• Title/Summary/Keyword: uniform convergence

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Development of a Criterion for Efficient Numerical Calculation of Structural Vibration Responses

  • Kim, Woonkyung M.;Kim, Jeung-Tae;Kim, Jung-Soo
    • Journal of Mechanical Science and Technology
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    • v.17 no.8
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    • pp.1148-1155
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    • 2003
  • The finite element method is one of the methods widely applied for predicting vibration in mechanical structures. In this paper, the effect of the mesh size of the finite element model on the accuracy of the numerical solutions of the structural vibration problems is investigated with particular focus on obtaining the optimal mesh size with respect to the solution accuracy and computational cost. The vibration response parameters of the natural frequency, modal density, and driving point mobility are discussed. For accurate driving point mobility calculation, the decay method is employed to experimentally determine the internal damping. A uniform plate simply supported at four corners is examined in detail, in which the response parameters are calculated by constructing finite element models with different mesh sizes. The accuracy of the finite element solutions of these parameters is evaluated by comparing with the analytical results as well as estimations based on the statistical energy analysis, or if not available, by testing the numerical convergence. As the mesh size becomes smaller than one quarter of the wavelength of the highest frequency of interest, the solution accuracy improvement is found to be negligible, while the computational cost rapidly increases. For mechanical structures, the finite element analysis with the mesh size of the order of quarter wavelength, combined with the use of the decay method for obtaining internal damping, is found to provide satisfactory predictions for vibration responses.

Tolerance Analysis of Focus-adjustable Head-mounted Displays

  • Choi, Hojong;Ryu, Jae Myung;Kim, Jin Ha
    • Current Optics and Photonics
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    • v.1 no.5
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    • pp.474-490
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    • 2017
  • Since the recent slowdown in the smartphone market, studies for wearable devices are briskly being carried out to find new markets, such as virtual reality devices. In this paper, a head-mounted display (HMD) which provides expanded virtual images before human eyes by enlarging images of a small display was designed, and the tolerance analysis method for a focus-adjustable HMD based on afocal optical systems was studied. There are two types of HMDs: a see-through type that allows the user to view the surroundings, and a see-close type where the user can only view the display screen; the former is used in this study. While designing the system, we allowed a lens within the system to be shifted to adjust its focus from +1 to -4 D (diopters). The yield of the designed systems was calculated by taking the worst-case scenario of a uniform distribution into account. Additionally, a longitudinal aberration was used rather than MTF for the tolerance analysis with respect to system performance. The sensitivity of the designed system was calculated by assigning a certain tolerance, and the focus lens shift was calculated to adjust the image surface variations resulting from the tolerance. The smaller the tolerance, the more expensive the unit price of the products. Very small tolerances may even be impossible to fabricate. Considering this, the appropriate tolerance was assigned; the maximum shift of the focus lens in which the image surface can be adjusted was obtained to find the changes in aberration and a good yield.

Vibrations of Complete Paraboloidal Shells with Variable Thickness form a Three-Dimensional Theory

  • Chang, Kyong-Ho;Shim, Hyun-Ju;Kang, Jae-Hoon
    • Journal of Korean Association for Spatial Structures
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    • v.4 no.4 s.14
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    • pp.113-128
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    • 2004
  • A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of solid paraboloidal and complete (that is, without a top opening) paraboloidal shells of revolution with variable wall thickness. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. The ends of the shell may be free or may be subjected to any degree of constraint. Displacement components $u_r,\;u_{\theta},\;and\;u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in ${\theta}$, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the paraboloidal shells of revolution are formulated, and the Ritz method is used to solve the eigenvalue problem, thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four digit exactitude is demonstrated for the first five frequencies of the complete, shallow and deep paraboloidal shells of revolution with variable thickness. Numerical results are presented for a variety of paraboloidal shells having uniform or variable thickness, and being either shallow or deep. Frequencies for five solid paraboloids of different depth are also given. Comparisons are made between the frequencies from the present 3-D Ritz method and a 2-D thin shell theory.

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Hydrophobic and Mechanical Characteristics of Hydrogenated Amorphous Carbon Films Synthesized by Linear Ar/CH4 Microwave Plasma

  • Han, Moon-Ki;Kim, Taehwan;Cha, Ju-Hong;Kim, Dong-Hyun;Lee, Hae June;Lee, Ho-Jun
    • Applied Science and Convergence Technology
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    • v.26 no.2
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    • pp.34-41
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    • 2017
  • A 2.45 GHz microwave plasma with linear antenna has been prepared for hydrophobic and wear-resistible surface coating of carbon steel. Wear-resistible properties are required for the surface protection of cutting tools and achieved by depositing a hydrogenated amorphous carbon film on steel surface through linear microwave plasma source that has $TE_{10}-TEM$ waveguide. Compared to the existing RF plasma source driven by 13.56 MHz, linear microwave plasma source can easily generate high density plasma and provide faster deposition rate and wider process windows. In this study, $Ar/CH_4$ gas mixtures are used for hydrogenated amorphous carbon film deposition. When microwave power of 1000 W is applied, 40 cm long uniform $Ar/CH_4$ plasma could be obtained in gas pressure of 200~400 mTorr. The Vickers hardness measurement of hydrogenated amorphous carbon film on steel surface was evaluated. It was found the optimized deposition condition at $Ar:CH_4=25:25$ sccm, 300 mTorr with microwave power of 1000W and RF bias power of 100W. By deposition of hydrogenated amorphous carbon film, contact angle on steel surfaces increases from $43.9^{\circ}$ to $93.2^{\circ}$.

The Effects of Precursor on the Formation and Their Properties of Spin-on Dielectric Films Used for Sub-50 nm Technology and Beyond (50 nm 이상의 CMOS 기술에 이용되는 Spin-on Dielectric 박막 형성과 그 특성에 미치는 전구체의 영향)

  • Lee, Wan-Gyu
    • Journal of the Korean Vacuum Society
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    • v.20 no.3
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    • pp.182-188
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    • 2011
  • Polysilazane and polymethylsilazane based precursor films were deposited on Si-substrate by spin-coating, subsequently annealed at $150{\sim}850^{\circ}C$, and characterized. Structural analysis, shrink, compositional change, etch rate, and gap-filling were observed. Annealing the precursor films led to formation of spin-on dielectric films. C-containing precursor films showed that less loss of N, H, and C while less gain of O than that of C-free precursor films at $400^{\circ}C$, but more loss of N, H, and C while more gain of O at $850^{\circ}C$. Thus polysilazane based precursor films exhibited less reduction in thickness of 14.5% than silazane based one of 15.6% at $400^{\circ}C$ but more 37.4% than 19.4% at $850^{\circ}C$. FTIR indicated that C induced smaller amount of Si-O bond, non-uniform property, and lower resistance to chemical etching.

Vibration analysis of FG porous rectangular plates reinforced by graphene platelets

  • Zhou, Changlin;Zhang, Zhongxian;Zhang, Ji;Fang, Yuan;Tahouneh, Vahid
    • Steel and Composite Structures
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    • v.34 no.2
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    • pp.215-226
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    • 2020
  • The aim of this study is to investigate free vibration of functionally graded porous nanocomposite rectangular plates where the internal pores and graphene platelets (GPLs) are distributed in the matrix either uniformly or non-uniformly according to three different patterns. The elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. The GPL-reinforced plate is modeled using a semi-analytic approach composed of generalized differential quadrature method (GDQM) and series solution adopted to solve the equations of motion. The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made between the present results and those reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. New results reveal the importance of porosity coefficient, porosity distribution, graphene platelets (GPLs) distribution, geometrical and boundary conditions on vibration behavior of porous nanocomposite plates. It is observed that the maximum vibration frequency obtained in the case of symmetric porosity and GPL distribution, while the minimum vibration frequency is obtained using uniform porosity distribution.

Comparative analysis of turbulence models in hydraulic jumps

  • Lobosco, Raquel J.;da Fonseca, David O.;Jannuzzia, Graziella M.F.;Costa, Necesio G.
    • Coupled systems mechanics
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    • v.8 no.4
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    • pp.339-350
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    • 2019
  • A numerical simulation of the incompressible multiphase hydraulic jump flow was performed to compare the interface prediction through the use of the three RANS turbulence models: $k-{\varepsilon}$, $RNGk-{\varepsilon}$ and SST $k-{\omega}$. A three dimensional no submerged hydraulic jump and a two dimensional submerged hydraulic jump were modeled. Both the geometry and the mesh were created using the open source Gmsh code. The project's geometry consists of a rectangular channel with length and height differences between the two dimensional and three dimensional simulations. Uniform hexahedral cells were used for the mesh. Three refining meshes were constructed to allow to verify simulation convergence. The Volume of Fluid (abbr. VOF) method was used for treatment of the air-water surface. The turbulence models were evaluated in three distinct set up configurations to provide a greater accuracy in the flow representation. In the two-dimensional analysis of a submerged hydraulic jump simulation, the turbulence model RNG RNG $k-{\varepsilon}$ provided a better interface adjust with the experimental results than the model $k-{\varepsilon}$ and SST $k-{\omega}$. In the three-dimensional simulation of a no-submerged hydraulic jump the k-# showed better results than the SST $k-{\omega}$ and RNG $k-{\varepsilon}$ capturing the height and length of the ledge with a better fit with the experimental results.

Content Recommendation Techniques for Personalized Software Education (개인화된 소프트웨어 교육을 위한 콘텐츠 추천 기법)

  • Kim, Wan-Seop
    • Journal of Digital Convergence
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    • v.17 no.8
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    • pp.95-104
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    • 2019
  • Recently, software education has been emphasized as a key element of the fourth industrial revolution. Many universities are strengthening the software education for all students according to the needs of the times. The use of online content is an effective way to introduce SW education for all students. However, the provision of uniform online contents has limitations in that it does not consider individual characteristics(major, sw interest, comprehension, interests, etc.) of students. In this study, we propose a recommendation method that utilizes the directional similarity between contents in the boolean view history data environment. We propose a new item-based recommendation formula that uses the confidence value of association rule analysis as the similarity level and apply it to the data of domestic paid contents site. Experimental results show that the recommendation accuracy is improved than when using the traditional collaborative recommendation using cosine or jaccard for similarity measurements.

Effect on Flow Distortion of S-Duct by Boundary Layer Suction (경계층 흡입이 S-Duct의 유동 왜곡에 미치는 영향성 연구)

  • Baeg, Seungyong;Lee, Jihyeong;Cho, Jinsoo
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.47 no.1
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    • pp.17-25
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    • 2019
  • An intake of Aircraft becomes S-shaped geometry due to spatial limitation or procuring survivability. But curvature of the S-shaped geometry makes secondary flow or flow separation which is the cause of non-uniform pressure distribution. In this study, boundary layer suction is applied to RAE M 2129 S-Duct by attaching sub duct. Design variable is suction location and angle. A mass flow rate drawn out by suction at the sub duct outlet is constant over every model. A grid dependency test was conducted to verify validity of computation. The comparison among the CFD (Computation Fluid Dynamics), ARA experimental result, and ARA computation result of non-dimensional pressure distribution on the Port side and Starboard Side confirmed the validity of CFD. In this study, Distortion Coefficient was used for evaluating aerodynamic performance of S-Duct. The analysis, which was about flow separation, vortex, mass flow rate distribution, and pressure distribution were also investigated. Maximum 26.14% reduction in Distortion Coefficient was verified.

The Effect of Nb-doped TiO2 Coating for Improving Stability of NiCrAl Alloy Foam (NiCrAl 합금 폼의 안정성 향상을 위해 코팅된 Nb-doped TiO2의 효과)

  • Jo, Hyun-Gi;Shin, Dong-Yo;Ahn, Hyo-Jin
    • Korean Journal of Materials Research
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    • v.29 no.5
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    • pp.328-335
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    • 2019
  • Nb-doped $TiO_2$(NTO) coated NiCrAl alloy foam for hydrogen production is prepared using ultrasonic spray pyrolysis deposition(USPD) method. To optimize the size and distribution of NTO particles based on good physical and chemical stability, we synthesize particles by adjusting the weight ratio of the Nb precursor solution(5 wt%, 10 wt% and 15 wt%). The morphological, chemical bonding, and structural properties of the NTO coated NiCrAl alloy foam are investigated by X-ray diffraction(XRD), X-ray photo-electron spectroscopy(XPS), and Field-Emission Scanning Electron Microscopy(FESEM). As a result, the samples of controlled Nb weight ratio exhibit a common diffraction pattern at ${\sim}25.3^{\circ}$, corresponding to the(101) plane, and have chemical bonding(O-Nb=O) at 534 eV. The NTO particles with the optimum weight ratio of N (10 wt%) show a uniform distribution with a size of ~18.2-21.0 nm. In addition, they exhibit the highest corrosion resistance even in the electrochemical stability estimation. As a result, the introduction of NTO coated NiCrAl alloy foam by USPD improves the chemical stability of the NiCrAl alloy foam by protecting the direct electrochemical reaction between the foam and the electrolyte. Thus, the optimized NTO coating can be proposed for excellent protection of NiCrAl alloy foam for hydrocarbon-based steam methane reforming(SMR).