• 제목/요약/키워드: Euler-lagrange method

검색결과 76건 처리시간 0.023초

새만금지구의 퇴적과정에 관한 연구 (A study of sedimentation processes in seamangum coastal area)

  • 신문섭;유철웅
    • 한국수자원학회:학술대회논문집
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    • 한국수자원학회 1996년도 학술발표회 논문집
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    • pp.689-694
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    • 1996
  • 새만금지구의 조류 변화와 만경강, 동진강의 부유사유입의한 퇴적 과정을 알아보았다. 퇴적과정은 새만금지구해역의 조석잔차류와 수온, 염분에 의한 잔차류, 바람에 의한 잔차류성분을 포함한 흐름 성분과 입자의 침강속도를 고려한 3차원 수치실험에 의하여 재현하였다. 계산에서 안정성이 높고, 오차가 축적되지 않고, 복잡한 경계조건에서도 적용이 간단하다는 특성이 있는 Monte Carlo 방법을 사용하여 부유사의 분산, 퇴적과정을 수치실험한 결과와 농어촌진흥공사의 관측결과와 거의 유사하였다.

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크랙을 가진 유체유동 파이프의 동특성 해석 (Dynamic Behavior of a Simply Supported Fluid Flow Pipe with a Crack)

  • 유진석;손인수;윤한익
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2003년도 춘계학술대회논문집
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    • pp.689-694
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    • 2003
  • An iterative modal analysis approach is developed to determine the effect of transverse open cracks on the dynamic behavior of simply supported pipe conveying fluid subject to the moving mass. The equation of motion is derived by using Lagrange's equation. The influences of the velocity of moving mass and the velocity of fluid flow and a crack have been studied on the dynamic behavior of a simply supported pipe system by numerical method. The presence of crack results in higher deflections of pipe. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments i.e. the crack is modelled as a rotational spring. Totally, as the velocity of fluid flow and the crack severity are increased, the mid-span deflection of simply supported pipe conveying fluid is increased. The time which produce the maximum dynamic deflection of the simply supported pipe is delayed according to the increment of the crack severity.

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크랙과 이동질량을 가진 유체유동 단순지지 파이프의 동특성에 관한 연구 (A Study on Dynamic Behavior of Simply Supported Fluid Flow Pipe with Crack and Moving Mass)

  • 윤한익;진종태;손인수
    • 대한기계학회논문집A
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    • 제28권4호
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    • pp.419-426
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    • 2004
  • In this paper, studied about the effect of open crack and the moving mass on the dynamic behavior of simply supported pipe conveying fluid. The equation of motion is derived by using Lagrange's equation. The influences of the velocity of moving mass, the velocity of fluid flow and a crack have been studied on the dynamic behavior of a simply supported pipe system by numerical method. The crack section is represented by a local flexibility matrix connecting two undamaged beam segments. Therefore, the crack is modelled as a rotational spring. Totally, as the velocity of fluid flow is increased, the mid-span deflection of simply supported pipe conveying fluid is increased. The position of the crack is located in the middle point of the pipe, the mid-span deflection of simply supported pipe presents maximum deflection.

유체가 흐르는 인장 가능한 곡선관의 고유진동수 해석 (Natural Frequency Analysis of an Extensible Curved Pipe Conveying Fluid)

  • 정두한;정진태
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2005년도 추계학술대회논문집
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    • pp.792-795
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    • 2005
  • The vibration of a curved pipe conveying fluid is studied when the pipe is clamped at both ends. To consider the nonlinearity, this study adopts the Lagrange strain theory for large deformation and the extensible dynamics based on the Euler-Bemoulli beam theory for slenderness assumption. By using the Hamilton principle, the non-linear partial differential equations are derived. To investigate the dynamic characteristics of the system the discretized equations of motion are derived from the Galerkin method. The natural frequencies varying with the flow velocity are computed. From these results, we should consider the nonlinearity to analyze dynamics of a curved pipe conveying fluid more precisely.

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이중크랙을 가진 단순지지 보의 자유진동 해석 (Free Vibration Analysis of Simply Supported Beam with Double Cracks)

  • 안성진;손인수;윤한익
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2005년도 추계학술대회논문집
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    • pp.600-603
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    • 2005
  • In this paper we studied about the effect of the double cracks on the dynamic behavior of a simply supported beam. The equation of motion is derived by using Lagrange's equation and analyzed by numerical method. The simply supported beam is modeled by the Euler-Bernoulli beam theory. The crack section is represented by a local flexibility matrix connecting three undamaged beam segments. The influences of the crack depth and position of each crack on the vibration mode and the natural frequencies of a simply supported beam are analytically clarified. The theoretical results are also validated by a comparison with experimental measurements.

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이중크랙을 가진 보의 동특성에 미치는 끝단질량과 이동질량의 영향 (Influence of Tip Mass and Moving Mass on Dynamic Behavior of Beam with Double-Crack)

  • 손인수;윤한익
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 2004년도 추계학술대회논문집
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    • pp.713-716
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    • 2004
  • In this paper a dynamic behavior of a double-cracked cnatilver beam with a tip mass and the moving mass is presented. Based on the Euler-Bernoulli beam theory, the equation of motion is derived by using Lagrange's equation. The influences of the moving mass, a tip mass and double cracks have been studied on the dynamic behavior of a cantilever beam system by numerical method. The cracks section are represented by the local flexibility matrix connecting two undamaged beam segments. ,Therefore, the cracks are modelled as a rotational spring. Totally, as a tip mass is increased, the natural frequency of cantilever beam is decreased. The position of the crack is located in front of the cantilever beam, the frequencies of a double-cracked cantilever beam presents minimum frequency.

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Fluid-conveying piezoelectric nanosensor: Nonclassical effects on vibration-stability analysis

  • Kachapi, Sayyid H. Hashemi
    • Structural Engineering and Mechanics
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    • 제76권5호
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    • pp.619-629
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    • 2020
  • In current study, surface/interface effects for pull-in voltage and viscous fluid velocity effects on dimensionless natural frequency (DNF) of fluid-conveying piezoelectric nanosensor (FCPENS) subjected to direct electrostatic voltage DC with nonlinear excitation, harmonic force and also viscoelastic foundation (visco-pasternak medium and structural damping) are investigated using Gurtin-Murdoch surface/interface (GMSIT) theory. For this analysis, Hamilton's principles, the assumed mode method combined with Lagrange-Euler's are used for the governing equations and boundary conditions. The effects of surface/interface parameters of FCPENS such as Lame's constants (λI,S, μI,S), residual stress (τ0I,S), piezoelectric constants (e31psk,e32psk) and mass density (ρI,S) are considered for analysis of dimensionless natural frequency respect to viscous fluid velocity u̅f and pull-in voltage V̅DC.

Thermal post-buckling analysis of porous functionally graded pipes with initial geometric imperfection

  • Xu, Jia-Qin;She, Gui-Lin
    • Geomechanics and Engineering
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    • 제31권3호
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    • pp.329-337
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    • 2022
  • In this paper, the thermal post-buckling characteristics of functionally graded (FG) pipes with initial geometric imperfection are studied. Considering the influence of initial geometric defects, temperature and geometric nonlinearity, Euler-Lagrange principle is used to derive the nonlinear governing equations of the FG pipes. Considering three different boundary conditions, the two-step perturbation method is used to solve the nonlinear governing equations, and the expressions of thermal post-buckling responses are also obtained. Finally, the correctness of this paper is verified by numerical analyses, and the effects of initial geometric defects, functional graded index, elastic foundation, porosity, thickness of pipe and boundary conditions on thermal post-buckling response are analyzed. It is found that, bifurcation buckling exists for the pipes without initial geometric imperfection. In contrast, there is no bifurcation buckling phenomenon for the pipes with initial geometric imperfection. Meanwhile, the elastic stiffness can significantly improve thermal post-buckling load and thermal post-buckling strength. The larger the porosity, the greater the thermal buckling load and the thermal buckling strength.

Nonlinear resonances of nonlocal strain gradient nanoplates made of functionally graded materials considering geometric imperfection

  • Jia-Qin Xu;Gui-Lin She;Yin-Ping Li;Lei-Lei Gan
    • Steel and Composite Structures
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    • 제47권6호
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    • pp.795-811
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    • 2023
  • When studying the resonance problem of nanoplates, the existing papers do not consider the influences of geometric nonlinearity and initial geometric imperfection, so this paper is to fill this gap. In this paper, based on the nonlocal strain gradient theory (NSGT), the nonlinear resonances of functionally graded (FG) nanoplates with initial geometric imperfection under different boundary conditions are established. In order to consider the small size effect of plates, nonlocal parameters and strain gradient parameters are introduced to expand the assumptions of the first-order shear deformation theory. Subsequently, the equations of motion are derived using the Euler-Lagrange principle and solved with the help of perturbation method. In addition, the effects of initial geometrical imperfection, functionally graded index, strain gradient parameter, nonlocal parameter and porosity on the nonlinear forced vibration behavior of nanoplates under different boundary conditions are discussed.

Nonlinear resonance of porous functionally graded nanoshells with geometrical imperfection

  • Wu-Bin Shan;Gui-Lin She
    • Structural Engineering and Mechanics
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    • 제88권4호
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    • pp.355-368
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    • 2023
  • Employing the non-local strain gradient theory (NSGT), this paper investigates the nonlinear resonance characteristics of functionally graded material (FGM) nanoshells with initial geometric imperfection for the first time. The effective material properties of the porous FGM nanoshells with even distribution of porosities are estimated by a modified power-law model. With the guidance of Love's thin shell theory and considering initial geometric imperfection, the strain equations of the shells are obtained. In order to characterize the small-scale effect of the nanoshells, the nonlocal parameter and strain gradient parameter are introduced. Subsequently, the Euler-Lagrange principle was used to derive the motion equations. Considering three boundary conditions, the Galerkin principle combined with the modified Lindstedt Poincare (MLP) method are employed to discretize and solve the motion equations. Finally, the effects of initial geometric imperfection, functional gradient index, strain gradient parameters, non-local parameters and porosity volume fraction on the nonlinear resonance of the porous FGM nanoshells are examined.