• Journal of Korean Association for Spatial Structures
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• v.18 no.3
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• pp.83-91
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• 2018

In this study, we investigated the dynamic stability of the system and the semi-analytical solution of the shallow arch. The governing equation for the primary symmetric mode of the arch under external load was derived and expressed simply by using parameters. The semi-analytical solution of the equation was obtained using the Taylor series and the stability of the system for the constant load was analyzed. As a result, we can classify equilibrium points by root of equilibrium equation, and classified stable, asymptotical stable and unstable resigns of equilibrium path. We observed stable points and attractors that appeared differently depending on the shape parameter h, and we can see the points where dynamic buckling occurs. Dynamic buckling of arches with initial condition did not occur in low shape parameter, and sensitive range of critical boundary was observed in low damping constants.

• Earthquakes and Structures
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• v.26 no.2
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• pp.163-174
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• 2024

Dynamic equilibrium equations for finite element analysis were derived for the free field one-dimensional shear wave propagation through the horizontally layered soil deposits with the elastic half-space. We expressed Rayleigh's viscous damping consisting of mass and stiffness proportional terms. We considered two cases where damping matrices are defined in the total and relative displacement fields. Two forms of equilibrium equations are presented; one in terms of total motions and the other in terms of relative motions. To evaluate the performance of new equilibrium equations, we conducted two sets of site response analyses and directly compared them with the exact closed-form frequency domain solution. Results show that the base shear force as earthquake load represents the simpler form of equilibrium equation to be used for the finite element method. Conventional finite element procedure using base acceleration as earthquake load predicts exact solution reasonably well even in soil deposits with unrealistically high damping.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2005.04a
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• pp.408-415
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• 2005

Existing results of some related experiments report that variation in the magnitude of prestressing force may leads to a change of dynamic properties of a PSC girder system. Since a usual dynamic equilibrium equation doesn't explain these phenomena, a modified dynamic equilibrium equation is derived in this paper by considering prestressing force as an internal energy of the system. The derived equation is applied to a modified beam element model is proposed. The proposed model validated by comparing the natural frequencies computed by the model with those from an existing experiment result.

• Laser Solutions
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• v.5 no.1
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• pp.23-31
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• 2002

The uniform metal droplet generation using Nd-YAG laser was studied and experiment was carried out. The shape and volume of developed droplet was measured and the Young-Laplace equation and equilibrium condition of force were applied this model. The differential equation predicting shape of droplet using equilibrium condition of force instead of Navier-stokes equation was induced and numerical solution of differential equation compared with experimentation data. The differential equation was solved by Runge-Kutta method. Surface tension coefficient of droplet was determined with numerical solution relate to experimental result under the statical condition. In case of dynamic vibration, metal droplet shape and detaching critical volume are predicted by recalculating proposed model. The result revealed that this model could reasonably describe the behavior of molten metal droplet on vibration.

• Journal of the Korea Institute of Military Science and Technology
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• v.11 no.2
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• pp.116-124
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• 2008

Current paper investigates the dynamic behavior and stability of an infrared search and track subjected to external disturbance having gimbal structure with three rotating axes keeping constant angular velocity in the azimuth direction. Euler-Lagrange equation is applied to derive the coupled nonlinear dynamic equation of motion of infrared search and track and the characteristics of dynamic coupling are investigated. Two equilibrium points with small variations from the nonlinear coupling system are derived and the specific condition from which a coupled equation can be three independent equations is derived. Finally, to examine the stability of system, Lyapunov direct method was used and system stability and stability boundaries are investigated.

• Steel and Composite Structures
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• v.28 no.6
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• pp.671-679
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• 2018

The paper is devoted to the stability analysis of a simply supported five layer sandwich beam. The beam consists of five layers: two metal faces, the metal foam core and two binding layers between faces and the core. The main goal is to elaborate a mathematical and numerical model of this beam. The beam is subjected to an axial compression. The nonlinear hypothesis of deformation of the cross section of the beam is formulated. Based on the Hamilton's principle the system of four stability equations is obtained. This system is approximately solved. Applying the Bubnov-Galerkin's method gives an ordinary differential equation of motion. The equation is then numerically processed. The equilibrium paths for a static and dynamic load are derived and the influence of the binding layers is considered. The main goal of the paper is an analytical description including the influence of binding layers on stability, especially on critical load, static and dynamic paths. Analytical solutions, in particular mathematical model are verified numerically and the results are compared with those obtained in experiments.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.29 no.6
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• pp.583-590
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• 2016

This paper presents a dynamic crack propagation algorithm with Rayleigh damping effect based on the MLS(Moving Least Squares) Difference Method. Dynamic equilibrium equation and constitutive equation are derived by considering Rayliegh damping and governing equations are discretized by the MLS derivative approximation; the proportional damping, which has not been properly treated in the conventional strong formulations, was implemented in both the equilibrium equation and constitutive equation. Dynamic equilibrium equation including time relevant terms is integrated by the Central Difference Method and the discrete equations are simplified by lagging the velocity one step behind. A geometrical feature of crack is modeled by imposing the traction-free condition onto the nodes placed at crack surfaces and the effect of movement and addition of the nodes at every time step due to crack growth is appropriately reflected on the construction of total system. The robustness of the proposed numerical algorithm was proved by simulating single and multiple crack growth problems and the effect of proportional damping on the dynamic crack propagation analysis was effectively demonstrated.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.12
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• pp.2511-2518
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• 2002

Dynamic behaviors and stability of an optical disk drive coupled with an automatic ball balancer (ABB) are analyzed by a theoretical approach. The feeding system is modeled a rigid body with six degree-of-freedom. Using Lagrange's equation, we derive the nonlinear equations of motion for a non -autonomous system with respect to the rectangular coordinate. To investigate the dynamic stability of the system in the neighborhood of the equilibrium positions, the monodromy matrix technique is applied to the perturbed equations. On the other hand, time responses are computed by the Runge -Kutta method. We also investigate the effects of the damping coefficient and the position of ABB on the dynamic behaviors of the system.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.983-988
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• 2001

Dynamic behaviors and stability of an optical disk drive coupled with an automatic ball balancer(ABB) are analyzed by a theoretical approach. The feeding system is modeled a rigid body with six degree-of-freedom. Using Lagrange's equation, we derive the nonlinear equations of motion for a non-autonomous system with respect to the rectangular coordinate. To investigate the dynamic stability of the system in the neighborhood of the equilibrium positions, the monodromy matrix technique is applied to the perturbed equations. On the other hand, time responses are computed by the Runge-Kutta method. We also investigate the effects of the damping coefficient and the position of ABB on the dynamic behaviors of the system.

• Journal of KSNVE
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• v.9 no.2
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• pp.355-362
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• 1999

Vibration reduction of an optical disk drive is achieved by an automatic ball balancer and dynamic behaviors of the drive are studied by theoretical approaches. Using Lagrange's equation, we derive nonlinear equations of motion for a non-autonomous system with respect to the rectangular coordinate. To investigate the dynamic stability of the system in the neighborhood of equilibrium positions, the Floquet theory is applied to the perturbed equations. On the other hand, time responses are computed by an explicit time integration method. We also investigate the effects of mass center and the position of the ABB on the dynamic behaviors of the system.