• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.9
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• pp.1711-1721
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• 1992

A nonlinear dissipative dynamical system can often have multiple attractors. In this case, it is important to study the global behavior of the system by determining the global domain of attraction of each attractor. In this paper we study the global behavior of a forced beam with two mode interaction. The governing equation of motion is reduced to two second-order nonlinear nonautonomous ordinary differential equations. When .omega. /=3.omega.$_{1}$ and .ohm.=.omega $_{1}$, the system can have two asymptotically stable steady-state periodic solutions, where .omega./ sub 1/, .omega.$_{2}$ and .ohm. denote natural frequencies of the first and second modes and the excitation frequency, respectively. Both solutions have the same period as the excitation period. Therefore each of them shows up as a period-1 solution in Poincare map. We show how interpolated mapping method can be used to determine the two four-dimensional domains of attraction of the two solutions in a very effective way. The results are compared with the ones obtained by direct numerical integration.

• Transactions of the Korean Society of Automotive Engineers
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• v.15 no.4
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• pp.115-123
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• 2007

In this paper, an analytical model is developed to describe the dynamic characteristics of a roller bearing. In order to obtain accurate dynamic response of roller bearing, each roller is modeled as a rigid body, which has radial and axial movement and rotational constraints. Beam element between outer race segments is used to consider flexibility of outer race. Beam deflection is calculated from beam forces and used for contact between roller and outer race. The efficient contact search kinematics and algorithms in the context of the compliance contact model are implemented to detect the interactions between roller and race for the sake of speedy and robust solutions. The numerical results are validated with another analysis results which are calculated using waviness condition. Increasing rollers, dynamic responses are compared with each other. In order to confirm dynamic behavior and nonlinear characteristic of roller bearing, Poincare map is used.

• Journal of Ocean Engineering and Technology
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• v.7 no.1
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• pp.13-24
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• 1993

The dispersion in the oscillatory flow generated by gravitational waves above the spatially periodic repples is studied. The steady parts of equations describing the orbit of the passive particle in a two dimensional field are assumed to be simply trigonometric functions. From the view point of nonlinear dynamics, the motion of the particle is chaotic under externally time-periodic perturbations which come from the wave motion. Two cases considered here are; (i) shallow water, and (ii) deep water approximation.

• The Journal of the Korea institute of electronic communication sciences
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• v.6 no.5
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• pp.709-716
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• 2011

Recently, there are many difficult for maintenance in the power in established sensor networks. In order to solve this problems, the power development has been interested using vibration in MEMS that insert the MEMS oscillator. In this paper, we propose the MEMS system with Duffing equation to generate vibration signal that can be use power signal in MEMS and confirm and verify the chaotic behaviors in vibration signal of MEMS by computer simulation. As a verification methods, we confirm the existence of period motion and chaotic motion by parameter variation through the time series, phase portrait, power spectrum and poincare map.

• Proceedings of the KOSOMBE Conference
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• v.1996 no.11
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• pp.363-367
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• 1996

In general, the physiological systems have shown nonlinear complex phenomena. This study analyzes nonlinear characteristics of the flow of peripheral blood vessel dynamics in physiological systems using chaos theory. We performed this study by means of several quantity methods and power spectrum. The quantity methods are a phase space reconstruction and a poincare's map. And the power spectrum method is a conventional linear analysis. Experimental data have been acquired from examining 10 diabetic patients, and 10 control subjects in initial stable state. In acquisition experminetal data, we anlysized the differences of nonlinear characteristics between diabetic group and control group. The results of quality analysis methods showed the flow of peripheral blood vessel had the nonlinear and chaotic characteristics, screening a strange attractor on reconstructed phase space. In conclusion, the flow dynamics of peripheral blood vessel had a chaotic behavior of nonlinear dynamic systems, dynamic system, and differences of characteristic of nonlinear dynamic system.

• Structural Engineering and Mechanics
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• v.70 no.5
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• pp.623-637
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• 2019

This paper analyzes the non-stationary vibration and super-harmonic resonances in nonlinear dynamic motion of viscoelastic nano-resonators. For this purpose, a new coupled size-dependent model is developed for a plate-shape nano-resonator made of nonlinear viscoelastic material based on modified coupled stress theory. The virtual work induced by viscous forces obtained in the framework of the Leaderman integral for the size-independent and size-dependent stress tensors. With incorporating the size-dependent potential energy, kinetic energy, and an external excitation force work based on Hamilton's principle, the viscous work equation is balanced. The resulting size-dependent viscoelastically coupled equations are solved using the expansion theory, Galerkin method and the fourth-order Runge-Kutta technique. The Hilbert-Huang transform is performed to examine the effects of the viscoelastic parameter and initial excitation values on the nanosystem free vibration. Furthermore, the secondary resonance due to the super-harmonic motions are examined in the form of frequency response, force response, Poincare map, phase portrait and fast Fourier transforms. The results show that the vibration of viscoelastic nanosystem is non-stationary at higher excitation values unlike the elastic ones. In addition, ignoring the small-size effects shifts the secondary resonance, significantly.

• Progress in Medical Physics
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• v.8 no.1
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• pp.75-82
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• 1997

The human physiological systems are so complex and irregular dynamics. Dynamics of peripheral blood vessel, in particular, have quite sensitive and complex. Before, the linear analytic method have been used to analyze the system. But, the method have many problems to predict the following results. In the other hand, the nonlinear analytic method, chaotic time series analysis method, is suitable for measuring complex, vary system. In this study, the scalar data of the blood flow of peripheral blood vessel of rabbits, in accordance with injection of glucose, was obtained and redefined as multi-dimensional vectors, with time-series analytic methods. This study also intended to confirm that the peripheral blood flow is chaotic dynamics and evaluate the availability of non-linear analytic method. As a result, the existing FFT, and mean could show the difference of blood flow of peripheral blood vessel by injection of glucose, but the nonlinear analytic method could show the definite difference. The hemodynamics is a chaotic phenomenon.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.43 no.8
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• pp.692-698
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• 2015

This paper represents a trajectory design and analysis technique which uses invariant manifolds of the circular restricted three body problem. Instead of the classical patched conic method based on 2-body problem, the equation of motion and dynamical behavior of spacecraft in the circular restricted 3-body problem are introduced, and the characteristics of Lyapunov orbits near libration points and their invariant manifolds are covered in this paper. The trajectories from/to Lyapunov orbits are numerically generated with invariant manifolds in the Earth-moon system. The trajectories in the Sun-Jupiter system are also analyzed with various initial conditions in the boundary surface. These methods can be effectively applied to interplanetary trajectory designs.