• Title/Summary/Keyword: Euler-Lagrange model

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A Study of Sedimentation Processes of Saemangeum Reclamation(II) - A Study of Sedimentation Processes after Saemangeum Reclamation - (새만금간척 퇴적과정에 관한 연구(II) -새만금간척 시행 후를 중심으로-)

  • 신문섭
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.44 no.5
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    • pp.33-40
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    • 2002
  • The purpose of this study is to find the variation of sedimentation patterns after Saemangeum reclamation. Residual flow after Saemangeum reclamation was calculated prognostically from the observed water temperature and salinity data in May 1992 by the Marine Development Institute of Gunsan National University and wind data which were obtained from spring 1969 through winter 1977 by the Kunsan Meteorological Observatory. Three dimensional movements of injected particles due to currents, turbulence and sinking velocity are tracked by the Euler-Lagrange method. When suspended sediments with the size of soil grain of 30 ㎛ are injected in the Sinsi drainage sluice, their dispersion range of sediment is around Gogunsan islands. When suspended sediments with the size of soil grain of 200 ㎛ are injected in the Garyeok drainage sluice, their dispersion range of sediment was around the Garyeok drainage sluice and Byeonsan coastal area.

Numerical Study on the Effects of Air Decking in Half Charge Blasting Using AUTODYN (AUTODYN을 이용한 하프장전 발파공법의 에어데크 효과에 대한 수치해석적 연구)

  • Baluch, Khaqan;Kim, Jung-Kyu;Kim, Seung-Jun;Jin, Guochen;Jung, Seung-Won;Yang, Hyung-Sik;Kim, Nam-Soo;Kim, Jong-Gwan
    • Explosives and Blasting
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    • v.36 no.4
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    • pp.1-8
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    • 2018
  • This numerical study was intended to evaluate the applicability of the half charge blasting to mining and tunnelling. The half charge blasting is a method that two separate rounds are sequentially blasted for the rock burdens in which long blast holes have already been drilled at one operation. The aim of the method is to decrease the construction cost and period in mining and tunnelling projects as well as to increase the blasting efficiency. Several numerical analyses were conducted by using the Euler-Lagrange solver on ANSYS AUTODYN to identify the effects of the suggested method on the blasting results in underground excavations. The overall performance of the suggested method was also compared to an ordinary blasting method. The analysis model was comprised of the Eulerian parts (explosive, air, and stemming materials) and the Lagrangian parts (rock material). As a result, it was found that, owing to the air decks formed in the bottom parts of the long blast holes, the first round of the suggested method presented a higher shock pressure and particle velocities in the vicinity of the blast holes compared to the ordinary blasting method.

Design on the Controller of Flexible Robot using Sliding Sector Control (슬라이딩 섹터 제어를 이용한 유연한 로봇 팔에 대한 제어기 설계)

  • Han, Jong-Kil;Bae, Sung-Hwan;Yang, Keun-Ho
    • The Journal of the Korea institute of electronic communication sciences
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    • v.5 no.5
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    • pp.541-546
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    • 2010
  • When a flexible arm is rotated by a motor about an joint axis, transverse vibration may occur. The motor torque should be controlled in such a way that the moter rotates by a specified angle, while simultaneously stabilizing vibration of the flexible arm so that it is arrested at the end of rotation. In this paper, the dynamic model of flexible robot arm is modeled by using Bernoulli-Euler beam theory and Lagrange equation. Nonlinear control with hysteresis deadzone using the sliding sector theory with continued input function in the sector is proposed.

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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    • v.65 no.6
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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.

A study of Sedimentation Processes of Saemangeum Reclamation( I ) - A study of Sedimentation Processes before Saemangeum Reclamation - (새만금간척 퇴적과정에 관한 연구( I ) -새만금간척 시행 전을 중심으로-)

  • Shin, Moon-Seup
    • Magazine of the Korean Society of Agricultural Engineers
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    • v.44 no.4
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    • pp.62-74
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    • 2002
  • The purpose of this study is to find the variation of sedimentation patterns before Saemangeum reclamation. Residual flow before Saemangeum reclamation was calculated diagnostically from the observed water temperature and salinity data in May 1992 by the Marine Development Institute of Kunsan National University and wind data which were obtained from spring 1969 through winter 1977 by the Gunsan Meteorological Observatory. Three dimensional movements of injected particles due to currents, turbulence and sinking velocity are tracked by the Euler-Lagrange method. Calculated sedimentation patterns of riverine materials are highly similar to the observed ones. When suspended sediments with the size of soil grain of 60 ${\mu}m$ are injected from the Mangyeong River, their dispersion range of sediment is about 25km for 24 hours after the injection, while about 35km for 72 hours after the injection. When suspended sediments with the size of soil grain of 200 ${\mu}m$ are injected, their dispersion range of sediment is about 18km for 24 hours after the injection, while about 21km for 72 hours after the injection.

EEG model by statistical mechanics of neocortical interaction

  • Park, J.M.;Whang, M.C.;Bae, B.H.;Kim, S.Y.;Kim, C.J.
    • Journal of the Ergonomics Society of Korea
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    • v.16 no.2
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    • pp.15-27
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    • 1997
  • Brain potential is described using the mesocolumnar activity defined by averaged firings of excitatory and inhibitory neuron of neocortex. Lagrangian is constructed based on SMNI(Statistical Mechanics of Neocortical Interaction) and then Euler Lagrange equation is obtained. Excitatory neuron firing is assumed to be amplitude- modulated dominantly by the sum of two modes of frequency .omega. and 2 .omega. . Time series of this neuron firing is calculated numerically by Euler Lagrangian equation. I .omega. L related to low frequency distribution of power spectrum, I .omega. H hight frequency, and Sd(standard deviation) were introduced for the effective extraction of the dynamic property in the simulated brain potential. The relative behavior of I .omega. L, I .omega. H, and Sd was found by parameters .epsilon. and .gamma. related to nonlinearity and harmonics respectively. Experimental I .omega L, I .omega. H, and Sd were obtained from EEG of human in rest state and of canine in deep sleep state and were compared with theoretical ones.

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Analytical wave dispersion modeling in advanced piezoelectric double-layered nanobeam systems

  • Ebrahimi, F.;Haghi, P.;Dabbagh, A.
    • Structural Engineering and Mechanics
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    • v.67 no.2
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    • pp.175-183
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    • 2018
  • This research deals with the wave dispersion analysis of functionally graded double-layered nanobeam systems (FG-DNBSs) considering the piezoelectric effect based on nonlocal strain gradient theory. The nanobeam is modeled via Euler-Bernoulli beam theory. Material properties are considered to change gradually along the nanobeams' thickness on the basis of the rule of mixture. By implementing a Hamiltonian approach, the Euler-Lagrange equations of piezoelectric FG-DNBSs are obtained. Furthermore, applying an analytical solution, the dispersion relations of smart FG-DNBSs are derived by solving an eigenvalue problem. The effects of various parameters such as nonlocality, length scale parameter, interlayer stiffness, applied electric voltage, relative motions and gradient index on the wave dispersion characteristics of nanoscale beam have been investigated. Also, validity of reported results is proven in the framework of a diagram showing the convergence of this model's curve with that of a previous published attempt.

Wave propagation of CNTRC beams resting on elastic foundation based on various higher-order beam theories

  • Yi-Wen Zhang;Hao-Xuan Ding;Gui-Lin She;Abdelouahed Tounsi
    • Geomechanics and Engineering
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    • v.33 no.4
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    • pp.381-391
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    • 2023
  • The aim of this work is to analyze and predict the wave propagation behavior of the carbon nanotube reinforced composites (CNTRC) beams within the framework of various higher order shear deformation beam theory. Using the Euler-Lagrange principle, the wave equations for CNTRC beams are derived, where the determining factor is to make the determinant equal to zero. Based on the eigenvalue method, the relationship between wave number and circular frequency is obtained. Furthermore, the phase and group velocities during wave propagation are obtained as a function of wave number, and the material properties of CNTRC beams are estimated by the mixture rule. In this paper, various higher order shear beam theory including Euler beam theory, Timoshenko beam theory and other beam theories are mainly adopted to analyze the wave propagation problem of the CNTRC beams, and by this way, we conduct a comparative analysis to verify the correctness of this paper. The mathematical model provided in this paper is verified numerically by comparing it with some existing results. We further investigate the effects of different enhancement modes of CNTs, volume fraction of CNTs, spring factor and other aspects on the wave propagation behaviors of the CNTRC beams.

IMAGE SEGMENTATION BASED ON THE STATISTICAL VARIATIONAL FORMULATION USING THE LOCAL REGION INFORMATION

  • Park, Sung Ha;Lee, Chang-Ock;Hahn, Jooyoung
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.18 no.2
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    • pp.129-142
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    • 2014
  • We propose a variational segmentation model based on statistical information of intensities in an image. The model consists of both a local region-based energy and a global region-based energy in order to handle misclassification which happens in a typical statistical variational model with an assumption that an image is a mixture of two Gaussian distributions. We find local ambiguous regions where misclassification might happen due to a small difference between two Gaussian distributions. Based on statistical information restricted to the local ambiguous regions, we design a local region-based energy in order to reduce the misclassification. We suggest an algorithm to avoid the difficulty of the Euler-Lagrange equations of the proposed variational model.

Numerical Investigation on the Thermal and Flow Characteristics of Combustion Heater for Commercial Vehicle (차량용 연소식 난방기의 열 및 유동특성에 대한 수치연구)

  • Hwang, Chang-Hwan;Baek, Seung-Wook
    • Journal of the Korean Society of Combustion
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    • v.16 no.2
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    • pp.40-46
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    • 2011
  • The diesel pre-heater has being used in cabin heating and coolant heating of engine to reduce the engine warm up time for commercial vehicle. The pre-heaters are classified as diesel spray combustor and it forms diffusion flame. By using swirler, a recirculation flow of hot product gases is established near the fuel nozzle and it helps the maintaining of diffusion flame. The design difference of swirler can affect on reaction characteristics and temperature distribution inside pre-heater. The purpose of this study is the investigation of the effect of swirler configuration on combustion characteristics. To solve spray combustion problem, the Euler-Lagrange approach discrete model is used to track droplet trajectory and evaporation history. The PDF equilibrium model is used for chemical reaction model. These models are implemented into the FLUENT code.