• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.270-275
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• 2003

The nonlinear dynamic characteristic of a straight tube conveying fluid with constraints and an attached mass on the tube is examined in this study. An experimental apparatus composed of an elastomer tube conveying water which has an attached mass and constraints is made and comparisons are done between the theoretical results from non-linear equation of motion of piping system and experimental results. And the results show that the tube is destabilized as the mass of the attached mass increases, and stabilized as the position of the attached mass close to the fixed end. In case of a small end-mass, the system shows rich and different types of periodic solutions. For a constant end-mass, the system undergoes a series of bifurcations after the first Hopf bifurcation, as the flow velocity increases, which causes chaotic motion of the tube eventually.

• Journal of the Korean Society for Precision Engineering
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• v.31 no.10
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• pp.929-934
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• 2014

Reaction force compensation (RFC) mechanism can relieve the vibration of base system caused by acceleration and deceleration of mover. In this paper, we propose a new passive RFC mechanism with a movable additional mass to reduce vibration of the system base as well as displacement of the magnet track. First, equation of motion for the new passive RFC mechanism is derived and simulated to tune design parameters such as masses and spring coefficients. Simulation results show that the vibration of the system base of the stage with the new RFC mechanism.

• Coupled systems mechanics
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• v.7 no.6
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• pp.707-729
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• 2018

The semi-active optimal vibration control of nonlinear torsion-bar suspension vehicle systems under random road excitations is an important research subject, and the boundedness of MR dampers and the uncertainty of vehicle systems are necessary to consider. In this paper, the differential equations of motion of the coupling torsion-bar suspension vehicle system with MR damper under random road excitation are derived and then transformed into strongly nonlinear stochastic coupling vibration equations. The dynamical programming equation is derived based on the stochastic dynamical programming principle firstly for the nonlinear stochastic system. The semi-active bounded parametric optimal control law is determined by the programming equation and MR damper dynamics. Then for the uncertain nonlinear stochastic system, the minimax dynamical programming equation is derived based on the minimax stochastic dynamical programming principle. The worst-case disturbances and corresponding semi-active bounded parametric optimal control are obtained from the programming equation under the bounded disturbance constraints and MR damper dynamics. The control strategy for the nonlinear stochastic vibration of the uncertain torsion-bar suspension vehicle system is developed. The good effectiveness of the proposed control is illustrated with numerical results. The control performances for the vehicle system with different bounds of MR damper under different vehicle speeds and random road excitations are discussed.

• Journal of the Society of Naval Architects of Korea
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• v.43 no.1 s.145
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• pp.22-31
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• 2006

Recent studies have shown that the short time solution of the equation of motion for the rolling of ships is important in deciding the possibility of capsize of ships due to the excessive heel. Since most of known solutions for nonlinear equations of motion are long time or steady periodic solutions, here a simple way is described to get the short time solutions of the Duffing equation, which was chosen for deriving a criterion for the capsize of the ship. With the small external rolling moment, we first assume the state of the small damping and near resonance. Then, for cases when the frequency of the external moment is higher than the resonant one, an inequality was derived as a criterion for the capsize. This gives the range of the initial condition and the magnitude of the external moment which should be avoided for a ship to be safe from capsize. Furthermore, from the linearized equation, it is also shown that a simple and self-explanatory solution can be obtained consistent with that for the case of no damping, which yields the well-known linear growth with time.

• Structural Engineering and Mechanics
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• v.44 no.4
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• pp.521-538
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• 2012

In this study, the transverse vibrations of an axially moving flexible beams resting on multiple supports are investigated. The time-dependent velocity is assumed to vary harmonically about a constant mean velocity. Simple-simple, fixed-fixed, simple-simple-simple and fixed-simple-fixed boundary conditions are considered. The equation of motion becomes independent from geometry and material properties and boundary conditions, since equation is expressed in terms of dimensionless quantities. Then the equation is obtained by assuming small flexural rigidity. For this case, the fourth order spatial derivative multiplies a small parameter; the mathematical model converts to a boundary layer type of problem. Perturbation techniques (The Method of Multiple Scales and The Method of Matched Asymptotic Expansions) are applied to the equation of motion to obtain approximate analytical solutions. Outer expansion solution is obtained by using MMS (The Method of Multiple Scales) and it is observed that this solution does not satisfy the boundary conditions for moment and incline. In order to eliminate this problem, inner solutions are obtained by employing a second expansion near the both ends of the flexible beam. Then the outer and the inner expansion solutions are combined to obtain composite solution which approximately satisfying all the boundary conditions. Effects of axial speed and flexural rigidity on first and second natural frequency of system are investigated. And obtained results are compared with older studies.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.828-833
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• 2004

The performance of a mixed $H_{\infty}/H_2$ design with pole placement constraints based on robust vibration control for a piezo/beam system is investigated. The governing equation of motion for the piezo/beam system is derived by Hamilton's principle. The assumed mode method is used to discretize the governing equation into a set of ordinary differential equation. A robust controller is designed by $H_{\infty}/H_2$ feedback control law that satisfies additional constraints on the closed-loop pole location in the face of model uncertainties, which are derived for a general class of convex regions of the complex plane. These constraints are expressed in terms of linear matrix inequalities (LMIs) approach for the multiobjective synthesis. The validity and applicability of this approach for vibration suppressions of SMART structural systems are discussed by damping out the multiple vibrational modes of the piezo/beam system.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.1026-1031
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• 2001

In this paper. the dynamic characteristics of a super high-speed tilting-pad air bearing(TPGB) used in a turbo expander with high expansion ratio are analyzed. The dynamic behavior and stability of a rotary system supported by two journal air bearings are investigated numerically. The transient response of the shaft is obtained by simultaneously solving the equation of motion of the shaft and the dynamic Reynolds equation. The stiffness and damping coefficients of the bearing are calculated from the loading coefficients of the bearing are calculated from the loading capacity. shaft velocity and displacement by using a curve fitting method. The natural frequencies of the 1st and 2nd rigid modes can be calculated from these coefficients. The theoretical method of a rigid rotor system is verified by experimentsut.

• Journal of Navigation and Port Research
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• v.40 no.6
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• pp.361-368
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• 2016

A ship's rolling motion can make crew and passengers sick and/or apply forces to the structure that cause damage.. Therefore bilge keels are equipped in most ships for anti-rolling. In special cases, anti-rolling tanks (ARTs), fin stabilizers, or gyroscopes can be installed. However, ARTs require a large area to install, and fin stabilizers and gyroscopes are costly to install and expensive to operate. This paper suggests a Anti-rolling pendulum (ARP) to reduce roll motion. ARPs acts like ARTs. However, the ARP has a circular shaped guidance arc instead of the string or wire of a simple pendulum. The device suggested has about 1/ 8 the weight and 1/ 6 the volume of a ART and is more effective. This study derives the nonlinear and linear differential equations of system motion.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.2
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• pp.137-145
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• 2011

This study is proposed to develop a numerical interaction model of the magnetically levitated(maglev) train and guideway. For this purpose, equation of motion for 6-DOF vehicle model, EMS, guideway and guideway irregularity are derived as the state-space equation. In order to solve the state space equations, the present work was performed via matlab simulation using Runge-Kutta method. Through the simulation, the effect of dynamic response of maglev system to different vehicle speeds, guideway rigidity(EI) and masses is investigated.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.05a
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• pp.692-695
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• 2000

This paper is concerned with Accuracy Design of LM Guide System in Machine Tools. Elastic deformation of bearing is calculated by Hertz contact theory and motion error of LM block is analyzed. A new algorithm using block stiffness is proposed fur the analysis of motion accuracy of the table. The best advantage of this algorithm is fast analysis speed because it isn't necessary iteration processes for satisfying equilibrium equation of the table. Motion errors of the table analyzed under artificial form error of rail theoretically and experimentally. Only one of two rails is bent by putting a thickness gauge into horizontal direction. This form error of rail is measured by gap sensor against the other rail. Then, motion errors of the table are predicted by proposed new algorithm theoretically and measured by laser interferometer. Measurements are carried out by changing the preload and thickness. The results show that the table motion errors are reduced from 1/2 to 1/60 times than form error of rail according to its height and width. And the effect of preloading is almost negligible.