• Structural Engineering and Mechanics
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• v.30 no.4
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• pp.427-444
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• 2008

A mathematical model for the nonlinear dynamics of a rotating beam with flexible root attached to a rotating hub with elastic foundation is developed. The model is developed based on the large planar and flexural deformation theory and the potential energy method to account for axial shortening due to bending deformation. In addition the exact nonlinear curvature is used in the system potential energy. The Lagrangian dynamics and the assumed mode method is used to derive the nonlinear coupled equations of motion hub rotation, beam tip deflection and hub horizontal and vertical displacements. The derived nonlinear model is simulated numerically and the results are presented and discussed for the effect of root flexibility, hub stiffness, torque type, torque period and excitation frequency and amplitude on the dynamic behavior of the rotating beam-hub and on its stability.

• Proceedings of the KWS Conference
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• 2002.10a
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• pp.600-605
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• 2002

The keyhole formed by high energy density laser-material interaction periodically collapses due to surface tension of the molten metal in partial penetration welds. The collapse sometimes traps a void at the bottom of the keyhole, and it remains as welding defects. This phenomenon is seen as one cause of the instability of the keyhole during laser beam welding. Thus, it seems likely that improving the stability of the keyhole can reduce voids and uniform the penetration depth. The goal of this work is to develop techniques for controlling laser weld keyhole dynamics to reduce weld defects such as voids and inconsistent penetration. Statistical analysis of the penetration depth signals in glycerin determined that keyhole dynamics are chaotic. The chaotic nature of keyhole fluctuations and the ability of laser power modulation to control them have been demonstrated by high-speed video images of laser welds in glycerin. Additionally, an incident leading beam angle is applied to enhance the stability of the keyhole. The quasi-sinusoidal laser beam power of 400Hz frequency and 15$^{\circ}$ incident leading beam angle were determined to be the optimum parameters for the reduction of voids. Finally, chaos analyses of uncontrolled signals and controlled signals were done to show the effectiveness of modulation on the keyhole dynamics. Three-dimensional phase plots for uncontrolled system and controlled system are produced to demonstrate that the chaotic keyhole dynamics is converted to regular periodic behavior by control methods: power modulation and incident leading beam angle.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11a
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• pp.403-403
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• 2002

The use of frequency-dependent spectral element matrix (or exact dynamic stiffness matrix) in structural dynamics is known to provide very accurate solutions, while reducing the number of degrees-of-freedom to resolve the computational and cost problems. Thus, in the present paper, the spectral element model is formulated for the axially moving Timoshenko beam under a uniform axial tension. (omitted)

• International Journal of Precision Engineering and Manufacturing
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• v.3 no.4
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• pp.54-63
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• 2002

In recent years, mechanical systems such as high speed vehicles and railway trains moving on elastic beam structures have become a very important issue to consider. In this paper, a general approach, which can predict the dynamic behavior of a constrained mechanical system moving on a flexible beam structure, is proposed. Various supporting conditions for the foundation support are considered for the elastic beam structure. The elastic structure is assumed to be a non-uniform and linear Bernoulli-Euler beam with a proportional damping effect. Combined differential-algebraic equation of motion is derived using the multi-body dynamics theory and the finite element method. The proposed equations of motion can be solved numerically using the generalized coordinate partitioning method and predictor-corrector algorithm, which is an implicit multi-step integration method.

• Structural Engineering and Mechanics
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• v.30 no.3
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• pp.369-382
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• 2008

An oscillator of two lumped masses linked through a vertical spring moves forward in the horizontal direction, initially at a certain height, over a horizontal Euler beam and descends on it due to its own weight. Vibration of the beam and the oscillator is excited at the onset of the ensuing impact. The impact produced by the descending oscillator is assumed to be either perfectly elastic or perfectly plastic. If the impact is perfectly elastic, the oscillator bounces off and hits the beam a number of times as it moves forward in the longitudinal direction of the beam, exchanging its dynamics with that of the beam. If the impact is perfectly plastic, the oscillator (initially) sticks to the beam after its first impact and then may separate and reattach to the beam as it moves along the beam. Further events of separation and reattachment may follow. This interesting and seemingly simple dynamic problem actually displays rather complicated dynamic behaviour and has never been studied in the past. It is found through simulated numerical examples that multiple events of separation and impact can take place for both perfectly elastic impact and perfectly plastic impact (though more of these in the case of perfectly elastic impact) and the dynamic response of the oscillator and the beam looks noisy when there is an event of impact because impact excites higher-frequency components. For the perfectly plastic impact, the oscillator can experience multiple events of consecutive separation from the beam and subsequent reattachment to it.

• Journal of the Korean Vacuum Society
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• v.4 no.S2
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• pp.139-147
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• 1995

The mechanism of the ionized cluster beam deposition has been studied using Molecular Dynamics Simulation. The Embedded Atom Method(EAM) potential were used in the simulation. The impact of a Au95-cluster on Au(100) substrate was studied for the impact energies 0.15-10eV/atom. The dependency of the impact energy of cluster beam was observed. For the cluster energy impact of 10eV per atom, the defects on surface were created and the cluster embedded into substrate as an amorphous state. For the energy of 0.5eV per atom, the defect free homoepitaxial growth was observed and atomic scale nucleation was formated, which are in good agreement with experiment. Thus molecular dynamics simulation is very useful to study the mechanism of the ionized cluster beam deposition.

• International Journal of Precision Engineering and Manufacturing
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• v.3 no.4
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• pp.64-71
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• 2002

Recently, mechanical systems such as a high-speed vehicles and railway trains moving on flexible beam structures have become a very important issue to consider. Using the general approach proposed in the first part of this paper, it is possible to predict motion of the constrained mechanical system and the elastic structure, with various kinds of foundation supporting conditions. Combined differential-algebraic equation of motion derived from both multibody dynamics theory and finite element method can be analyzed numerically using a generalized coordinate partitioning algorithm. To verify the validity of this approach, results from the simply supported elastic beam subjected to a moving load are compared with the exact solution from a reference. Finally, parametric study is conducted for a moving vehicle model on a simply supported 3-span bridge.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.1066-1071
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• 2002

The use of frequency-dependent spectral element matrix (or exact dynamic stiffness matrix) in structural dynamics is known to provide very accurate solutions, while reducing the number of degrees-of-freedom to resolve the computational and cost problems. Thus, in the present paper, the spectral element model is formulated for the axially moving Timoshenko beam under a uniform axial tension. The high accuracy of the present spectral element is then verified by comparing its solutions with the conventional finite element solutions and exact analytical solutions. The effects of the moving speed and axial tension on the vibration characteristics, the dispersion relation, and the stability of a moving Timoshenko beam are investigated, analytically and numerically.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.11a
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• pp.534-539
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• 2000

A flexible rotating beam test bed has been developed for experimental verification of flexible rotating beam dynamics and vibration. It consists of a flexible arm, harmonic driver reducer, ac servo motor and DSP board with PC. To capture the motion induced stiffening effects of the flexible rotating beam, substructuring model has been established in multibody dynamics simulation. Substructuring model provides better results comparing with experimental data.

• International Journal of Precision Engineering and Manufacturing
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• v.5 no.4
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• pp.50-60
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• 2004

A very flexible beam can be used to model various types of continuous mechanical parts such as cables and wires. In this paper, the dynamic properties of a very flexible beam, included in a multibody system, are analyzed using absolute nodal coordinates formulation, which is based on finite element procedures, and the general continuum mechanics theory to represent the elastic forces. In order to consider the dynamic interaction between a continuous large deformable beam and a rigid multibody system, a combined system equations of motion is derived by adopting absolute nodal coordinates and rigid body coordinates. Using the derived system equation, a computation method for the dynamic stress during flexible multibody simulation is presented based on Euler-Bernoulli beam theory, and its reliability is verified by a commercial program NASTRAN. This method is significant in that the structural and multibody dynamics models can be unified into one numerical system. In addition, to analyze a multibody system including a very flexible beam, formulations for the sliding joint between a very deformable beam and a rigid body are derived using a non-generalized coordinate, which has no inertia or forces associated with it. In particular, a very flexible catenary cable on which a multibody system moves along its length is presented as a numerical example.