• International Journal of Aeronautical and Space Sciences
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• v.4 no.2
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• pp.1-8
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• 2003

Satellite formation flying is the placing micro-satellites with the same mission into nearby orbits to form a cluster. Clohessy-Wiltshire equations are used to describe the relative motion and control strategies between satellites within a cluster, which are known as Hill's equations. Even though Hill's equations are powerful in determining initial conditions for the satellite formation flying, they can not accurately express the relative motion under J2 perturbation. Some methods have been developed for the determination of initial conditions to avoid limits of Hill's equation. This paper gives a new method of determining initial conditions using mean elements. For this research mean elements were transformed to osculating elements using Brouwer's theory and the orbit was propaeated with the consideration of J2-J8 to get a relative position. The results show that satellites within a cluster are maintained in the desired boundary for long period and the method is effective on a fuel saving for satellite formation flying.

• Journal of Astronomy and Space Sciences
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• v.20 no.4
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• pp.365-374
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• 2003

Satellite formation flying is currently an active area of research in the aerospace engineering. So it has been researched by various authors. In this study, a tracking controller using sliding mode techniques was designed to control a satellite for the satellite formation flying. In general, Hill's equations are used to describe the relative motion of the follower satellite with respect to the leader satellite. However the modified Hill's equations considering the $J_2$ perturbation were used for the design of sliding mode controller. The extended Kalman filter was applied to estimate the state vector based on the measurements of relative distance and velocity between two satellites. The simulation results show that the follower satellite tracks the desired trajectory well by thruster operations based on the sliding mode control law.

• Journal of Korean Society for Atmospheric Environment
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• v.14 no.3
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• pp.219-228
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• 1998

In the present investigation, a numerical model developed for the prediction of the wind flow over complex terrain is validated by comparing with the field experiments. For the solution of the Reynolds - Averaged Clavier- stokes equations which are the governing equations of the microscale atmospheric flow, the model is constructed based on the finite-volume formulation and the SIMPLEC pressure-correction algorithm for the hydrodynamic computation. The boundary- fitted coordinate system is employed for the detailed depiction of topography. The boundary conditions and the modified turbulence constants suitable for an atmospheric boundary- layer are applied together with the k- s turbulence model. The full- scale experiments of Cooper's Ridge, Kettles Hill and Askervein Hill are chosen as the validation cases . Comparisons of the mean flow field between the field measurements and the predicted results show good agreement. In the simulation of the wind flow over Askervein Hill , the numerical model predicts the three dimensional flow separation in the downslope of the hill including the blockage effect due to neighboring hills . Such a flow behavior has not been simulated by the theoretical predictions. Therefore, the present model may offer the most accurate prediction of flow behavior in the leeside of the hill among the existing theoretical and numerical predictions.

• Bulletin of the Korean Space Science Society
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• 2003.10a
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• pp.41-41
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• 2003

Satellite formation flying is currently an active area of research in the aerospace engineering. There are many categories for this research such as the determination of initial conditions, formation keeping, configuration and reconfiguration. In this study, a tracking controller using sliding mode techniques is designed to control a satellite for the satellite formation flying. In general, Hill's equations are used to describe the relative motion of the follower satellite with respect to the leader satellite. But, the modified Hill's equations considering J2 perturbation were used for the design of sliding mode controller. Sliding mode control law causes the chattering phenomenon because it is a discontinuous control. Dead-zone was used to avoid the chattering. The Extended Kalman filter was applied to estimate the state vector based on the measurements of relative distance and velocity between two satellites.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2013.04a
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• pp.141-146
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• 2013

This research investigates the stability analysis for the rotating and the stationary grooved journal bearing. The dynamic coefficients of the journal bearing are calculated by using FEM and the perturbation method. When journal bearing is in whirling motion, the dynamic coefficients have time-varying components as a sine wave due to the reaction force of oil film toward the center of journal even in the steady state. The solutions for the equations of motion can be assumed as the Fourier series expansion. The equations of motion can be rewritten as the linear algebraic equations with respect to the Fourier coefficients. Then, stability of the grooved journal bearing can be calculated by Hill's infinite determinant. The periodic function of dynamic coefficients is derived using Fourier Fast Transform(FFT).The stability of journal bearing is determined as rotating speed increases and the stability of rotating grooved journal bearing is compared and discussed with the stability of stationary grooved journal bearing.

• Structural Engineering and Mechanics
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• v.61 no.4
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• pp.497-510
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• 2017

A framed structure may be composed of two sub-structures, which are linked by a hinged joint. One sub-structure is the primary system and the other is the secondary system. The primary system, which is subjected to the periodic external load, can give rise to an auto-parametric resonance of the second system. Considering the geometric-stiffness effect produced by the axially internal force, the element equation of motion is derived by the extended Hamilton's principle. The element equations are then assembled into the global non-homogeneous Mathieu-Hill equations. The Newmark's method is introduced to solve the time-history responses of the non-homogeneous Mathieu-Hill equations. The energy-growth exponent/coefficient (EGE/EGC) and a finite-time Lyapunov exponent (FLE) are proposed for determining the auto-parametric instability boundaries of the structural system. The auto-parametric instabilities are numerically analyzed for the two frames. The influence of relative stiffness between the primary and secondary systems on the auto-parametric instability boundaries is investigated. A phenomenon of the "auto-parametric internal resonance" (the auto-parametric resonance of the second system induced by a normal resonance of the primary system) is predicted through the two numerical examples. The risk of auto-parametric internal resonance is emphasized. An auto-parametric resonance experiment of a ${\Gamma}$-shaped frame is conducted for verifying the theoretical predictions and present calculation method.

• International Journal of Fluid Machinery and Systems
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• v.8 no.3
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• pp.169-182
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• 2015

When simulating the dynamic behaviour of a hydro power plant, it is essential to have a good representation of the turbine behaviour. The pressure transients in the system occurs because the flow changes, which the turbine defines. The flow through the turbine is a function of the pressure, the speed of rotation and the wicket gate opening and is, most often described in a performance diagram or Hill diagram. In the Hill diagram, the efficiency is drawn like contour lines, hence the name. A turbines Hill diagram is obtained by performance tests on scaled model in a laboratory. However, system dynamic simulations have to be performed in the early stage of a project, before the turbine manufacturer has been chosen and the Hill diagram is known. Therefore one have to rely on diagrams for a turbine with similar speed number. The Hill diagram is drawn through measured points, so for using the diagram in a simulation program, one have to iterate in the diagram based on curve fitting of the measured points. This paper describes an alternative method. By means of the Euler turbine equation, it is possible to set up two differential equations which represents the turbine performance with good enough accuracy for the dynamic simulations. The only input is the turbine's main geometry, the runner blade in- and outlet angle and the guide vane angle at best efficiency point of operation (BEP). In the paper, simulated turbine characteristics for a high head Francis turbine, and for a reversible pump turbine are compared with laboratory measured characteristics.

• Structural Engineering and Mechanics
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• v.8 no.2
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• pp.193-205
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• 1999

A formulation for the dynamic stability analysis of cylindrical shells resting on elastic foundations is presented. In this previously not studied problem, a normal-mode expansion of the partial differential equations of motion, which includes the effects of the foundation as well as a harmonic axial loading, yields a system of Mathieu-Hill equations the stability of which is analyzed using Bolotin's method. The present study examines the effects of the elastic foundation on the instability regions of the cylindrical shell for the transverse, longitudinal and circumferential modes.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.12
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• pp.2647-2655
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• 2002

This research presents an analytical model to investigate the stability due to the ball bearing waviness i n a rotating system supported by two ball bearings. The stiffness of a ball bearing changes periodically due to the waviness in the rolling elements as the rotor rotates, and it can be calculated by differentiating the nonlinear contact forces. The linearized equations of motion can be represented as a parametrically excited system in the form of Mathieu's equation, because the stiffness coefficients have time -varying components due to the waviness. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as the simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving the Hill's infinite determinant of these algebraic equations. The validity of this research is proved by comparing the stability chart with the time responses of the vibration model suggested by prior researches. This research shows that the waviness in the rolling elements of a ball bearing generates the time-varying component of the stiffness coefficient, whose frequency is called the frequency of the parametric excitation. It also shows that the instability takes place from the positions in which the ratio of the natural frequency to the frequency of the parametric excitation corresponds to i/2 (i=1,2,3..).

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.05a
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• pp.181-189
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• 2002

This research presents an analytical model to investigate the stability due to the ball bearing waviness in a rotating system supported by two ball bearings. The stiffness of a ball bearing changes periodically due to the waviness in the rolling elements as the rotor rotates, and it can be calculated by differentiating the nonlinear contact forces. The linearized equations of motion can be represented as a parametrically excited system in the form of Mathieu's equation, because the stiffness coefficients have time-varying components due to the waviness. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as the simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving the Hill's infinite determinant of these algebraic equations. The validity of this research is proved by comparing the stability chart with the time responses of the vibration model suggested by prior researches. This research shows that the waviness in the rolling elements of a ball bearing generates the time-varying component of the stiffness coefficient, whose frequency is called the frequency of the parametric excitation. It also shows that the instability takes place from the positions in which the ratio of the natural frequency to the frequency of the parametric excitation corresponds to i/2 (i= 1,2,3..).