• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.11a
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• pp.853-861
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• 2007

To understand the concept of dynamic motion in two degree nonlinear coupled system, free vibration not including damping and excitation is investigated with the concept of nonlinear normal mode. Stability analysis of a coupled system is conducted, and the theoretical analysis performed for the bifurcation phenomenon in the system. Bifurcation point is estimated using harmonic balance method. When the bifurcation occurs, the saddle point is always found on Poincare's map. Nonlinear phenomenon result in amplitude modulation near the saddle point and the internal resonance in the system making continuous interchange of energy. If the bifurcation in the normal mode is local, the motion remains stable for a long time even when the total energy is increased in the system. On the other hand, if the bifurcation is global, the motion in the normal mode disappears into the chaos range as the range becomes gradually large.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2002.04a
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• pp.261-265
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• 2002

In the machining tool avoid vibration problem have an effect on high precision as well as statical and thermal characteristics. Therefore overcome this problem is essential to advance of machine tool and machining skill. Even though vibration arises owing to a variety of causes, in this paper vibration analysis of column as a major part of machine tool structures is presented. At this procedure vibration analysis applied to mode synthesis method using a attachment mode .

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1994.10a
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• pp.21-28
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• 1994

The forced vibration with the symmetric boundary condition in nonlinear structure is studied by utilizing the characteristic of the free vibration which have two modes with the similar natural frequency. Two linear modes exist to have no concern with the amplitude. It is found that the normal mode or elliptic orbit as the newly coupled modes is generated in accordance with changing the stability. It is also known that responses for forced vibration having the small external force and damping are near mode of free vibration and the stability for each response is determined according to the stability for each response is determined according to the stability in mode of free vibration. Finally the stability and bifurcation are analyzed in proportion to increment of external force and damping.

• Journal of Mechanical Science and Technology
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• v.17 no.12
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• pp.1922-1927
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• 2003

Nonlinear normal mode (NNM) vibration, in a nonlinear dual mass Hamiltonian system, which has 6$\^$th/ order homogeneous polynomial as a nonlinear term, is studied in this paper. The existence, bifurcation, and the orbital stability of periodic motions are to be studied in the phase space. In order to find the analytic expression of the invariant curves in the Poincare Map, which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space, Whittaker's Adelphic Integral, instead of the direct integration of the equations of motion or the Birkhoff-Gustavson (B-G) canonical transformation, is derived for small value of energy. It is revealed that the integral of motion by Adelphic Integral is essentially consistent with the one obtained from the B-G transformation method. The resulting expression of the invariant curves can be used for analyzing the behavior of NNM vibration in the Poincare Map.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.435-440
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• 2000

It is shown, in nonlinear two-degree-of freedom system, that the bifurcating modes are created by the stability changes of normal modes. There are four types of stability criterion, each of which gives rise to a distinct functional form of bifurcating modes; the bifurcating mode is born in the form of eigenfunction through which the stability is changed. Then a procedure is formulated to compute the bifurcating mode by the method of harmonic balance. Application of bifurcating mode to forced vibrations is introduced.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.799-804
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• 2001

Nonlinear normal mode (NNM) vibration, in a nonlinear dual mass Hamiltonian system, which has 6th order homogeneous polynomial as a nonlinear term, is studied in this paper. The existence, bifurcation, and the orbital stability of periodic motions are to be studied in the phase space. In order to find the analytic expression of the invariant curves in the Poincare Map, which is a mapping of a phase trajectory onto 2 dimensional surface in 4 dimensional phase space, Whittaker's Adelphic Integral, instead of the direct integration of the equations of motion or the Birkhotf-Gustavson (B-G) canonical transformation, is derived for small value of energy. It is revealed that the integral of motion by Adelphic Integral is essentially consistent with the one obtained from the B-G transformation method. The resulting expression of the invariant curves can be used for analyzing the behavior of NNM vibration in the Poincare Map.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1998.04a
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• pp.392-398
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• 1998

In order to check the validity of nonlinear normal modes of continuous, systems by means of the energy-based formulation, we consider a beam with a nonlinear boundary condition. The initial and boundary e c6nsl of a linear partial differential equation and a nonlinear boundary condition is reduced to a linear boundary value problem consisting of an 8th order ordinary differential equations and linear boundary conditions. After obtaining the asymptotic solution corresponding to each normal mode, we compare this with numerical results by the finite element method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.04a
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• pp.177-183
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• 1996

By utilizing the concept of normal modes, nonlinear dynamics is studied on pendulum dynamic absorber. When the spring mode loses the stability in undamped free system, a dynamic two-well potential is formed in Poincare map. A procedure is formulated to compute the forced responses associated with bifurcating mode and predict double saddle-loop phenomenon. It is found that quasiperiodic motion and stable periodic motion coexist in some parameter ranges, and only periodic motions or rotation of pendulum with chaotic fluctuation are observed in other ranges.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.441-448
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• 2000

An investigation into the nonlinear free vibrations of a cantilever beam which can have not only planar motion but also nonplanar motion is made. Using Galerkin's method based on the first mode in each motion, we transform the boundary and initial value problem into an initial value problem of two-degree-of-freedom system. The system turns out to have two normal modes. By Synge's stability concept we examine the stability of each mode. In order to check validity of the stability we obtain the numerical Poincare map of the motions neighboring on each mode.

• Journal of the Korean Chemical Society
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• v.64 no.6
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• pp.350-353
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• 2020

The validity of the calculation method based on the local mode in hydrogen-bonded water molecules was investigated by comparing the frequencies of the local and normal modes of OH stretching vibration in water molecules. By calculating a monomer, dimer, and trimer of water molecules using a quantum chemical ab initio theory, we examined how the frequencies of the local and normal modes and the anharmonicity of local modes vary with molecular cluster size. It was shown that, as the number of molecules increases from monomer to trimer, the anharmonicity of OH bonds increases and the difference between local and normal mode frequencies decreases. This confirms that local-mode-based calculations that can easily handle the anharmonicity can be appropriate for the calculation of the OH stretching frequency of water molecules in the condensed phase.