• 제목/요약/키워드: fourier series

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수산화마그네슘의 합성과 솔비톨계 계면활성제를 이용한 표면개질 (Synthesis of Magnesium Hydroxide and Surface Modification by Sorbitol Surfactants)

  • 강국현;현미호;유건성;이동규
    • 한국응용과학기술학회지
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    • 제31권1호
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    • pp.92-100
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    • 2014
  • 비이온계면활성제 가운데 솔비톨계 계면활성제인 Span을 이용해 수열합성법으로 수산화마그네슘을 합성하였다. 수산화마그네슘 합성의 전구체는 염화마그네슘과 수산화나트륨을 사용하였다. 비이온 계면활성제는 안정제와 분산제 그리고 표면 개질제로 적용하였다. 비이온 계면활성제를 첨가하였을 경우 수산화마그네슘 입자는 좀 더 작고 균일한 크기와 좋은 분산성을 나타내었으며, 소수성 성질을 나타내었다. 합성된 입자의 특성은 PSA, SEM, EDS, XRD 그리고 FT-IR을 통해 확인하였다. 기기 분석을 통해 개질 전과 후의 수산화마그네슘의 소수성, 분산성 특성을 비교하였다. 또한 실험조건에 따라 수산화마그네슘 입자의 표면 개질 특성 변화를 확인하였다.

분포하중(分布荷重)을 받는 구형판(矩形板)의 탄성해석(彈性解析) (Analysis of Rectangular Plates under Distributed Loads of Various Intensity with Interior Supports at Arbitrary Positions)

  • 장석윤
    • 대한조선학회지
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    • 제13권1호
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    • pp.17-23
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    • 1976
  • Some methods of analysis of rectangular plates under distributed load of various intensity with interior supports are presented herein. Analysis of many structures such as bottom, side shell, and deck plate of ship hull and flat slab, with or without internal supports, Floor systems of bridges, included crthotropic bridges is a problem of plate with elastic supports or continuous edges. When the four edges of rectangular plate is simply supported, the double Fourier series solution developed by Navier can represent an exact result of this problem. If two opposite edges are simply supported, Levy's method is available to give an "exact" solution. When the loading condition and supporting condition of a plate does not fall into these cases, no simple analytic method seems to be feasible. Analysis of a simply supported rectangular plate under irregularly distributed loads of various intensity with internal supports is carried out by applying Navier solution well as the "Principle of Superposition." Finite difference technique is used to solve plates under irregularly distributed loads of various intensity with internal supports and with various boundary conditions. When finite difference technique is applied to the Lagrange's plate bending equation, any of fourth order derivative term in this equation produces at least five pivotal points leading to some troubles when the resulting linear algebraic equations are to be solved. This problem was solved by reducing the order of the derivatives to two: the fourth order partial differential equation with one dependent variable, namely deflection, is changed to an equivalent pair of second order partial differential equations with two dependent variables. Finite difference technique is then applied to transform these equations to a set of simultaneous linear algebraic equations. Principle of Superposition is then applied to handle the problems caused by concentrated loads and interior supports. This method can be used for the cases of plates under irregularly distributed loads of various intensity with arbitrary conditions such as elastic supports, or continuous edges with or without interior supports, and this method can also be solve the influence values of deflection, moment and etc. at arbitrary position of plates under the live load.

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2차원 다층 반무한해를 이용한 지하구조계의 동적 경계요소 해석 (Dynamic Boundary Element Analysis of Underground Structures Using Multi-Layered Half-Plane Fundamental Solutions)

  • 김문겸;이종우;조성용
    • 한국지진공학회논문집
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    • 제1권4호
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    • pp.59-68
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    • 1997
  • 터널 등과 같은 지하구조계를 유한요소법 등의 수치적 방법으로 해석할 경우 인위적인 경제에서 파의 반사가 발생하게 되어 실제 결과의 큰 차이를 발생시킨다. 따라서 동역학적 하중을 받는 지하구조계는 실질적인 반무한 구조계로 고려되어야 한다. 특히 지하구조계는 실제 다층구조로 구성되어 있으므로 이러한 다층문제를 고려할 수 있어야 한다. 이를 위해 본 연구에서는 외부영역 경제적문제로 해석하기 위한 동적 수치기본해를 개발하였다. 주파수영역의 정적인 경우에 대한 엄밀 적분해와 Bessel 함수의 점근식을 이용한 적분을 통해 축대치문제를 2차원 문제로 보다 쉽게 적용할 수 있도록 하였다. 이와 같이 개발된 동적 수치기본해를 경제 적분 방정식에 적용하여 해석한 결과와 기존 해석결과와의 비교를 통해 그 효율성을 입증하였다. 또한 다층지반내 지하구조물에 대해 지반매체의 각 물성 및 공동의 깊이에 따른 민감도분석을 수해하여 지하구조계의 동적 거동특성 파악의 적용성을 다루었다.

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Bending behaviour of FGM plates via a simple quasi-3D and 2D shear deformation theories

  • Youcef, Ali;Bourada, Mohamed;Draiche, Kada;Boucham, Belhadj;Bourada, Fouad;Addou, Farouk Yahia
    • Coupled systems mechanics
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    • 제9권3호
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    • pp.237-264
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    • 2020
  • This article investigates the static behaviour of functionally graded (FG) plates sometimes declared as advanced composite plates by using a simple and accurate quasi-3D and 2D hyperbolic higher-order shear deformation theories. The properties of functionally graded materials (FGMs) are assumed to vary continuously through the thickness direction according to exponential law distribution (E-FGM). The kinematics of the present theories is modeled with an undetermined integral component and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate; therefore, it does not require the shear correction factor. The fundamental governing differential equations and boundary conditions of exponentially graded plates are derived by employing the static version of principle of virtual work. Analytical solutions for bending of EG plates subjected to sinusoidal distributed load are obtained for simply supported boundary conditions using Navier'is solution procedure developed in the double Fourier trigonometric series. The results for the displacements and stresses of geometrically different EG plates are presented and compared with 3D exact solution and with other quasi-3D and 2D higher-order shear deformation theories to verify the accuracy of the present theory.

테이퍼 전송선 이론을 이용한 마이크로파 여파기 설계 (Microwave Filter Design using Tapered Transmission Line Theory)

  • 권진욱;최형석;장호성
    • 대한전자공학회논문지TC
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    • 제37권3호
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    • pp.28-34
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    • 2000
  • 본 논문에서는 선형화된 리카티(Riccati) 방정식에 후리에 변환을 적용하여 주파수 특성함수와 불균일 테이퍼 전송선상의 새로운 임피던스 분포를 구한다. 리카티 방정식을 선형화 함으로써 발생할 수 있는 오차를 보상하기 위해 임의의 Taylor 급수를 임피던스 항에 추가한다. 추가된 항은 불균일 전송선 양단의 임피던스 불연속을 제거하는 역할을 한다. 설계과정을 통해서 여파기의 과녁 주파수 특성에 접근해 가는 것을 축차법을 통해서 보이며, 위상함수의 역할을 예제를 통해서 보인다. 본 논문에서 제시한 설계법은 불균일 테이퍼 전송선의 설계에 뛰어난 융통성을 제공하므로, 임의의 주파수 대역특성을 만족시키는 여파기 및 임피던스 정합회로 설계에 응용할 수 있다.

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Polystyrene-b-poly(oligo(ethylene oxide) Monomethyl Ether Methacrylate)-b-polystyrene Triblock Copolymers as Potential Carriers for Hydrophobic Drugs

  • You, Qianqian;Chang, Haibo;Guo, Qipeng;Zhang, Yudong;Zhang, Puyu
    • Bulletin of the Korean Chemical Society
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    • 제34권2호
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    • pp.558-564
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    • 2013
  • A simple and effective method is introduced to synthesize a series of polystyrene-b-poly(oligo(ethylene oxide) monomethyl ether methacrylate)-b-polystyrene (PSt-b-POEOMA-b-PSt) triblock copolymers. The structures of PSt-b-POEOMA-b-PSt copolymers were characterized by Fourier-transform infrared spectroscopy (FTIR) and nuclear magnetic resonance ($^1H$ NMR) spectroscopy. The molecular weight and molecular weight distribution of the copolymer were measured by gel permeation chromatography (GPC). Furthermore, the self-assembling and drug-loaded behaviours of three different ratios of PSt-b-POEOMA-b-PSt were studied. These copolymers could readily self-assemble into micelles in aqueous solution. The vitamin E-loaded copolymer micelles were produced by the dialysis method. The micelle size and core-shell structure of the block copolymer micelles and the drug-loaded micelles were confirmed by dynamic light scattering (DLS) and transmission electron microscopy (TEM). The thermal properties of the copolymer micelles before and after drug-loaded were investigated by different scanning calorimetry (DSC). The results show that the micelle size is slightly increased with increasing the content of hydrophobic segments and the micelles are still core-shell spherical structures after drug-loaded. Moreover, the glass transition temperature (Tg) of polystyrene is reduced after the drug loaded. The drug loading content (DLC) of the copolymer micelles is 70%-80% by ultraviolet (UV) photolithography analysis. These properties indicate the micelles self-assembled from PSt-b-POEOMA-b-PSt copolymers would have potential as carriers for the encapsulation of hydrophobic drugs.

DYNAMICAL CHARACTERISTICS OF SUNSPOT CHROMOSPHERES II. ANALYSIS OF CA II H, K AND ${\lambda}8498$ LINES OF A SUNSPOT (SPO 5007) FOR OSCILLATORY MOTIONS

  • Yoon, Tae-Sam;Yun, Hong-Sik;Kim, Jeong-Hoon
    • 천문학회지
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    • 제28권2호
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    • pp.245-253
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    • 1995
  • We have analyzed the time series of Ca II H,K and ${\lambda}8498$ line profiles taken for a sunspot (SPO 5007) with the Echelle spectrograph attached to Vacuum Tower Telescope at Sacramento Peak Solar Observatory. Each set of spectra was taken simultaneously for 20 minutes at a time interval of 30 seconds. A total of 40 photographic films for each line was scanned by a PDS at Korea Astronomy Observatory. The central peak intensity of Ca II H ($I_{max}$), the intensity measured at ${\Delta}{\lambda}=-0.1{\AA}$ from the line center of ${\lambda}8498(I_{{\lambda}8489})$, the radial velocity ($V_r$) and the Doppler width (${\Delta}{\lambda}_D$) estimated from Ca II H have been measured to study the dynamical behaviors of the sunspot chromosphere. Fourier analysis has been carried out for these measured quantities. Our main results are as follows: (1) We have confirmed the 3-minute oscillation being dominant throughout the umbra. The period of oscillations jumps from 180 sec in the umbra to 500 to 1000 sec in the penumbra. (2) The nonlinear character of the umbral oscillation is noted from the observed sawtooth shaped radial velocity fluctuations with amplitudes reaching up to $5{\sim}6\;km/sec$. (3) The spatial distribution of the maximum powers shows that the power of oscillations is stronger in the umbra than in the penumbra. (4) The spatial distributions of the time averaged < $I_{max}$ > and < $V_r$ > across the spot are found to be nearly axially symmetric, implying that the physical quantities derived from the line profiles of Ca II H and ${\lambda}8498$ are inherently associated with the geometry of the magnetic field distribution of the spot. (5) The central peaks of the CaII H emission core lead the upward motions of the umbral atmosphere by $90^{\circ}$, while no phase delay is found in intensities between $I_{max}$ and $I_{{\lambda}8498}$, suggesting that the umbral oscillation is of standing waves.

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Spherical Harmonics Power-spectrum of Global Geopotential Field of Gaussian-bell Type

  • Cheong, Hyeong-Bin;Kong, Hae-Jin
    • 한국지구과학회지
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    • 제34권5호
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    • pp.393-401
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    • 2013
  • Spherical harmonics power spectrum of the geopotential field of Gaussian-bell type on the sphere was investigated using integral formula that is associated with Legendre polynomials. The geopotential field of Gaussian-bell type is defined as a function of sine of angular distance from the bell's center in order to guarantee the continuity on the global domain. Since the integral-formula associated with the Legendre polynomials was represented with infinite series of polynomial, an estimation method was developed to make the procedure computationally efficient while preserving the accuracy. The spherical harmonics power spectrum was shown to vary significantly depending on the scale parameter of the Gaussian bell. Due to the accurate procedure of the new method, the power (degree variance) spanning over orders that were far higher than machine roundoff was well explored. When the scale parameter (or width) of the Gaussian bell is large, the spectrum drops sharply with the total wavenumber. On the other hand, in case of small scale parameter the spectrum tends to be flat, showing very slow decaying with the total wavenumber. The accuracy of the new method was compared with theoretical values for various scale parameters. The new method was found advantageous over discrete numerical methods, such as Gaussian quadrature and Fourier method, in that it can produce the power spectrum with accuracy and computational efficiency for all range of total wavenumber. The results of present study help to determine the allowable maximum scale parameter of the geopotential field when a Gaussian-bell type is adopted as a localized function.

한반도 동남부에 분포하는 제3기 퇴적분지에 대한 중력탐사 (Gravity Survey of the Tertiary Basin in the Southern Part of Korean Peninsula)

  • 민경덕;방성수;현용호
    • 자원환경지질
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    • 제25권2호
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    • pp.167-177
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    • 1992
  • The gravity measurement has been conducted at 53 and 34 stations with an interval of 1~1.5 km along the national roads of about 47 km and 34 km running from Duksungri to Yangpori and from Angangri to Byungpori, Kyungsangbookdo, respectively. The subsurface geology and geologic structure of Tertiary Pohang and Janggi basins along two survey lines are interpreted quantitatively by applying Fourier series and Talwani methods for Bouguer gravity anomaly. The depths of Conrad discontinuity vary from 11.8 to 12.5 km and 11.5 to 13.2 km along the survey lines between Duksungri and Yangpori, and Angangri and Byungpori, respectively. The depths of pre-Cambrian Gneiss complex underneath Kyungsang Supergroup vary from 3.8 to 4.2 km and 3.8 to 4.6 km along the survey lines between Duksungri and Yangpori, and Angangri and Byungpori, respectively. Massive granite bodies which are not exposed along the survey line between Duksungri and Yangpori are distributed on a large scale at the subsurface between Duksungri and Ochun, and Daegokri and Yangpori. Along the survey line between Angangri and Byungpori, it is exposed at Angangri, and extends underneath Chungrimdong, Pohang city. Andesite is distributed on a small scale underneath Pohang city and Ochun. The thicknesses of Tertiary Yonil and Janggi Groups are 0.2~0.9 km and 0.1~0.5 km, respectively. The Tuffaceous rocks which are the lowest formation of Tertiary sedimentary rocks are distributed with the thickness of 0.2 km at the surface and between Kyungsang Supergroup and Yonil or Janggi Groups. The Yonil and Janggi Groups are in fault contact by a fault running through Ochun and Chungrimdong, Pohang city. Two other faults are newly found near Heunghae-eup and Hyungsan river.

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전단변형과 시간변화 이동자기력을 고려한 레일의 강제진동모델링 (Forced Vibration Modeling of Rail Considering Shear Deformation and Moving Magnetic Load)

  • 김준수;김성종;이혁;하성규;이영현
    • 대한기계학회논문집A
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    • 제37권12호
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    • pp.1547-1557
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    • 2013
  • 시간변화 이동자기력이 작용하는 레일의 변형을 티모센코 보 이론(Timoshenko beam theory)로 가정하였으며, 보의 진동특성에 영향을 미치는 탄성체기초의 감쇠효과 및 강성을 고려하였다. 푸리에 급수와 수치해석을 이용해 강제진동모델의 동적응답과 임계속도를 구하였다. 레일의 진동모델을 유한요소 해석 및 오일러 보 이론(Euler beam theory)과 비교 검증하였다. 강제진동모델을 이용하여 레일의 영구변형을 예측하였으며, 실험결과 레일표면의 영구변형 및 마모를 확인하였다. 보의 설계변수인 레일의 형상, 재료, 탄성체 기초의 감쇠효과 및 강성이 레일의 임계속도 및 레일의 처짐, 축 방향 응력, 전단 응력에 미치는 영향에 대한 매개변수적 연구를 진행하였으며, 보의 설계방향을 얻을 수 있었다.