• Title/Summary/Keyword: equations of motion

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Finite Element Modal Analysis of a Spinning Flexible Disk-spindle System Supported by Hydro Dynamic Bearings and Flexible Supporting Structures in a HDD (유연한 지지 구조와 유체 동압 베어링으로 지지되는 HDD의 회전 유연 디스크-스핀들 시스템에 대한 유한 요소 고유 진동 해석)

  • Han, Jaehyuk;Jang, Gunhee
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.15 no.3 s.96
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    • pp.251-258
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    • 2005
  • The free vibration of a spinning flexible disk-spindle system supported by hydro dynamic bearings (HDB) in an HDD is analyzed by FEM. The spinning flexible disk is described using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. It is discretized by annular sector element. The rotating spindle which includes the clamp, hub, permanent magnet and yoke, is modeled by Timoshenko beam including the gyroscopic effect. The flexible supporting structure with a complex shape which includes stator core, housing, base plate, sleeve and thrust pad is modeled by using a 4-node tetrahedron element with rotational degrees of freedom to satisfy the geometric compatibility. The dynamic coefficients of HDB are calculated from the HDB analysis program, which solves the perturbed Reynolds equation using FEM. Introducing the virtual nodes and the rigid link constraints defined in the center of HDB, beam elements of the shaft are connected to the solid elements of the sleeve and thrust pad through the spring and damper element. The global matrix equation obtained by assembling the finite element equations of each substructure is transformed to the state-space matrix-vector equation, and the associated eigen value problem is solved by using the restarted Arnoldi iteration method. The validity of this research is verified by comparing the numerical results of the natural frequencies with the experimental ones. Also the effect of supporting structures to the natural modes of the total HDD system is rigorously analyzed.

Finite Element Modal Analysis of a Spinning Flexible Disk-Spindle System Supported by Hydro Dynamic Bearings and Flexible Supporting Structures In a HDD (유연한 지지 구조와 유체 동압 베어링으로 지지되는 HDD의 회전 유연 디스크-스핀들 시스템에 대한 유한 요소 고유 진동 해석)

  • 한재혁;장건희
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2003.11a
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    • pp.572-578
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    • 2003
  • The free vibration of a spinning flexible disk-spindle system supported by hydro dynamic bearings in a HDD is analyzed by FEM. The spinning flexible disk is described using Kirchhoff plate theory and von Karman non-linear strain, and its rigid body motion is also considered. It is discretized by annular sector element. The rotating spindle which includes the clamp, hub, permanent magnet and yoke, is modeled by Timoshenko beam including the gyroscopic effect. The flexible supporting structure with a complex shape which includes stator core, housing, base plate, sleeve and thrust pad is modeled by using a 4-node tetrahedron element with rotational degrees of freedom to satisfy the geometric compatibility. The dynamic coefficients of HDB are calculated from the HDB analysis program, which solves the perturbed Raynolds equation using FEM. Introducing the virtual nodes and the rigid link constraints defined in the center of HDB, beam elements of the shaft are connected to the solid elements of the sleeve and thrust pad through the spring and damper element. The global matrix equation obtained by assembling the finite element equations of each substructure is transformed to the state-space matrix-vector equation, and the associated eigenvalue problem is solved by using the restarted Arnoldi iteration method. The validity of this research is verified by comparing the numerical results of the natural frequencies with the experimental ones. Also the effect of supporting structures to the natural modes of the total HDD system is rigorously analyzed.

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Dynamic Interaction Analysis of Low, Medium and Super-high Speed Maglev and Guideways (열차-교량의 동적 상호작용을 고려한 중·저속 및 초고속 자기부상열차와 가이드웨이의 동특성 해석)

  • Min, Dong-Ju;Jung, Myung-Rag;Lee, Jun-Seok;Kim, Lee-Hyeon;Kim, Moon-Young
    • Journal of the Earthquake Engineering Society of Korea
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    • v.15 no.3
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    • pp.1-9
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    • 2011
  • The purpose of this study is to examine the dynamic characteristics of low, medium and high speed Maglev trains and guideways through dynamic interaction analysis. The coupled dynamic equations of motion for a vehicle of 10-dof and the associated guideway girders are developed by superposing vibration modes of the girder itself. The controller used in the UTM-01 Maglev vehicle is adopted to control the air gap between the bogie and guideway in this study. The effect of roughness, the guideway deflection-ratio and vehicle speed on the dynamic response of the maglev vehicle and guideway are then investigated using the 4th Runge-Kutta method. From the numerical simulation, it is found that the air gap increases with an increase of vehicle speed and the roughness condition. In particular, the dynamic magnification factor of the guideway girder is small at low and medium speeds, but the factor is noticeable at super-high speeds.

Numerical analysis of 2-DOF motions of an ocean floater with sloshing effects (슬로싱 영향을 동반한 해양 부유체의 2자유도 거동 수치해석)

  • Kim, HyunJong;Choi, Yoon-Hwan;Lee, Yeon-Won
    • Journal of Advanced Marine Engineering and Technology
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    • v.37 no.6
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    • pp.617-622
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    • 2013
  • The sloshing of liquid inside an ocean floater is caused by disturbances due to waves. For the analysis of sloshing impact within the floater and that of waves on the floater, the coupled analysis method is used. The Stokes $5^{th}$ order non-linear wave theory equations were adapted for wave making. Furthermore, Navier-Stokes equation and Shear-Stress Transport (SST) turbulent model were used to Computational Fluid dynamics, where the ocean floater motions are considered the heave and the pitch motion. The results obtained confirms the mutual relationship between the rigid body motions and that of sloshing, where the sloshing behaviour within the floater is characterized by the wave effects on the floater.

Nonlinear Dynamic Analysis of Reinforced Concrete Shells Using Layered Elements with Drilling DOF (회전자유도를 갖는 층상화 요소를 이용한 철근콘크리트 쉘구조의 비선형 동적해석)

  • 김태훈;이상국;신현목
    • Journal of the Earthquake Engineering Society of Korea
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    • v.5 no.6
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    • pp.21-27
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    • 2001
  • In this paper, a nonlinear finite element procedure is presented for the dynamic analysis of reinforced concrete shells. A computer program, named RCAHEST(reinforced concrete analysis in higher evaluation system technology), for the analysis of reinforced concrete structures was used. A 4-node flat shell element will drilling rotational stiffness is used for spatial discretization. The layered approach is used to discretize behavior of concrete and reinforcement through the thickness. Material nonlinearity is taken into account by comprising tensile, compressive and shear models of cracked concrete and a model of reinforcing steel. The smeared crack approach is incorporated. Solution of the equations of motion is obtained by numerical integration using Hilber-Hughes-Taylor(HHT) algorithm. The proposed numerical method for the nonlinear dynamic analysis of reinforced concrete shells is verified by comparison with reliable analytical results.

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A Study on Dynamic Characteristics of Directional Control Logic Valve (방향제어 조직밸브의 동특성에 관한 연구)

  • Lee, Il-Yeong;Oh, Se-Kyung
    • Journal of the Korean Society of Fisheries and Ocean Technology
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    • v.24 no.4
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    • pp.172-179
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    • 1988
  • A cartridge type hydraulic logic valve consists of simple two port valve whose poppet is closed or opened by means of pressure signal of a pilot line. Accordingly, the logic valve can be used not only for direction, flow and pressure control purpose but also for versatile function valve which enables all above mentioned functions. In addition, the valve has little internal leakage and pressure loss, superior response characteristics and easiness in making small block type valve. The above mentioned good performances being recognized recently, the logic valve has been used widely in the large scale hydraulic system such as a hydraulic press system, for the performance requirements of high speed operation and precise control characteristics. However, there are scarce reports until now, except for a few ones from Aachen Institute of Technology in West Germany, so it is necessary to be studied on development and investigation for practical application. This paper showed that the static and dynamic characteristics of a logic valve when the logic valve is used for directional control, to investigate the relations between the valve operating characteristics and the valve design conditions. From the above mentioned procedure, it was ascertained that the valve operation characteristics obtained by numerical analysis showed good agreements with experimental results. The representative results obtained are as follows; 1. During the valve is closing, the poppet velocity is almost constant in the logic valve. 2. The pilot pressure P sub(3) and the resistance R in the pilot line have much influences on the valve operation time. 3. Spring strength have not such a severe influence on the valve operating time. 4. The operation characteristics of the logic valve can be estimated with good accuracy comparatively by numerical analysis with the equations describing poppet motion.

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A Study on Efficiency Improvement of the Catenary-Pantograph Dynamic Interaction Analysis Program using Shift Forward Method (Shift Forward 방법을 이용한 가선계-판토그래프 동적 상호작용 해석 프로그램의 효율성 향상에 관한 연구)

  • Lee, Jin-Hee;Park, Tae-Won
    • Journal of the Korean Society for Railway
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    • v.15 no.6
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    • pp.572-578
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    • 2012
  • In the electric railway vehicles, securing stable current collection performance is an important factor which determines the quality of operation and the maximum speed. In order to predict such current collection performance, various analysis methods have been proposed for a long time. Also, investigations for improving the accuracy of the results and the efficiency of the analysis process have been performed. In this paper, a method for the efficiency improvement has been proposed. This method is based on the basic concept that the system equations of motion of a catenary numerical model include only interactive range with a pantograph. In this paper, an algorithm and generalized process for applying proposed method are introduced. Also, validity of the results and utility of the method was verified and studied.

A Numerical Study on Hydrodynamic Interactions between Dynamic Positioning Thrusters (동적위치제어용 스러스터 사이의 유체역학적 상호작용에 대한 수치해석 연구)

  • Jin, Doo Hwa;Lee, Sang Wook
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.41 no.6
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    • pp.373-380
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    • 2017
  • In this study, we conducted computational fluid dynamics (CFD) simulations for the unsteady hydrodynamic interaction of multiple thrusters by solving Reynolds averaged Navier-Stokes equations. A commercial CFD software, STAR-CCM+ was used for all simulations by employing a ducted thruster model with combination of a propeller and No. 19a duct. A sliding mesh technique was used to treat dynamic motion of propeller rotation and non-conformal hexahedral grid system was considered. Four different combinations in tilting and azimuth angles of the thrusters were considered to investigate the effects on the propulsion performance. We could find that thruster-hull and thruster-thruster interactions has significant effect on propulsion performance and further study will be required for the optimal configurations with the best tilting and relative azimuth angle between thrusters.

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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Development of Multi-Purpose Satellite 2 with Deployable Solar Arrays: Part 1. Dynamic Modeling (다목적2호기 태양전지판의 전개시스템 개발: PART 1. 동적 모델링)

  • Gwak,Mun-Gyu;Heo,Seok
    • Journal of the Korean Society for Aeronautical & Space Sciences
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    • v.31 no.9
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    • pp.38-45
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    • 2003
  • This research is concerned with the dynamic modeling of the multi-purpose satellite with deployable solar arrays equipped with strain energy hinges(SEH). To this end, we proposed the use of the equivalent torsional spring for the SEH and derived the equations of motion assuming that the satellite and solar arrays are being rigid. We also considered the effect of the support string for the ground experiment model, which has been observed as a critical factor affecting the deployment in the ground experiments. From the numerical simulation results, it is found that solar arrays are deployed in a similar pattern but the hub motions are different because of the support strings. It was concluded that the non-gravity deployment of the solar arrays can be approximately simulated by the ground experimental facility. The effects of the support string are also investigated by varying the length of the string. It was found that the current length of the string is adequate for the ground experiment. Ground experimental results will follow.