• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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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.

• Journal of Astronomy and Space Sciences
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• v.15 no.1
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• pp.209-220
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• 1998

The stability problem of steady motion of a rigid body with multi-elastic appendages and multi-liquid-filled cavities, in the presence of no external forces or torque, is considered in this paper. The flexible appendages are modeled as the clamped -free-free-free rectangular plates, or/and as the discrete mass- spring sub-system. The motion of liquid in every single ellipsoidal cavity is modeled as the uniform vortex motion with a finite number of degrees of freedom. Assuming that stationary holonomic constraints imposed on the body allow its rotation about a spatially fixed axis, the equation of motion for such a systematic configuration can be very complex. It consists of a set of ordinary differential equations for the motion of the rigid body, the uniform rotation of the contained liquids, the motion of discrete elastic parts, and a set of partial differential equations for the elastic appendages supplemented by appropriate initial and boundary conditions. In addition, for such a hybrid system, under suitable assumptions, their equations of motion have four types of first integrals, i.e., energy and area, Helmholtz' constancy of liquid - vortexes, and the constant of the Poisson equation of motion. Chetaev's effective method for constructing Liapunov functions in the form of a set of first integrals of the equations of the perturbed motion is employed to investigate the sufficient stability conditions of steady motions of the complete system in the sense of Liapunov, i.e., with respect to the variables determining the motion of the solid body and to some quantities which define integrally the motion of flexible appendages. These sufficient conditions take into account the vortexes of the contained liquids, the vibration of the flexible components, and coupling among the liquid-elasticity solid.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.5
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• pp.756-768
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• 1997

In order to control a dynamic gait of quadrupedal walking robot, the equations of motion of the whole mechanism are required. In this research, the equations of motion are formulated analytically using Kane's dynamic approach. As a dynamic gait model, a trot gait has been adopted. The degree of freedom of whole mechanism could be reduced to 7 by idealizing the kinematic feature of the trot gait. Using the equations of motion formulated, the results of the redundant-joint torque analysis and the simulation of dynamic walking motion are presented.

• Journal of Mechanical Science and Technology
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• v.18 no.2
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• pp.193-202
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• 2004

This paper presents a computer method for the dynamic analysis of a system of rigid bodies in plane motion. The formulation rests upon the idea of replacing a rigid body by a dynamically equivalent constrained system of particles. Newton's second law is applied to study the motion of the resulting system of particles without introducing any rotational coordinates. A velocity transformation is used to transform the equations of motion to a reduced set. For an open-chain, this process automatically eliminates all of the non-working constraint forces and leads to an efficient integration of the equations of motion. For a closed-chain, suitable joints should be cut and few cut-joints constraint equations should be included. An example of a closed-chain is used to demonstrate the generality and efficiency of the proposed method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.10a
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• pp.189-196
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• 1996

Vibration of a beam translating over supports in vertical motion is investigated in this paper. Equations of motion are formulated using the virtual work principle by regarding the supports as kinematical constraints imposed on an unrestrained beam and by discretizing the beam via the assumed mode method. Differential-algebraic equations of motion are derived and reduced to differential equations in independent generalized coordinates by the generalized coordinate partitioning method. Geometric stiffness of the beam due to translating motion is considered and how the geometric stiffness of beam affects dynamic stability is also investigated. Instability of the beam. in various conditions is also investigated using Floquet theory and then the results are verified through the dynamic response analysis. Results of numerical simulation are presented for various prescribed motions of the beam.

• Journal of KSNVE
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• v.7 no.5
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• pp.773-780
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• 1997

Using Generalized Inverse Method presented by Udwadia and Kalaba in 1992, we can obtain equations to exactly describe the motion of constrained systems. When the differential equations are numerically integrated by any numerical integration scheme, the numerical results are generally found to veer away from satisfying constraint equations. Thus, this paper deals with the numerical integration of the differential equations describing constrained systems. Based on Baumgarte method, we propose numerical methods for reducing the errors in the satisfaction of the constraints.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.10
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• pp.915-922
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• 2010

This paper presents an efficient method for determining the forced response of a spinning flexible disk-spindle system supported by fluid dynamic bearings(FDBs) in a computer hard disk drive(HDD). The spinning flexible disk-spindle system is represented by the asymmetric finite element equations of motion originating from the asymmetric dynamic coefficients of the FDBs and the gyroscopic moment of a spinning disk-spindle system. The proposed method utilizes only the right eigenvectors of the eigenvalue problem to transform the large asymmetric finite element equations of motion into a small number of coupled equations, guaranteeing the accuracy of their numerical integration. The results are then back-substituted into the equations of motion to determine the forced response. The effectiveness of the proposed method was verified by comparing it with the responses from the classical methods of mode superposition with the general eigenvalue problems, and mode superposition with modal approximation. The proposed method was shown to be effective in determining the forced response represented by the asymmetric finite element equations of motion of a spinning flexible disk-spindle system supported by FDBs.

• Proceedings of the KIEE Conference
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• 2000.11d
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• pp.765-768
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• 2000

Linearization of the biped dynamic equations and design of linear controller for the linearized equations are studied in this paper. The biped robot with inverted pendulum type trunk, used to stabilize the dynamic balancing of the biped robot during dynamic walking period, is modelled with 14 DOF and simulated. Despite of well defined linear control theories so far, the linear control methods was limited to the applications for a walking robot, because they have been inherently strong nonlinear properties, such as a modeling parameter uncertainties, external forces as noise, inertial and Coriolis terms by three dimensional modeling and so on. To linearize the nonlinear equations of motion of biped robot on MIMO and time varying linear equations of motion, 1st order Taylor series is used to formulate the linear equation. And a 2nd order numerical perturbation method Is used to approximate partial differential equations. Using the linearized equations of motion, a linear controller is designed by pole placement method with feed forward compensation. Using the obtained linearized equations and linear controller, the continuous walking simulation is performed.

• Journal of the Korean Society for Precision Engineering
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• v.22 no.4
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• pp.128-135
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• 2005

Overhead crane systems consist of trolley, girder, rope, objects, trolley motor, girder motor, and hoist motor. The dynamic system of these systems becomes a nonlinear state equations. These equations are obtained by the nonlinear equations of motion which are derived from transfer functions of driving motors and equations of motion for objects. From these state equations, Lyapunov functions of overhead crane systems are derived from integral method. These functions secure stability of autonomous overhead crane systems. Also constraint equations of driving motors of trolley, girder, and hoist are derived from these functions. From the results of computer simulation, it is founded that overhead crane systems is secure.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.67 no.3
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• pp.427-432
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• 2018

This paper uses a recursive least squares method to estimate the projectile motion trajectory of an object in real time. The equations of motion of the object are obtained considering the air resistance which occurs in the actual experiment environment. Because these equations consider air resistance, parameter estimation of nonlinear terms is required. However, nonlinear recursive least squares estimation is not suitable for estimating trajectory of projectile in that it requires a lot of computation time. Therefore, parameter estimation for real-time trajectory prediction is performed by recursive least square estimation after using Taylor series expansion to approximate nonlinear terms to polynomials. The proposed method is verified through experiments by using VICON Bonita motion capture system which can get three dimensional coordinates of projectile. The results indicate that proposed method is more accurate than linear Kalman filter method based on the equations of motion of projectile that does not consider air resistance.