• 제목/요약/키워드: Dispersion equation

검색결과 330건 처리시간 0.029초

On the attenuation of the axisymmetric longitudinal waves propagating in the bi-layered hollow cylinder made of viscoelastic materials

  • Kocal, Tarik;Akbarov, Surkay D.
    • Structural Engineering and Mechanics
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    • 제61권1호
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    • pp.143-160
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    • 2017
  • The paper studies the attenuation of the axisymmetric longitudinal waves propagating in the bi-layered hollow cylinder made of linear viscoelastic materials. Investigations are made by utilizing the exact equations of motion of the theory of viscoelasticity. The dispersion equation is obtained for an arbitrary type of hereditary operator of the materials of the constituents and a solution algorithm is developed for obtaining numerical results on the attenuation of the waves under consideration. Specific numerical results are presented and discussed for the case where the viscoelasticity of the materials is described through fractional-exponential operators by Rabotnov. In particular, how the rheological parameters influence the attenuation of the axisymmetric longitudinal waves propagating in the cylinder under consideration, is established.

Influences of the Filter Effect on Pulse Splitting in Passively Mode-Locked Fiber Laser with Positive Dispersion Cavity

  • Chen, Xiaodong
    • Journal of the Optical Society of Korea
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    • 제19권2호
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    • pp.130-135
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    • 2015
  • Based on the extended nonlinear Schr$\ddot{o}$dinger equation, the influences of the filter effect on pulse splitting in a passively mode-locked erbium-doped fiber laser with positive dispersion cavity are investigated theoretically. Numerical results show that, as the bandwidth of the spectral filter decreases, the nonlinear chirp appended to the pulse increases under the combined action of the filter effect of the super-Gaussian spectral filter and the self-phase modulation effect. On further decreasing the bandwidth, the wave breaking of the pulse takes place. In addition, by varying the pump power of the laser or the profile of the spectral filter, the influences of the filter effect on pulse splitting also change accordingly.

차량터널 오염물질 농도 예측 시뮬레이션 모델 연구 (Simulation Modelling of the Pollutant Concentration in Vehicle Tunnels)

  • 이창우;양원철;이송희
    • 터널과지하공간
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    • 제6권1호
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    • pp.57-63
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    • 1996
  • The goal of this study is to develop a simulation model of the pollutant dispersion in vehicle tunnels, which can be utilized to optimize the tunnel ventilation system. Contaminant dispersion is modelled using a FDM solution of advective diffusion equation. Taking into consideration the local vehicle emission rates by year, it is user-oriented and its logic is generalized. Therefore, differences in the ventilation scheme can be easily adapted. The results of its application to a urban tunnel show that the relative errors are 1.1~6.8% for the natural velocity, 1.3% for the traffic-induced velocity and 2.9% for the total air quantity. Simulated CO concentrations along the entire tunnel show about 13% of the relative error.

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Numerical modelling of contaminant transport using FEM and meshfree method

  • Satavalekar, Rupali S.;Sawant, Vishwas A.
    • Advances in environmental research
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    • 제3권2호
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    • pp.117-129
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    • 2014
  • Groundwater contamination is seeking a lot of attention due to constant degradation of water by landfills and waste lagoons. In many cases heterogeneous soil system is encountered and hence, a finite element model is developed to solve the advection-dispersion equation for layered soil system as FEM is a robust tool for modelling problems of heterogeneity and complex geometries. Recently developed Meshfree methods have advantage of eliminating the mesh and construct approximate solutions and are observed that they perform effectively as compared to conventional FEM. In the present study, both FEM and Meshfree method are used to simulate phenomenon of contaminant transport in one dimension. The results obtained are agreeing with the values in literature and hence the model is further used for predicting the transport of contaminants. Parametric study is done by changing the dispersion coefficient, average velocity, geochemical reactions, height of leachate and height of liner for obtaining suitability.

Analysis of elastic wave propagation in long beam using Fourier transformation

  • Mohammad Tahaye Abadi
    • Structural Engineering and Mechanics
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    • 제87권2호
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    • pp.165-172
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    • 2023
  • This paper presents a novel method for modeling elastic wave propagation in long beams. The proposed method derives a solution for the transient transverse displacement of the beam's neutral axis without assuming the separation of variables (SV). By mapping the governing equation from the space domain to the frequency domain using Fourier transformation (FT), the transverse displacement function is determined as a convolution integral of external loading functions and a combination of trigonometric and Fresnel functions. This method determines the beam's response to general loading conditions as a linear combination of the analytical response of a beam subjected to an abrupt localized loading. The proposed solution method is verified through finite element analysis (FEA) and wave propagation patterns are derived for tone burst loading with specific frequency contents. The results demonstrate that the proposed solution method accurately models wave dispersion, reduces computational cost, and yields accurate results even for high-frequency loading.

국내산 조전분 호화액의 유동특성 (Rheological Properties of Gelatinized Millet Starch Dispersions)

  • 김남수;남영중
    • 한국식품과학회지
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    • 제21권6호
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    • pp.742-748
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    • 1989
  • 국내산 메조 및 차조의 호화전분액의 농도와 온도에 따른 유동특성을 구명하였다. 메조 및 차조의 호화전분액은 의가고성 유체의 성질을 보여주었으며, 각각의 호화전분액 농도에서 일정 전단속도에 대한 전단응력의 크기는 메조전분보다 차조전분이 높았다. 메조와 차조의 호화전분액의 유동특성은 지수법칙에 잘 적용되었으며 이 때 유동지수 n값은 1% 호화전분액에 있어 메조전분의 경우 0.96, 차조전분의 경우 0.74이나, 5% 호화전분액에 있어서는 메조전분의 경우 0.35, 차조전분의 경우 0.24로 농도증가에 따라 의가소성이 증대되었다. 점조도지수 K값의 경우 농도의존성이 보다 현저하였다. 조전분 호화액은 일정농도 이상에서 항복응력을 보이며, 이 때 농도와 항복응력의 평방근 사이에는 직선관계가 있었고 항복응력이 영이되는 호화전분액 농도는 메조전분의 경우 2.19%, 차조전분의 경우 1.69%로 예측되었다. 3% 조전분 호화액에 대하여 온도에 따른 유동특성을 분석시 일정 전단속도에 대한 전단 응력의 크기는 온도가 낮아짐에 따라 증가하였으며, 특히 $20^{\circ}C$의 측정온도에서 이런 현상이 현저하였다. 이때, 측정온도가 높아지면 유동지수 n값은 증가하고 점조도지수 K값은 감소하였는데 이는 메조 및 차조전분에 공통적인 현상이었다. 점조도지수 K값과 온도와의 관계는 아레니우스 식에 잘 적용되었으며, 3% 호화전분액의 경우 활성화에너지는 메조전분의 경우 2.89kcal/mol, 차조전분의 경우 3.18kca1/mo1이었다.

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On Propagation of Love waves in dry sandy medium sandwiched between fiber-reinforced layer and prestressed porous half-space

  • Gupta, Shishir;Ahmed, Mostaid
    • Earthquakes and Structures
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    • 제12권6호
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    • pp.619-628
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    • 2017
  • The intent of this paper is to investigate the propagation of Love waves in a dry sandy medium sandwiched between fiber-reinforced layer and prestressed porous half-space. Separate displacement components have been deduced in order to characterize the dynamics of individual materials. Using suitable boundary conditions, the frequency equation has been derived by means of separation of variables which reveals the significant role of reinforcement parameters, sandiness, thickness of layers, porosity and prestress on the wave propagation. The phase velocity of the Love wave has been discussed in accordance with its typical cases. In both cases when fiber-reinforced and dry sandy media are absent, the derived equation of Love type wave coincides with the classical Love wave equation. Numerical computations have been performed in order to graphically illustrate the dependencies of different parameters on phase velocity of Love waves. It is observed that the phase velocity decreases with the increase of parameters pertaining to reinforcement and prestress. The results have certain potential applications in earthquake seismology and civil engineering.

유해 대기오염물질의 난류확산 수치모의에서 침적한과 부력항 추가에 따른 효과 (Addition Effect of the Deposition and Buoyancy Terms in Modeling Turbulence Diffusion of Hazardous Air Pollutants)

  • 원경미;이화운;지효은;김철희;송창근
    • 한국대기환경학회지
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    • 제22권1호
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    • pp.73-84
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    • 2006
  • Hazardous Air Pollutants (HAPs) are characterized by being relatively heavier and denser than that of ambient air due to the various reasons such as higher molecular weight, low temperature and other complicated chemical transformations (Witlox, 1994). In an effort to investigate transport and diffusion from instantaneous emission of heavy gas, Lagrangian Particle Dispersion Model (LPDM) coupled with the RAMS output was employed. Both deposition process and buoyancy term were added on the atmospheric diffusion equations of LPDM, and the locations and concentrations of dense gas particle released from instantaneous single point source (emitting initially for 10 minutes only) were analyzed. The result overall shows that adding deposition process and buoyancy terms on the diffusion equation of LPDM has very small but detectable effect on the vertical and horizontal distribution of Lagrangian particles that especially transported for a fairly long traveling time. Also the slumping of dense gas can be found to be ignored horizontally compared to the advection by the horizontal wind suggesting that it was essential to couple the Lagrangian particle dispersion model coupled with the RAMS model in order to explain the dispersion of HAPs more accurately. However, during the initial time of instantaneous emission, buoyancy term play an important role on the vertical locations of dense particles for near surface atmosphere and around source area, indicating the importance of densities of HAPs in the beginning stage or short duration for the risk assessment of HAPs or management of heavy vapors during the explosive accidents.

$\lambda$=1.55 $\mu$m에서 포물선분포-이중클래드, 분산보상 단일모드 광섬유의 설계 (Design of double-clad, dispersion-compensating single-mode fiber with parabolic-index profile for $\lambda$=1.55 $\mu$m)

  • 김동각;김창민;이상배;강희전
    • 한국광학회지
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    • 제8권2호
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    • pp.134-141
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    • 1997
  • 기존의 .lambda.=1.31.mu.m에서 분산 최적화된 광통신시스템을 .lambda.=1.55.mu.m 광전송시스템으로 향상시키는데 필요한 분산보상 단일모드 광섬유(DCF)를 설계하였다. 총분산이 .lambda.=1.55.mu.m에서 큰 마이너스 분산치를 갖는 굴절율 분포를 얻기 위해 포물선 분포-이중클래드 광섬유의 분산특성을 해석하였다. 광섬유 스칼라 파동방정식으로부터 분산특성을 얻기 위해 1차원 유한요소법을 적용하였다. Reel에 감긴 DCF의 macro-bending에 의한 손실을 적절히 제한하기 위해, L $P_{01}$모드의 차단 파장이 .lambda.=1.80.mu.m이상이 되도록 설계하였다. 이 조건에 맞는 굴절율분포의 .lambda.=1.55.mu.m에서 분산의 하한치는 약 -120 ps/nm.km정도로 제한됨을 볼 수 있었다.다.

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포로히-블루머(Forouhi-Bloomer) 분산식을 이용한 유기발광물질 Alq3의 광학 상수 결정 (Determination of optical constants for organic light emitting material of Alq3 using Forouhi-Bloomer dispersion relations)

  • 정부영;우석훈;이석목;황보창권
    • 한국광학회지
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    • 제14권1호
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    • pp.1-7
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    • 2003
  • 유기발광물질 Alq$_3$ 복소굴절률을 양자역학적 흡수이론인 바탕인 포로히-블루머(Forouhi-Bloomer) 분산식[Phys. Rev. B 34. 7018(1986)]을 이용하여 1.5~6 ev의 영역에서 계산하였다. 분광광도계를 이용하여 측정한 Alq$_3$ 박막의 흡수 스펙트럼에서 흡수 피크의 위치와 폭으로부터 포로히-블루머 분산식의 변수 $A_{i}$ , B$_{i}$, $C_{i}$ 의 초기 근사값을 결정하였다. 기판으로 사용한 비정질실리카(fused silica)의 굴절률은 분광광도계로부터 측정된 투과율과 반사율 스펙트럼으로부터 셀마이어(Sellmeier)분산식을 적용하여 계산하였다. 기판의 굴절률과 분광광토계에서 측정한 Alq$_3$박막의 투과율과 반사율 스펙트럼에 포로히-블루머 분산식을 이용한 비선형 최소자승법 곡선맞춤을 하여 Alq$_3$의 복소굴절률을 계산할 수 있었다.