• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.8
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• pp.817-825
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• 2007

During thirty years, deterministic chaos has moved center stage in many areas of applied mathematics. One important stimulus for this, particularly in the early 1970s, was work on nonlinear aspects of the dynamics of plant and animal populations. There are many situations, at least to a crude first approximation, by a simple first-order difference equation. Past studies have shown that such equations, even though simple and deterministic, can exhibit a surprising array of dynamical behavior, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations. But higher-order spectral analyses of such behavior are usually not considered. Higher-order spectra of a signal contain important information that is not present in its power spectrum. So, if we find the spectral pattern and get information from it, it will be able to be used effectively in so many fields. Hence, this paper uses auto bicoherence and bicoherence residue which are sort of bispectrum. Applying these to behavior of logistic difference equation, which is typical chaotic signal, the phenomenon of phase coupling and the appearance of frequency band can be analyzed. Such information means that bispectral analysis is useful to detect nonlinearity of signal.

• Journal of Korean Tunnelling and Underground Space Association
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• v.7 no.3
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• pp.249-257
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• 2005

There are basically two methods for the seismic design of underground structures ; analytical or pseudo-static, and dynamical method. In pseudo-static analysis approach, the ground deformations are imposed as a static load and soil-structure interaction does not include dynamic or wave propagation effects. However the behavior of soil structure interaction is nonlinear, it needs to consider nonlinear soil-structure interaction effects. In this study simplified seismic analysis method to consider soil-structure interaction by iterative procedure is proposed and the results are compared and analyzed by a finite difference computer program.

• International Journal of Control, Automation, and Systems
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• v.6 no.6
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• pp.859-872
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• 2008

In this paper, the problem of partial asymptotic stabilization of nonlinear control cascaded systems with integrators is considered. Unfortunately, many controllable control systems present an anomaly, which is the non complete stabilization via continuous pure-state feedback. This is due to Brockett necessary condition. In order to cope with this difficulty we propose in this work the partial asymptotic stabilization. For a given motion of a dynamical system, say x(t,$x_0,t_0$)=(y(t,$y_0,t_0$),z(t,$z_0,t_0$)), the partial stabilization is the qualitative behavior of the y-component of the motion(i.e., the asymptotic stabilization of the motion with respect to y) and the z-component converges, relative to the initial vector x($t_0$)=$x_0$=($y_0,z_0$). In this work we present new results for the adding integrators for partial asymptotic stabilization. Two applications are given to illustrate our theoretical result. The first problem treated is the partial attitude control of the rigid spacecraft with two controls. The second problem treated is the partial orientation of the underactuated ship.

• Journal of the Korean Society for Precision Engineering
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• v.28 no.7
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• pp.821-826
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• 2011

This paper deals with an analysis of dynamic mechanism for the industrial two-step folding automatic door. A nonlinear equation of motion was derived in terms of folding angle to estimate driving forces. Based on this dynamic behavior, time taken during the door's opening well as their velocities were controlled so that the operating conditions can be obtained for the purpose of design. The stiffness of twisting spring was also investigated when the automatic door closed, because a dangerous accident takes place from the door's free falling. The current research will be a very useful tool in the near future for the dynamic analysis for the multi-step folding automatic door.

• Journal of the Ergonomics Society of Korea
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• v.18 no.3
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• pp.141-152
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• 1999

In this paper, We performed the human body dynamic modelling for the realistic animation based on the dynamical behavior of human body, and designed controller for the effective control of complicate human dynamic model. The human body was simplified as a rigid body which consists of 18 actuated degrees of freedom for the real time computation. Complex human kinematic mechanism was regarded as a composition of 6 serial kinematic chains : left arm, right arm, support leg, free leg, body, and head. Based on the this kinematic analysis, dynamic model of human body was determined using Newton-Euler formulation recursively. The balance controller was designed in order to control the nonlinear dynamics model of human body. The effectiveness of designed controller was examined by the graphical simulation of human walking motion. The simulation results were compared with the model base control results. And it was demonstrated that, the balance controller showed better performance in mimicking the dynamic motion of human walking.

• Journal of The Korean Digital Architecture Interior Association
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• v.9 no.3
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• pp.15-23
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• 2009

Chaos theory, qualitative study of unstable aperiodic behavior in deterministic nonlinear dynamical systems, is dominant paradigm in the twenty first century. Fractal geometry, as an expressed form of chaos, now influences many areas such as architecture, art, music, economics, literature, etc. The purpose of this study is to analyze fractal geometry and fractal formative elements in architectural design. There are scaling, superimposition, distortion, deformation and repetition in the fractal form generator that can be applied to design concept and process in architecture. This study shows fractal geometry can be the architectural form creation method. Fractal geometry similar to nature's patterned order can be provided endless possibilities for design analysis and methodology in architecture. Therefore the further study of fractal geometry should progress synthetically through the basis of the study.

• Advances in Computational Design
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• v.5 no.2
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• pp.177-193
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• 2020

In the present research, dynamic analysis of functionally graded (FG) graphene-reinforced beams under thermal loading has been carried out based on finite element approach. The presented formulation is based on a higher order refined beam element accounting for shear deformations. The graphene-reinforced beam is exposed to transverse periodic mechanical loading. Graphene platelets have three types of dispersion within the structure including uniform-type, linear-type and nonlinear-type. Convergences and validation studies of derived results from finite element approach are also presented. This research shows that the resonance behavior of a nanocomposite beam can be controlled by the GPL content and dispersions. Therefore, it is showed that the dynamical deflections are notably influenced by GPL weight fractions, types of GPL distributions, temperature changes, elastic foundation and harmonic load excitation frequency.

• Journal of the Optical Society of Korea
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• v.3 no.2
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• pp.41-46
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• 1999

Spatial and temporal dynamics arising in a photorefractive crystal(BaTiO3) during the process of double phase conjugation was studied experimentally. We studied the dynamical effects caused by the buildup of the diffraction grating and turn on of phase conjugated beams, as well as the spatial effects caused by the finite transverse coupling of beams and the propagation direction of beams. We observed conical emission in DPCM. We believe that various temporal and spatial instabilities are due to movement of the nonlinear grating. For a real beam coupling and constructive interaction of interference fringes in the crystal, we observed steady, periodic, irregular temporal behavior. And, by the calculation of the correlation index, we found that the spatial correlation decreased as the transverse interaction region was increased.

• Journal of the Korean Society of Marine Environment & Safety
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• v.24 no.2
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• pp.140-145
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• 2018

This paper deals with the dynamical analysis of a two-point mooring vessel under surge excitations. The characteristics of nonlinear behaviors are investigated completely including bifurcation and limit cycle according to particular input parameter changes. The strong nonlinearity of the mooring system is mainly caused by linear and cubic terms of restoring force. The numerical simulation is performed based on the fourth order Runge-Kutta algorithm. The bifurcation diagram and several instability phenomena are observed clearly by varying amplitudes as well as frequencies of surge excitations. Stable periodic solutions, called the periodic windows, can be obtained in succession between chaotic clouds of dots in case of frequency ${\omega}=0.4rad/s$. In addition, the chaotic region is unexpectedly increased when external forcing amplitude exceeds 1.0 with the angular frequency of ${\omega}=0.7rad/s$. Compared to the cases for ${\omega}=0.4$, 0.7rad/s, the region of chaotic behavior becomes more fragile than in the case of ${\omega}=1.0rad/s$. Finally, various types of steady states including sub-harmonic motion, limit cycle, and symmetry breaking phenomenon are observed in the two-point mooring system at each parameter value.

• Smart Structures and Systems
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• v.19 no.1
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• pp.21-31
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• 2017

To control the stochastic vibration of a vibration-sensitive instrument supported on a beam, the beam is designed as a sandwich structure with magneto-rheological visco-elastomer (MRVE) core. The MRVE has dynamic properties such as stiffness and damping adjustable by applied magnetic fields. To achieve better vibration control effectiveness, the optimal bounded parametric control for the MRVE sandwich beam with supported mass under stochastic and deterministic support motion excitations is proposed, and the stochastic and shock vibration suppression capability of the optimally controlled beam with multi-mode coupling is studied. The dynamic behavior of MRVE core is described by the visco-elastic Kelvin-Voigt model with a controllable parameter dependent on applied magnetic fields, and the parameter is considered as an active bounded control. The partial differential equations for horizontal and vertical coupling motions of the sandwich beam are obtained and converted into the multi-mode coupling vibration equations with the bounded nonlinear parametric control according to the Galerkin method. The vibration equations and corresponding performance index construct the optimal bounded parametric control problem. Then the dynamical programming equation for the control problem is derived based on the dynamical programming principle. The optimal bounded parametric control law is obtained by solving the programming equation with the bounded control constraint. The controlled vibration responses of the MRVE sandwich beam under stochastic and shock excitations are obtained by substituting the optimal bounded control into the vibration equations and solving them. The further remarkable vibration suppression capability of the optimal bounded control compared with the passive control and the influence of the control parameters on the stochastic vibration suppression effectiveness are illustrated with numerical results. The proposed optimal bounded parametric control strategy is applicable to smart visco-elastic composite structures under deterministic and stochastic excitations for improving vibration control effectiveness.