• Title/Summary/Keyword: dispersion equations

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Wave dispersion characteristics of nonlocal strain gradient double-layered graphene sheets in hygro-thermal environments

  • Ebrahimi, Farzad;Dabbagh, Ali
    • Structural Engineering and Mechanics
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    • 제65권6호
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    • pp.645-656
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    • 2018
  • Importance of procuring adequate knowledge about the mechanical behavior of double-layered graphene sheets (DLGSs) incensed the authors to investigate wave propagation responses of mentioned element while rested on a visco-Pasternak medium under hygro-thermal loading. A nonlocal strain gradient theory (NSGT) is exploited to present a more reliable size-dependent mechanical analysis by capturing both softening and hardening effects of small scale. Furthermore, in the framework of a classical plate theory the kinematic relations are developed. Incorporating kinematic relations with the definition of Hamilton's principle, the Euler-Lagrange equations of each of the layers are derived separately. Afterwards, combining Euler-Lagrange equations with those of the NSGT the nonlocal governing equations are written in terms of displacement fields. Interaction of the each of the graphene sheets with another one is regarded by the means of vdW model. Then, a widespread analytical solution is employed to solve the derived equations and obtain wave frequency values. Subsequently, influence of each participant variable containing nonlocal parameter, length scale parameter, foundation parameters, temperature gradient and moisture concentration is studied by plotting various figures.

Hygro-thermal effects on wave dispersion responses of magnetostrictive sandwich nanoplates

  • Ebrahimi, Farzad;Dabbagh, Ali;Tornabene, Francesco;Civalek, Omer
    • Advances in nano research
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    • 제7권3호
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    • pp.157-167
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    • 2019
  • In this paper, a classical plate model is utilized to formulate the wave propagation problem of magnetostrictive sandwich nanoplates (MSNPs) while subjected to hygrothermal loading with respect to the scale effects. Herein, magnetostriction effect is considered and controlled on the basis of a feedback control system. The nanoplate is supposed to be embedded on a visco-Pasternak substrate. The kinematic relations are derived based on the Kirchhoff plate theory; also, combining these obtained equations with Hamilton's principle, the local equations of motion are achieved. According to a nonlocal strain gradient theory (NSGT), the small scale influences are covered precisely by introducing two scale coefficients. Afterwards, the nonlocal governing equations can be derived coupling the local equations with those of the NSGT. Applying an analytical solution, the wave frequency and phase velocity of propagated waves can be gathered solving an eigenvalue problem. On the other hand, accuracy and efficiency of presented model is verified by setting a comparison between the obtained results with those of previous published researches. Effects of different variants are plotted in some figures and the highlights are discussed in detail.

확장형 Boussinesq 방정식의 유한요소모형 개발 (Development of Finite Element Method for the Extended Boussinesq Equations)

  • 우승범;최영광;윤병일
    • 한국해양학회지:바다
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    • 제12권3호
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    • pp.133-141
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    • 2007
  • 장파와 단파의 거동을 동시에 모의할 수 있는 확장형 Boussinesq 방정식에 대한 유한요소모형을 개발하였다. 3차 공간 미분항을 처리하기 위한 추가변수를 도입하고 Galerkin 가중잔차방법을 적용하여 모형을 수립하였으며, 시간적분방법으로 Adams-Bashforth-Moulton Predictor Corrector 기법을 적용하여 비물리적인 수치분산이나 수치소산 현상을 줄일 수 있도록 하였다. 이 개발된 모형을 검증하기 위해 고립파가 전파하는 문제에 적용을 하였다. 개발된 모형을 적용한 결과 이론해 또는 수리실험 결과에 매우 양호한 일치를 보였다.

Modal Characteristics of Photonic Crystal Fibers

  • Lee, Yong-Jae;Song, Dae-Sung;Kim, Se-Heon;Huh, Jun;Lee, Yong-Hee
    • Journal of the Optical Society of Korea
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    • 제7권3호
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    • pp.188-192
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    • 2003
  • The modal characteristics of the photonic crystal fibers are analyzed using the reliable and efficient plane wave expansion method. The mode profile, effective index and group velocity dispersion are obtained by solving Maxwell's vector wave equations without any approximation. The zero dispersion condition of a photonic crystal fiber is derived over a wide range of wavelengths. Higher-order modes are also easily found as a by-product of the plane wave expansion method. This method can be used to quickly and accurately design various optical properties of photonic crystal fibers.

유한요소법에 의한 하구의 수질모델 BAYQUAL (BAYQUAL Model for the Water Quality Simulation of a Bay Using Finite Element Method)

  • 류병로;한양수
    • 한국환경과학회지
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    • 제8권3호
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    • pp.355-361
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    • 1999
  • The aim of this study is to develop the water quality simulation model (BAYQUAL) that deal with the physical, chemical and biological aspects of fate/behavior of pollutants in the bay. BAYQUAL is a two dimensional, time-variable finite element water quality model based on the flow simulation model in bay(BAYFLOW). The algorithm is composed of a hydrodynamic module which solves the equations of motion and continuity, a pollutnat dispersion module which solves the dispersion-advection equation. The applicability and feasibility of the model are discussed by applications of the model to the Kwangyang bay of south coastal waters of Korea. Based on the field data, the BAYQUAL model was calibrated and verified. The results were in good agreement with measured value within relative error of 14% for COD, T-N, T-P. Numerical simulations of velocity components and tide amplitude(M2) were agreed closely with the actual data.

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기-액흐름 연속누출에 의한 개방공간 증기운 폭발사고를 중심으로 중.소규모 사업장을 위한 사고 영향평가 방법 (The Method of Consequence Analysis of the Unconfined Vapor Cloud Explosion Accident by the Continuous Release of Gas-Liquid Flow for the Small and Medium Size Enterprises(SMS))

  • 장서일;이헌창;조지훈;김태옥
    • 한국안전학회지
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    • 제18권1호
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    • pp.64-70
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    • 2003
  • For the unconfined vapor cloud explosion(UVCE) accident by the continuous release of gas-liquid flow of various saturated liquids in a vessel at ground level, overpressures were estimated by TNT equivalency model with two estimation methods, such as UVCE I model based on a constant release time and UVCEII model based on a real travel time of vapor by dispersion and analyzed with various release conditions. As a simulation result the simple, easy, and correct method of evaluation of consequences of the UVCE accident was proposed by using consequences of UVCE I model and correlation equations for differences of overpressures between UVCE models, so that this evaluation method could be used easily in the small and medium size enterprises without using the dispersion model.

都市交通計劃 모델과 大氣汚染 擴散모델을 이용한 都市地域 大氣汚染 豫測 (Air Pollution Forecasting Using Urban Transportation Planning Models and Air Pollution Dispersion Models)

  • 董宗仁;趙康來;金良均;兪 浣
    • 한국대기환경학회지
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    • 제2권2호
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    • pp.31-40
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    • 1986
  • Motor vehicle related air pollution has become more serious because of rapid increase of number of cars, specially in the urban area. The increase trend seems to be accelerated, however, the fact is that road conditions, parking facilities and traffic control systems are far behind coping with this situation. In spite of the lack of related basic data, urban transportation planning (UPT) and air pollution dispersion models were applied to predict air pollution level. In standard UPT model, trip generation, distribution, modal split and network assignment were estimated by experimental equations and appropriate models. The air pollution level in the central business area was believed to be higher and it will increase continuously due to the increase of traffic demand. To meet this situation, air pollution problem should be considered as a part of integrated plannings of urban plans or transportation plans as well as more stringent motor vehicle emission standards, have to be enforced.

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TM Mode Analysis of a Periodic Thick Mushroom Structure

  • Woo, Dae Woong;Park, Wee Sang
    • International journal of advanced smart convergence
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    • 제1권2호
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    • pp.43-46
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    • 2012
  • We analyzed a periodic thick mushroom structure for use as an artificial magnetic conductor using mode-matching method. The fields in each region were represented by either Floquet modes or waveguide modes. By applying tangential electric and magnetic field continuity conditions and using matrix equations, unknown coefficients and dispersion diagram were calculated. The proposed model can account for the effects of oblique incidence. Simulation time using the method was much faster than the commercial tools. We found that the current method produces accurate results of reflection phase and dispersion diagram.

갈수기(渴水期) 하천(河川)에서의 오염물질(汚染物質)의 확산(擴散) 및 이동(移動) (Low Flow Pollutant Transport in Natural Rivers)

  • 서일원
    • 상하수도학회지
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    • 제7권1호
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    • pp.29-36
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    • 1993
  • The complex nature of low flow mixing in natural channels has been investigated using both laboratory experiments and the numerical solution of a proposed mathematical model that is based on a set of mass balance equations describing the mixing and mass exchange mechanisms. Laboratory experiments, which involved collection of channel geometry, hydraulic, and dye dispersion test data, were conducted in a model of four pool and riffle sequences in a 49-m long tilting flume. The experimental results show that flow over the model pool-riffle sequences is highly non-uniform. Concentration-time curves are significantly skewed with long tails. Comparison between measured and predicted concentration-time curves shows good agreement in the general shape, peak concentration and time to peak. The proposed model shows significant improvement over the conventional one-dimensional dispersion model in predicting natural mixing processes in open channels under low flow conditions through pools and riffles.

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SIMULTANEOUS DETERMINATION OF OPTICAL CONSTANTS AND DEPTH-PROFILE OF SPUTTERED AMORPHOUS TiO$_2$ THIN FILMS

  • Rhee, Sung-Gyu;Lee, Soon-Il;Oh, Soo-Ghee
    • 한국표면공학회지
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    • 제29권6호
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    • pp.654-659
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    • 1996
  • Amorphous $TiO_2$ thin films were deposited on silicon substrates by the RF magnetron sputtering under various conditions, and studied by the spectroscopic ellipsometry (SE). To determine the optical constants as a function of photon energy and also to depth-profile the as-deposited $TiO_2$ thin films, we analyzed the ellipsometric spectra using the effective medium approximation and the dispersion equations. Especially, we improved the modeling accuracy by selectively using either the Sellmeier or the Forouhi and Bloomer dispersion equation in different energy regions.

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