• Title/Summary/Keyword: Series Expansion

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Fourier Series Expansion Method for Free Vibration Analysis of a Partially Liquid-Filled Circular Cylindrical Shell (Fourier 급수전걔를 이용한 부분적으로 유체가 채워진 원통형 셸의 고유진동 해석)

  • 정경훈;이성철
    • Journal of KSNVE
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    • v.4 no.2
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    • pp.163-175
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    • 1994
  • An analytical method for nautral frequencies of a partially liquid- filled circular cylindrical shell with various boundary conditions is developed by means of the Stokes's transformation and Fourier series expansion on the basis of Sanders' shell equation. The liquid-shell coupled system is divided into two regions for convenient formulation. One is the empty shell region in which the Sanders' shell equations are formulated without the lipuid effect, the other is wetted shell region in which the shell equations are formulated with consideration of the liquid dynamic effect. The shell equations for each regions are combined by the geometry and the force continuities at the junction of the two regions. For the vibration relevant to the liquid motion, the velocity potential of liquid is assumed as a sum of linear combination of suitable harmonic functions in axial direction. The unknown parameters are selected to satisfy the boundary condition along the wetted shell surface. The natural frequencies of the liquid filled cylindraical shells with the clamped- free and the clamped-clamped boundary conditions examined in the previous works, are obtained by this analytical method. The results are compared with the previous works, and excllent agreement is found for the natural frequencies of the shells.

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A Simple Static Overmodulation Scheme using Space Vector PWM Method (공간벡터 PWM을 이용한 간단한 정적 과변조기법)

  • Lee, Dong-Myung;Kim, Jin-Ho;Yang, Hyun-Suk;Jung, Jin-Woo
    • The Transactions of the Korean Institute of Power Electronics
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    • v.16 no.3
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    • pp.234-241
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    • 2011
  • This paper proposes a simple static overmodulation strategy that extends the linearity of the inverter output voltage. The proposed method obtains the reference vector having the instantaneous value directly from the modulation index based on the magnitude of fundamental voltage, and has a simplified form of phase command. This method does not need trigonometric functions for calculating the magnitude of the reference vector. The magnitude of reference voltage and holding angle in the overmodulation region corresponding to the modulation index are determined in advance to have the same fundamental voltage magnitude by using the result of Fourier series expansion.

Frequency analysis of liquid sloshing in prolate spheroidal containers and comparison with aerospace spherical and cylindrical tanks

  • Mohammad Mahdi Mohammadi;Hojat Taei;Hamid Moosazadeh;Mohammad Sadeghi
    • Advances in aircraft and spacecraft science
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    • v.10 no.5
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    • pp.439-455
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    • 2023
  • Free surface fluid oscillation in prolate spheroidal tanks has been investigated analytically in this study. This paper aims is to investigate the sloshing frequencies in spheroidal prolate tanks and compare them with conventional cylindrical and spherical containers to select the best tank geometry for use in space launch vehicles in which the volume of fuel is very high. Based on this, the analytical method (Fourier series expansion) and potential fluid theory in the spheroidal coordinate system are used to extract and analyze the governing differential equations of motion. Then, according to different aspect ratios and other parameters such as filling levels, the fluid sloshing frequencies in the spheroidal prolate tank are determined and evaluated based on various parameters. The natural frequencies obtained for a particular tank are compared with other literature and show a good agreement with these results. In addition, spheroidal prolate tank frequencies have been compared with sloshing frequencies in cylindrical and spherical containers in different modes. Results show that when the prolate spheroidal tank is nearly full and in the worst case when the tank is half full and the free fluid surface is the highest, the prolate spheroidal natural frequencies are higher than of spherical and cylindrical tanks. Therefore, the use of spheroidal tanks in heavy space launch vehicles, in addition to the optimal use of placement space, significantly reduces the destructive effects of sloshing.

Two Algorithms for Constructing the Voronoi Diagram for 3D Spheres and Applications to Protein Structure Analysis (삼차원 구의 보로노이 다이어그램 계산을 위한 두 가지 알고리듬 및 단백질구조채석에의 응용)

  • Kim D.;Choi Y.;Kim D.S.
    • Korean Journal of Computational Design and Engineering
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    • v.11 no.2
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    • pp.97-106
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    • 2006
  • Voronoi diagrams have been known for numerous important applications in science and engineering including CAD/CAM. Especially, the Voronoi diagram for 3D spheres has been known as very useful tool to analyze spatial structural properties of molecules or materials modeled by a set of spherical atoms. In this paper, we present two algorithms, the edge-tracing algorithm and the region-expansion algorithm, for constructing the Voronoi diagram of 3D spheres and applications to protein structure analysis. The basic scheme of the edge-tracing algorithm is to follow Voronoi edges until the construction is completed in O(mn) time in the worst-case, where m and n are the numbers of edges and spheres, respectively. On the other hand, the region-expansion algorithm constructs the desired Voronoi diagram by expanding Voronoi regions for one sphere after another via a series of topology operations, starting from the ordinary Voronoi diagram for the centers of spheres. It turns out that the region-expansion algorithm also has the worst-case time complexity of O(mn). The Voronoi diagram for 3D spheres can play key roles in various analyses of protein structures such as the pocket recognition, molecular surface construction, and protein-protein interaction interface construction.

Expansion Ratio of Pulse Power Underreamed Anchor (펄스방전 그라운드 앵커의 확공 특성에 관한 연구)

  • Kim, Nak-Kyung;Ju, Yonh-Sun;Kim, Sung-Kyu;Seo, Hyo-Kyun;Kim, Sun-Ju
    • Proceedings of the Korean Geotechical Society Conference
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    • 2009.03a
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    • pp.1107-1112
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    • 2009
  • Ground anchor should not be used in soft clay, because anchor resistance can not be guaranteed. However, there is a way to increase the capacity of anchors. The pulse powered anchor is an underreamed anchor by using high voltage electrokinetic pulse energy. In this study, a series of field test were carried out in order to find expansion rate related in number of pulse charge. and Anchor pull-out tests were performed at the Geotechnical Experimentation Site at Sungkyunkwan University in Suwon, Korea. Data were analyzed in order to define a relation between expansion rate and ultimate pullout load.

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A Study on Environmental Impact Assessment on the Area Expansion of Limestone Mining with regard to Cumulative Impact Assessment (누적영향평가 측면에서 환경영향평가제도의 문제점과 개선방안 연구 - 석회석광산 채굴규모 확장을 대상으로 -)

  • Kim, Cho;Yeon, Ik-Jun;Jung, Ju-Yong;Lee, Sang-Woo
    • Journal of Environmental Impact Assessment
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    • v.23 no.1
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    • pp.1-9
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    • 2014
  • This study, focusing on the area expansion of limestone mines, identifies the problems of Environmental Impact Assessment(EIA) and what impact the current problems exert on another mines developing process. The legal relations analysis reveals that the Management of Mountainous Districts Act and other related laws effect on EIA process, especially the case of area expansion of limestone mines excluded from EIA. However, these problems can create mismatch with the policy goal of EIA system and have a negative impact on the environment in the future. A series of indepth interviews with managers in related agencies found that those agencies have been unaware of the seriousness of the problem. Without any strategy, negative result made by development activities would get more serious and sustainable development may not be possible at all. In order to solve these problems, government should modify the current interdependent legal provision and create the incentive structure to participate actively related agency in the EIA system.

Spatial Features and Issues in the Process of Establishing and Expanding the Milwaukee Art Museum (밀워키미술관 신·증축에서 나타나는 공간적 특성과 쟁점)

  • Lee, Seung-youp;Byun, Nahyang
    • Journal of the Architectural Institute of Korea Planning & Design
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    • v.35 no.1
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    • pp.107-115
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    • 2019
  • This research explores a historical trajectory of the Milwaukee Art Museum from its establishment to the third expansion over the last six decades. After established in 1957 by the architect, Eero Saarinen, this museum underwent three expansions led by three different architects including, David Kahler, Santiago Calatrava, and James Shields. Reasons for expanding the museum were varied. A lack of exhibition space, an absence of visual identity, and path interruption problem within urban contexts were the main factors of a series of expansion. Furthermore, this research points out that there are three issues in the process of the expansion. The first is connection issues between the downtown and the lakefront in which the museum has blocked the public flow. The second, there were controversies on the allocation of the expanded space among the main body of the decision including architects, curators, and stakeholders. The last one is relationships among architects. This is related to each architect's attitude toward the museum. Drawing on historical documents and interviews with the regional architects, I argue that the identity and values of the museum have changed over time through the expansions rather than having the invariable.

Frequency-Dependent Line Capacitance and Conductance Calculations of On-Chip Interconnects on Silicon Substrate Using Fourier cosine Series Approach

  • Ymeri, H.;Nauwelaers, B.;Vandenberghe, S.;Maex, K.;De Roest, D.;Stucchi, M.
    • JSTS:Journal of Semiconductor Technology and Science
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    • v.1 no.4
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    • pp.209-215
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    • 2001
  • In this paper a method for analysis and modelling of coplanar transmission interconnect lines that are placed on top of silicon-silicon oxide substrates is presented. The potential function is expressed by series expansions in terms of solutions of the Laplace equation for each homogeneous region of layered structure. The expansion coefficients of different series are related to each other and to potentials applied to the conductors via boundary conditions. In the plane of conductors, boundary conditions are satisfied at $N_d$ discrete points with $N_d$ being equal to the number of terms in the series expansions. The resulting system of inhomogeneous linear equations is solved by matrix inversion. No iterations are required. A discussion of the calculated line admittance parameters as functions of width of conductors, thickness of the layers, and frequency is given. The interconnect capacitance and conductance per unit length results are given and compared with those obtained using full wave solutions, and good agreement have been obtained in all the cases treated

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A Spectral Inverse Scattering Technique by Using the Moment Method with Series-Expanded Basis Function : Noise Effect (급수전개된 기저함수를 갖는 모멘트방법에 의한 파수영역의 역산란 방법 : 잡음의 영향)

  • 최현철;김세윤;라정웅
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.21 no.1
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    • pp.214-223
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    • 1996
  • Noise effects on image profiles reconstructed by the spectral inverse scattering technique is studied based on moment method with series-expanded basis function. It is found that the Fourier series expansion to the field distribution and the averaging of the reconstructed profile in each enlarged cell provides an effective tool for the reduction of noise effects.

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Joining of Ceramic and Metal using Active Metal Brazing (활성금속 브레이징을 사용한 세라믹과 금속의 접합)

  • Kee, Se-Ho;Xu, Zengfeng;Jung, Jae-Pil;Kim, Won-Joong
    • Journal of the Microelectronics and Packaging Society
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    • v.18 no.3
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    • pp.1-7
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    • 2011
  • Active brazing of ceramic to metal is reviewed in this paper. As one of the key aspect in joint techniques, active brazing has been developed to simplify the manufacturing procedure of brazed joints between ceramic and metal. The active filler metal includes Ag-Cu-Ti series, Cu-Ti series, Co-Ti series and so on. The active filler metal which supplies the chemical bonds between ceramic and metal, enhances the wetting of filler metal on ceramic surface and eliminates the need for metallization treatments. The residual stress caused by difference of coefficient of thermal expansion between ceramic and metal, holds a direct influence on the bonding strength and even results in a fracture. Good joints of ceramic to metal promote the miniaturization and simplicity of electronic components with multifunction.