• Title/Summary/Keyword: Equilibrium Position

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MIGRATION OF ELASTIC CAPSULE IN A CHANNEL FLOW (채널 유동 내 유연한 캡슐 움직임에 대한 수치해석)

  • Shin, S.J.;Sung, H.J.
    • 한국전산유체공학회:학술대회논문집
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    • pp.504-507
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    • 2011
  • The inertial migration of a two-dimensional elastic capsule in a channel flow was studied over the Reynolds number range $1{\leq}Re{\leq}100$. The lateral migration velocity, slip velocity, and the deformation and inclination angle of the capsule were investigated by varying the lateral position, Reynolds number, capsule-to-channel size ratio(${\lambda}$), membrane stretching coefficient(${\Phi}$), and membrane bending coefficient(${\gamma}$). During the initial transient motion, the lateral migration velocity increased with increasing Re and ${\lambda}$ but decreased with increases in ${\Phi}$, ${\gamma}$ and the lateral distance from the wall. The initial behavior of the capsule was influenced by variation in the initial lateral position ($y_0$), but the equilibrium position of the capsule was not affected by such variation. The balance between the wall effect and the shear gradient effect determined the equilibrium position. As Re increased, the equilibrium position initially shifted closer to the wall and then moved towards the channel center. A peak in the equilibrium position was observed near Re=30 for ${\gamma}=0.1$, and the peak shifted to higher Re as ${\gamma}$ increased. Depending on the lateral migration velocity, the equilibrium position moved toward the centerline for larger ${\gamma}$ but moved toward the wall for larger ${\Phi}$ and ${\gamma}$.

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Vibration Analysis and Non-linear Equilibrium Equations of a Curved Pipe Conveying Fluid (유체가 흐르는 곡선관의 진동 해석과 비선형 평형 방정식)

  • Jung, Du-Han;Chung, Jin-Tai
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • pp.983-986
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    • 2005
  • Free vibration characteristics of a curved pipe conveying fluid is studied when the pipe is clamped at both ends. Using the perturbation method, the non-linear governing equations divided into two parts; the steady state non-linear equilibrium equations and the linearized equations of motion in the neighborhood of the equilibrium position. The natural frequencies are computed from the linearized equations of motion. In this study, the equilibrium positions are determined by two types of equations, i.e., (1) the non-linear equations, and (2) the equations obtained by neglecting the non-linear terms. The natural frequencies obtained from the non-linear equilibrium equations are compared to those obtained from the linearized equilibrium equations. From the results, as the fluid velocity increases, the equilibrium position should be determined from the nonlinear equations for the vibration analysis of the curved pipe conveying fluid.

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A Study on the Methods for Finding Initial Equilibrium Position of a Lifting Block for the Safe Erection (블록의 탑재 안전성을 위한 초기 평형 자세 탐색 방법 연구)

  • Chun, Do-Hyun;Roh, Myung-Il;Ham, Seung-Ho;Lee, Hye-Won
    • Journal of the Society of Naval Architects of Korea
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    • v.55 no.4
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    • pp.297-305
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    • 2018
  • In a shipyard, block lifting is an important process in the production of ships and offshore structures. Block lifting is a sensitive process because lifting blocks have to be erected with exact positions and orientations. If we use a numerical method for the process, it is important to find tensions of wires and positions of equalizers to maintain the initial equilibrium position of the block. At this time, equations of motion of the block should be solved to calculate the initial equilibrium position of the block. Because the solving technique changes according to the number of equalizers, a suitable equation for the corresponding problem is required. In this study, three types of equations are proposed to find the initial equilibrium position of the block according to the number of equalizers. The Newton-Raphson's method is used to solve nonlinear simultaneous equations and the optimization method is used to determine the appropriate solution to the undetermined problem. To evaluate the applicability of the proposed methods, the dynamic simulations are performed using the tensions calculated from the proposed methods, and the results are discussed. The results show that the proposed methods can be effectively used to determine initial equilibrium position of the block for the block lifting.

Damped Oscill ations of the (Hard)Contact Lenses Posterior to the Blink (순목 후 콘택트(하드)렌즈의 감쇄 진동)

  • Kim, Dae-Soo
    • Journal of Korean Ophthalmic Optics Society
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    • v.10 no.3
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    • pp.173-184
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    • 2005
  • A capillary action-induced tension develops in the tear layer between the contact lens and cornea, which leads to the restoring force due to difference in the layer thickness between either upper and lower or left and right side of the lens when it is displaced off the equilibrium position as a result of blinking. Suppose the lens was displaced a certain distance from the equilibrium position, lens starts to oscillate toward the equilibrium position with the decreasing amplitude due to the restoring force as well as the velocity dependent viscous damping force in the tear layer. A mathematical model which consists of the differential equations and their numerical solution was proposed to analyze the damped oscillations of lenses. The model predicts the time dependence of lenses after the blink varying the various parameters such as Be, diameters, masses and positions displaced from equilibrium. As the Be and mass of lens increases the rate of amplitude reduction decreases, which requires a more time for the lens to return to the equilibrium position. It seems that varying the lens' displacement and diameters affect the lens' motion very little.

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Analytical Method to Analyze the Effect of Tolerance on the Modal Characteristic of Multi-body Systems in Dynamic Equilibrium (동적 평형위치에 있는 다물체계의 모드특성에 미치는 공차의 영향 분석을 위한 해석적 방법)

  • Kim, Bum-Suk;Yoo, Hong-Hee
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • pp.109-114
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    • 2007
  • Analytical method to analyze the effect of tolerance on the modal characteristic of multi-body systems in dynamic equilibrium position is suggested in this paper. Monte-Carlo Method is conventionally employed to perform the tolerance analysis. However, Monte-Carlo Method spends too much time for analysis and has a greater or less accuracy depending on sample condition. To resolve these problems, an analytical method is suggested in this paper. By employing the sensitivity information of mass, damping and stiffness matrices, the sensitivities of damped natural frequencies and the transfer function can be calculated at the dynamic equilibrium position. The effect of tolerance on the modal characteristic can be analyzed from tolerance analysis method.

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Analytical Method to Analyze the Effect of Tolerance on the Modal Characteristic of Multi-body Systems in Dynamic Equilibrium (동적 평형위치에 있는 다물체계의 모드특성에 미치는 공차의 영향 분석을 위한 해석적 방법)

  • Kim, Bum-Suk;Yoo, Hong-Hee
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.17 no.7
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    • pp.579-586
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    • 2007
  • Analytical method to analyze the effect of tolerance on the modal characteristic of multi-body systems in dynamic equilibrium position is suggested in this paper. Monte-Carlo method is conventionally employed to perform the tolerance analysis. However, Monte-Carlo method spends too much time for analysis and has a greater or less accuracy depending on sample condition. To resolve these problems, an analytical method is suggested in this paper. Sensitivity equations for damped natural frequencies and the transfer function are derived at the dynamic equilibrium position. By employing the sensitivity information of mass, damping and stiffness matrices, the sensitivities of damped natural frequencies and the transfer function can be calculated.

Composite Control for Inverted Pendulum System

  • Kwon, Yo-Han;Kim, Beom-Soo;Lee, Sang-Yup;Lim, Myo-Taeg
    • Transactions on Control, Automation and Systems Engineering
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    • v.4 no.1
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    • pp.84-91
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    • 2002
  • A new composite control method for a carriage balancing single inverted pendulum system is proposed and applied to swing up the pendulum and to stabilize it under the state constraint. The target inverted pendulum system has an extremely limited length of the cart(below 16cm). The proposed swing-up controller comprises a sliding mode control algorithm and an optimal control algorithm based on two regions: the region near the inverted unstable equilibrium position and the rest of the state space including the downward stable equilibrium position. The sliding mode controller uses a switching control action to converge along the specified path(hyperplane) derived from energy equation from a state around the path to desired state(standing position). An optimal control method is also used to guarantee the stability at unstable equilibrium position. Compared with the reported controllers, it is simpler and easier to implement. Experimental results are given to show the effectiveness of this controller.

3-Dimensional Equilibrium Position Searching of HDD/Head System using Multi-Dimensional Newton-Raphson Method (다차원 뉴튼-랩슨 방법을 이용한 하드 디스크/헤드 시스템의 3차원 평형위치 검색)

  • Chang, In-Bae
    • Journal of Industrial Technology
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    • v.15
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    • pp.203-208
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    • 1995
  • This paper suggests the three dimensional steady state searching techniques of hard disk/head system, which has some skew angle with flexure. In order to analyze the steady state behaviors of magnetic head slider, the localized Knudsen number and the localized bearing numbers are sued. For finding the steady state of magnetic head slider under the pre-loaded condition, I proposed multi-dimensional Newton-Raphson method which traces the equilibrium position of magnetic head slider, which has 3-degrees of freedom, using Jacobian matrix. The multi-dimensional Newton-Raphson method is very efficient technique for finding the steady state position of magnetic head slider because it approaches to the equilibrium position with changing three parameters simultaneously.

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Effect of Fluid Viscosity on the Suspension of a Single Particle in Channel Flow (채널 유동에서 점성이 단일 입자 혼합 유동의 suspension에 미치는 영향)

  • Choi, Hyoung-Gwon
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.33 no.3
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    • pp.194-200
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    • 2009
  • Suspension of a single solid particle in a channel flow with a constant pressure gradient is studied numerically. The interaction of a circular particle with a surrounding Newtonian fluid is formulated using a combined formulation. Numerical results are presented using two dimensionless variables: the sedimentation Reynolds number and the generalized Froude number. From the present results, it has been shown that a solid particle is suspended at a smaller generalized Froude number as the viscosity of the surrounding fluid increases. The time taken for equilibrium position is found to be smaller as fluid viscosity increases when both : the sedimentation Reynolds number and the generalized Froude number are the same while, at the same situation, the dimensionless time taken for equilibrium position is to be nearly the same regardless of fluid viscosity when a dimensionless time variable is introduced

Tolerance Analysis for Natural Frequencies of Multi-body Systems in Dynamic Equilibrium State (다물체계의 평형위치에서 고유진동수에 대한 공차해석)

  • Eom, Seung-Man;Choi, Dong-Hwan;Yoo, Hong-Hee
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.17 no.1
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    • pp.65-71
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    • 2007
  • Tolerance analysis method for natural frequencies of multi-body systems having a equilibrium position is suggested in this paper. To perform the tolerance analysis, the Monte-Carlo Method is conventionally employed. However, the Monte-Carlo Method has some weakness; spending too much time for analysis and having a low accuracy and hard to converge in the dynamical unstable area. To resolve these problems, a tolerance analysis method is suggested in this paper. Sensitivity equations of natural frequencies are derived at the equilibrium position. By employing the sensitivity information of mass, damping and stiffness matrices, the sensitivity of natural frequencies can be calculated.