air pollution. To show a documented trend of such pollutants during last years, plane tree species (Platanus orientalis) were suited to be studied as indicators, for the species have been planted throughout the city many years ago. Two areas (Saadatabad and Narmak districts) allotting different contents of crowed and highly-traffic routs but the same ecological characteristics were selected. Twelve sample individuals were cored twice perpendicularly in each area. Tree-rings of each core were measured by a binocular microscope and separated annually for the last 25 years. Two heavy metals including Cd and Pb accompanied by a mineral element (Ca) were analyzed using Hatch method. Treerings analysis of the two areas showed different groups in term of physiologically ability as the growths were plunged during the last 10 years in Saadatabad district and showed a slight decrease in the same period for another studying area. In direct contrast to decreasing growth trend in Saadatabad, all three mentioned elements increased sharply during last 25 years in the same area. When it came to Narmak district, the trend was completely different with Saadatabad. There were some fluctuations in absorbing trace elements like tree-rings widths were, yet calcium showed an upward trend all the last 25 years. The results of the study proved the possibility of using tree species of each region to monitor its air pollution trends of the past, hence to depict a pollution assessment of a populated city for last years and then to make appropriate decisions for the future as it is well-known what the trend is. On the other hand, risen values of calcium (as the stress-indicator element) accompanied by increased trace elements suggests non-sustainable state of the trees.

Keywords: Air pollution, Platanus orientalis, Tehran, Traceelements, Tree rings.

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Authors: Syed Javed Arif, Mohd Ayyub Khan, Saleem Anwar Khan

Abstract:

In this paper, a simple method is presented for measurement of power frequency deviations. A phase locked loop (PLL) is used to multiply the signal under test by a factor of 100. The number of pulses in this pulse train signal is counted over a stable known period, using decade driving assemblies (DDAs) and flip-flops. These signals are combined using logic gates and then passed through decade counters to give a unique combination of pulses or levels, which are further encoded. These pulses are equally suitable for both control applications and display units. The experimental circuit developed gives a resolution of 1 Hz within the measurement period of 20 ms. The proposed circuit is also simulated in Verilog Hardware Description Language (VHDL) and implemented using Field Programing Gate Arrays (FPGAs). A Mixed signal Oscilloscope (MSO) is used to observe the results of FPGA implementation. These results are compared with the results of the proposed circuit of discrete components. The proposed system is useful for frequency deviation measurement and control in power systems.

Keywords: Frequency measurement, digital control, phase locked loop, encoding, Verilog HDL.

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Authors: Fajaruddin Mustakim, Motohiro Fujita

Abstract:

This paper present the study carried out of accident analysis, black spot study and to develop accident predictive models based on the data collected at rural roadway, Federal Route 50 (F050) Malaysia. The road accident trends and black spot ranking were established on the F050. The development of the accident prediction model will concentrate in Parit Raja area from KM 19 to KM 23. Multiple non-linear regression method was used to relate the discrete accident data with the road and traffic flow explanatory variable. The dependent variable was modeled as the number of crashes namely accident point weighting, however accident point weighting have rarely been account in the road accident prediction Models. The result show that, the existing number of major access points, without traffic light, rise in speed, increasing number of Annual Average Daily Traffic (AADT), growing number of motorcycle and motorcar and reducing the time gap are the potential contributors of increment accident rates on multiple rural roadway.

Keywords: Accident Trends, Black Spot Study, Accident Prediction Model

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Authors: Ahmet Şahin Zaimoğlu

Abstract:

A number of studies have been conducted recently to investigate the influence of randomly oriented fibers on some engineering properties of cohesive and cohesionless soils. However, few studies have been carried out on freezing-thawing behavior of fine-grained soils modified with discrete fiber inclusions and additive materials. This experimental study was performed to investigate the effect of randomly distributed polypropylene fibers (PP) and some additive materials [e.g.., borogypsum (BG), fly ash (FA) and cement (C)] on freezing-thawing durability (mass losses) of a fine-grained soil for 6, 12, and 18 cycles. The Taguchi method was applied to the experiments and a standard L9 orthogonal array (OA) with four factors and three levels were chosen. A series of freezing-thawing tests were conducted on each specimen. 0-20% BG, 0-20% FA, 0- 0.25% PP and 0-3% of C by total dry weight of mixture were used in the preparation of specimens. Experimental results showed that the most effective materials for the freezing-thawing durability (mass losses) of the samples were borogypsum and fly ash. The values of mass losses for 6, 12 and 18 cycles in optimum conditions were 16.1%, 5.1% and 3.6%, respectively.

Keywords: Additive materials, Freezing-thawing, Optimization, Reinforced soil.

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Authors: J. Arashmehr, G. H. Rahimi, S.F.Rasouli

Abstract:

Grid composite structures have many applications in aerospace industry in which deal with transverse loadings abundantly. In present paper a stiffened composite cylindrical shell with clamped-free boundary condition under transverse end load experimentally and numerically was studied. Some electrical strain gauges were employed to measure the strains. Also a finite element analysis was done for validation of experimental result. The FEM software used was ANSYS11. In addition, the results between stiffened composite shell and unstiffened composite shell were compared. It was observed that intersection of two stiffeners has an important effect in decrease of stress in the shell. Fairly good agreements were observed between the numerical and the measured results. According to recent studies about grid composite structures, it should be noted that any investigation like this research has not been reported.

Keywords: Grid composite structure, Transverse loadings, Strain measurement, Finite element analysis

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Authors: J.S.C. Prentice

Abstract:

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe the propagation of local errors in this method, and show that the global order of RK5GL3 is expected to be six, one better than the underlying Runge- Kutta method.

Keywords: RK5GL3, RKrGLm, Runge-Kutta, Gauss-Legendre, initial value problem, order, local error, global error.

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Authors: F. Sokhanvar, A. B. Khoshnevis

Abstract:

In the present work steady inviscid hypersonic flows are calculated by approximate Method. Maslens' inverse method is the chosen approximate method. For the inverse problem, parabolic shock shape is chosen for the two-dimensional flow, and the body shape and flow field are calculated using Maslen's method. For the axisymmetric inverse problem paraboloidal shock is chosen and the surface distribution of pressure is obtained.

Keywords: Hypersonic flow, Inverse problem method

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Authors: P. S. Gomathi, B. Kalaavathi

Abstract:

The process in which the complementary information from multiple images is integrated to provide composite image that contains more information than the original input images is called image fusion. Medical image fusion provides useful information from multimodality medical images that provides additional information to the doctor for diagnosis of diseases in a better way. This paper represents the wavelet based medical image fusion algorithm on different multimodality medical images. In order to fuse the medical images, images are decomposed using Redundant Wavelet Transform (RWT). The high frequency coefficients are convolved with morphological operator followed by the maximum-selection (MS) rule. The low frequency coefficients are processed by MS rule. The reconstructed image is obtained by inverse RWT. The quantitative measures which includes Mean, Standard Deviation, Average Gradient, Spatial frequency, Edge based Similarity Measures are considered for evaluating the fused images. The performance of this proposed method is compared with Pixel averaging, PCA, and DWT fusion methods. When compared with conventional methods, the proposed framework provides better performance for analysis of multimodality medical images.

Keywords: Discrete Wavelet Transform (DWT), Image Fusion, Morphological Processing, Redundant Wavelet Transform (RWT).

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Authors: Adrian T.Pleşca

Abstract:

In this paper a three dimensional thermal model of high breaking capacity fuse with unequal fuse links is proposed for both steady-state or transient conditions. The influence of ambient temperature and electric current on the temperature distribution inside the fuse, has been investigated. A thermal analysis of the unbalanced distribution of the electric current through the fuse elements and their influence on fuse link temperature rise, has been performed. To validate the three dimensional thermal model, some experimental tests have been done. There is a good correlation between experimental and simulation results.

Keywords: Electric fuse, fuse links, temperature distribution, thermal analysis.

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Authors: Guangbin Wang, Liangliang Li, Fuping Tan

Abstract:

In this paper, we give the generalized alternating twostage method in which the inner iterations are accomplished by a generalized alternating method. And we present convergence results of the method for solving nonsingular linear systems when the coefficient matrix of the linear system is a monotone matrix or an H-matrix.

Keywords: Generalized alternating two-stage method, linear system, convergence.

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Authors: Saroj Kumar Sarangi, M. C. Ray

Abstract:

This paper deals with the analysis of active constrained layer damping (ACLD) of doubly curved laminated composite shells using active fiber composite (AFC) materials. The constraining layer of the ACLD treatment has been considered to be made of the AFC materials. A three dimensional energy based finite element model of the smart doubly curved laminated composite shell integrated with a patch of such ACLD treatment has been developed to demonstrate the performance of the patch on enhancing the damping characteristics of the doubly curved laminated composite shells. Particular emphasis has been placed on studying the effect of variation of piezoelectric fiber orientation angle in the constraining AFC layer on the control authority of the ACLD patch.

Keywords: Active constrained layer damping, Active fibercomposites, Finite element modeling, First order shear deformationtheory.

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Authors: G. Bhushan

Abstract:

Multilobe bearings are found to be more stable than circular bearings. A three lobe bearing also possesses good stability characteristics. Sometimes the line of action of the load does not pass through the axis of a bearing and is shifted on either side by a few degrees. Load orientation is one of the factors that affect the stability of a three lobe bearing. The effect of load orientation on the stability of a three-lobe has been discussed in this paper. The results show that stability of a three-lobe bearing supporting either rigid or flexible rotor is increased for the positive values of load orientation i.e. when the load line is shifted in the opposite direction of rotation.

Keywords: Thee-lobe bearing, load orientation, finite element method.

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Authors: Morteza Abbaszadeh, Parvin Nikpoorparizi, Mina Shahrooz

Abstract:

For the first time since 1940 and presentation of theodorson-s theory, distribution of thrust, torque and efficiency along the blade of a counter rotating propeller axial fan was studied with a novel method in this research. A constant chord, constant pitch symmetric fan was investigated with Reynolds Stress Turbulence method in this project and H.E.S. method was utilized to obtain distribution profiles from C.F.D. tests outcome. C.F.D. test results were validated by estimation from Playlic-s analytical method. Final results proved ability of H.E.S. method to obtain distribution profiles from C.F.D test results and demonstrated interesting facts about effects of solidity and differences between distributions in front and rear section.

Keywords: C.F.D Test, Counter Rotating Propeller, H.E.S. Method, R.S.M. Method

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Authors: T. Sakamoto, N. Hori

Abstract:

A multi-rate discrete-time model, whose response agrees exactly with that of a continuous-time original at all sampling instants for any sampling periods, is developed for a linear system, which is assumed to have multiple real eigenvalues. The sampling rates can be chosen arbitrarily and individually, so that their ratios can even be irrational. The state space model is obtained as a combination of a linear diagonal state equation and a nonlinear output equation. Unlike the usual lifted model, the order of the proposed model is the same as the number of sampling rates, which is less than or equal to the order of the original continuous-time system. The method is based on a nonlinear variable transformation, which can be considered as a generalization of linear similarity transformation, which cannot be applied to systems with multiple eigenvalues in general. An example and its simulation result show that the proposed multi-rate model gives exact responses at all sampling instants.

Keywords: Multi-rate discretization, linear systems, triangularization, similarity transformation, diagonalization, exponential transformation, multiple eigenvalues

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Authors: G. Viswanadh Raviteja

Abstract:

In this paper, a microstrip antenna array is designed for 5G applications. A corporate series feed is considered to operate with a center frequency between 27 to 28 GHz to be able to cover the 5G frequency bands 24.25-27.5 GHz, 26.5-29.5 GHz and 27.5-28.35 GHz. The substrate is taken to be Rogers RT/Duroid 6002. The corporate series 5G antenna array is designed stage by stage by taking into consideration a conventional antenna designed at 28 GHz, thereby constructing the 2X1 antenna array before arriving at the final design structure of 4-element corporate series feed antenna array. The discussions concerning S11 parameter, gain and voltage standing wave ratio (VSWR) for the design structures are considered and all the important findings are tabulated. The proposed antenna array’s S11 parameter was found to be -29.00 dB at a frequency of 27.39 GHz with a good directional gain of 12.12 dB.

Keywords: Corporate series feed, millimeter wave antenna array, 5G applications, millimeter-wave (mm-wave) applications

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Authors: Paul Akagwu, Aaron Aboshio

Abstract:

In this study, typical c-ɸ soils subjected to loadings were assessed with a view to understand the general stress distribution and settlement behaviour of the soils under drained conditions. Numerical estimations of the non-dimensional bearing capacity factors, N_q and N_γ for varied angles of friction in the soil mass were obtained using PLAXIS. Ultimate bearing capacity values over a Ф range of 0-30 degrees were also computed and compared with analytical results obtained from the traditional simplified uncoupled approach of Terzaghi and Meyerhof. Results from the numerical study agree well with theoretical findings.

Keywords: Bearing capacity factors, finite element method, safe bearing pressure, structure-soil interaction.

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Authors: Zdeňka Rendlová

Abstract:

This paper presents the mathematical description of the high-speed rotating system taking into account the influence of internal and external damping. The mathematical model is obtained by using the finite element method. The analyzed system is an automotive turbocharger understood as a rotor-bearing system. The circular cross-section shaft is equipped with one compressor wheel, one turbine wheel and is supported by two floating ring bearings. Based on the model, the dynamical analysis of a turbocharger is performed and stability conditions are evaluated.

Keywords: External damping, internal damping, journal bearing, stability, turbocharger.

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Authors: Adrián D. García-Soto, Alejandro Hernández-Martínez, Jesús G. Valdés-Vázquez, Reyna A. Vizguerra-Alvarez

Abstract:

Reinforced concrete bridges designed by code are intended to achieve target reliability levels adequate for the geographical environment where the code is applicable. Several methods can be used to estimate such reliability levels. Many of them require the establishment of an explicit limit state function (LSF). When such LSF is not available as a close-form expression, the simulation techniques are often employed. The simulation methods are computing intensive and time consuming. Note that if the reliability of real bridges designed by code is of interest, numerical schemes, the finite element method (FEM) or computational mechanics could be required. In these cases, it can be quite difficult (or impossible) to establish a close-form of the LSF, and the simulation techniques may be necessary to compute reliability levels. To overcome the need for a large number of simulations when no explicit LSF is available, the point estimate method (PEM) could be considered as an alternative. It has the advantage that only the probabilistic moments of the random variables are required. However, in the PEM, fitting of the resulting moments of the LSF to a probability density function (PDF) is needed. In the present study, a very simple alternative which allows the assessment of the reliability levels when no explicit LSF is available and without the need of extensive simulations is employed. The alternative includes the use of the PEM, and its applicability is shown by assessing reliability levels of reinforced concrete bridges in Mexico when a numerical scheme is required. Comparisons with results by using the Monte Carlo simulation (MCS) technique are included. To overcome the problem of approximating the probabilistic moments from the PEM to a PDF, a well-known distribution is employed. The approach mixes the PEM and other classic reliability method (first order reliability method, FORM). The results in the present study are in good agreement whit those computed with the MCS. Therefore, the alternative of mixing the reliability methods is a very valuable option to determine reliability levels when no close form of the LSF is available, or if numerical schemes, the FEM or computational mechanics are employed.

Keywords: Structural reliability, reinforced concrete bridges, mixing approaches, point estimate method, Monte Carlo simulation.

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Authors: A. Chillali, M. Sahmoudi

Abstract:

In this paper, we will give a cryptographic application over the integral closure O_Lof sextic extension L, namely L is an extension of Q of degree 6 in the form Q(a,b), which is a rational quadratic and monogenic extension over a pure monogenic cubic subfield K generated by a who is a root of monic irreducible polynomial of degree 2 andb is a root of irreducible polynomial of degree 3.

Keywords: Integral bases, Cryptography, Discrete logarithm problem.

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Authors: N. K. Paul, S. Saha

Abstract:

An innovative three dimensional finite element model has beed developed and tested under two point loading system to examine the structural behavior of the longitudinal reinforced concrete Tee-beam bridge girder, reinforcing with steel and shape memory alloy bars respectively. 25% of steel bars are replaced with superelastic Shape Memory Alloy bars in this study. Finite element analysis is performed using ANSYS 11.0 program. Experimentally a model of steel reinforced girder has been casted and its load deflection responses are checked with ANSYS analysis. A comparison of load carrying capacity for the model between steel RC girder and the girder combined reinforcement with SMA and steel are also performed.

Keywords: Shape memory alloy, bridge girder, ANSYS, load-deflection.

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Authors: Thanin Sitthiwirattham, Jiraporn Reunsumrit

Abstract:

We study the existence of positive solutions to the three points difference-summation boundary value problem. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones.

Keywords: Positive solution, Boundary value problem, Fixed point theorem, Cone.

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Authors: René Čechmánek, Jiří Junek, Bohdan Nešpor, Pavel Šteffan

Abstract:

Regarding previous research studies it was concluded that thin-walled fiber-cement composites are able to conduct electric current under specific conditions. This property is ensured by using of various kinds of carbon materials. Though carbon fibers are less conductive than metal fibers, composites with carbon fibers were evaluated as better current conductors than the composites with metal fibers. The level of electric conductivity is monitored by the means of impedance measurement of designed samples. These composites could be used for a range of applications such as heating of trafficable surfaces or shielding of electro-magnetic fields. The aim of the present research was to design an element with the ability to monitor internal processes in building structures and prevent them from collapsing. As a typical element for laboratory testing there was chosen a concrete column, which was repeatedly subjected to load by simple pressure with continual monitoring of changes in electrical properties.

Keywords: Carbon, conductivity, loading, monitoring.

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Authors: Khalide Jbilou

Abstract:

In the present paper, we propose numerical methods for solving the Stein equation AXC - X - D = 0 where the matrix A is large and sparse. Such problems appear in discrete-time control problems, filtering and image restoration. We consider the case where the matrix D is of full rank and the case where D is factored as a product of two matrices. The proposed methods are Krylov subspace methods based on the block Arnoldi algorithm. We give theoretical results and we report some numerical experiments.

Keywords: IEEEtran, journal, LATEX, paper, template.

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Authors: M. E. Abou-Hashem El Dib, M. K. Swailem, M. M. Metwally, A. I. El Awady

Abstract:

This paper presents the effect of stiffeners on the behavior of slender steel I-beams. Nonlinear three dimensional finite element models are developed to represent the stiffened steel I-beams. The well established finite element (ANSYS 13.0) program is used to simulate the geometric and material nonlinear nature of the problem. Verification is achieved by comparing the obtained numerical results with the results of previous published experimental work. The parameters considered in the analysis are the horizontal stiffener's position and the horizontal stiffener's dimensions as well as the number of vertical stiffeners. The studied dimensions of the horizontal stiffeners include the stiffener width, the stiffener thickness and the stiffener length. The results of the achieved numerical parametric study for slender steel I-beams show the significant effect of stiffeners on the beam behavior and its failure load.

Keywords: Steel I-beams, local buckling, slender, stiffener, thin walled section.

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Authors: Mohammad Taghi Darvishi, Maliheh Najafi, Mohammad Najafi

Abstract:

In this paper, using (G/G )-expansion method and modified F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modified F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation.

Keywords: Exact solution, The (3+1)-dimensional breaking soliton equation, ( G G )-expansion method, Riccati equation, Modified Fexpansion method.

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Authors: R. Ziaie Moayed , S. Tamassoki , E. Izadi

Abstract:

Investigation of sandy clay behavior is important since urban development demands mean that sandy clay areas are increasingly encountered, especially for transportation infrastructures. This paper presents the results of the finite element analysis of the direct shear test (under three vertical loading 44, 96 and 192 kPa) and discusses the effects of different parameters such as cohesion, friction angle and Young's modulus on the shear strength of sandy clay. The numerical model was calibrated against the experimental results of large-scale direct shear tests. The results have shown that the shear strength was increased with increase in friction angle and cohesion. However, the shear strength was not influenced by raising the friction angle at normal stress of 44 kPa. Also, the effect of different young's modulus factors on stress-strain curve was investigated.

Keywords: Shear strength, Finite element analysis, Large direct shear test, Sandy clay.

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Authors: M. Y. Ismail, Arslan Kiyani

Abstract:

Narrow bandwidth and high loss performance limits the use of reflectarray antennas in some applications. This article reports on the feasibility of employing strategic reflectarray resonant elements to characterize the reflectivity performance of reflectarrays in X-band frequency range. Strategic reflectarray resonant elements incorporating variable substrate thicknesses ranging from 0.016λ to 0.052λ have been analyzed in terms of reflection loss and reflection phase performance. The effect of substrate thickness has been validated by using waveguide scattering parameter technique. It has been demonstrated that as the substrate thickness is increased from 0.508mm to 1.57mm the measured reflection loss of dipole element decreased from 5.66dB to 3.70dB with increment in 10% bandwidth of 39MHz to 64MHz. Similarly the measured reflection loss of triangular loop element is decreased from 20.25dB to 7.02dB with an increment in 10% bandwidth of 12MHz to 23MHz. The results also show a significant decrease in the slope of reflection phase curve as well. A Figure of Merit (FoM) has also been defined for the comparison of static phase range of resonant elements under consideration. Moreover, a novel numerical model based on analytical equations has been established incorporating the material properties of dielectric substrate and electrical properties of different reflectarray resonant elements to obtain the progressive phase distribution for each individual reflectarray resonant element.

Keywords: Numerical model, Reflectarray resonant elements, Scattering parameter measurements, Variable substrate thickness.

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Authors: Jui P. Hung, Yuan L. Lai, Tzuo L. Luo, Hsi H. Hsiao

Abstract:

The machining performance is determined by the frequency characteristics of the machine-tool structure and the dynamics of the cutting process. Therefore, the prediction of dynamic vibration behavior of spindle tool system is of great importance for the design of a machine tool capable of high-precision and high-speed machining. The aim of this study is to develop a finite element model to predict the dynamic characteristics of milling machine tool and hence evaluate the influence of the preload of the spindle bearings. To this purpose, a three dimensional spindle bearing model of a high speed engraving spindle tool was created. In this model, the rolling interfaces with contact stiffness defined by Harris model were used to simulate the spindle bearing components. Then a full finite element model of a vertical milling machine was established by coupling the spindle tool unit with the machine frame structure. Using this model, the vibration mode that had a dominant influence on the dynamic stiffness was determined. The results of the finite element simulations reveal that spindle bearing with different preloads greatly affect the dynamic behavior of the spindle tool unit and hence the dynamic responses of the vertical column milling system. These results were validated by performing vibration on the individual spindle tool unit and the milling machine prototype, respectively. We conclude that preload of the spindle bearings is an important component affecting the dynamic characteristics and machining performance of the entire vertical column structure of the milling machine.

Keywords: Dynamic compliance, Milling machine, Spindle unit, Bearing preload.

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