• Transactions of the Korean Society of Mechanical Engineers B
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• v.34 no.9
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• pp.859-866
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• 2010

Nonlinear dynamics of pulsating instability-diffusional-thermal instability with Lewis numbers sufficiently higher than unity-in counterflow diffusion flames, is numerically investigated by imposing a Damkohler number perturbation. The flame evolution exhibits three types of nonlinear behaviors, namely, decaying pulsating behavior, diverging behavior (which leads to extinction), and stable limit-cycle behavior. The stable limit-cycle behavior is observed in counterflow diffusion flames, but not in diffusion flames with a stagnant mixing layer. The critical value of the perturbed Damkohler number, which indicates the region where the three different flame behaviors can be observed, is obtained. A stable simple limit cycle, in which two supercritical Hopf bifurcations exist, is found in a narrow range of Damkohler numbers. As the flame temperature is increased, the stable simple limit cycle disappears and an unstable limit cycle corresponding to subcritical Hopf bifurcation appears. The period-doubling bifurcation is found to occur in a certain range of Damkohler numbers and temperatures, which leads to extend the lower boundary of supercritical Hopf bifurcation.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10a
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• pp.299-304
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• 1991

A novel approach based on a nonlinear compensator is proposed to prevent 'windup', which is caused by the saturation of the actuator and the integration action of the controller. The anti-windup compensator is located between the conventional linear controller, designed neglecting the saturation, and the actuator. It was proven based on the describing function method that, if the closed loop control systems are stable assuming no saturation, then there exist a range of compensator gain which prevents any limit-cycle and hence, guarantees the system stability. The computer simulation results show that the compensator proposed in the manuscript can eliminate unstable limit cycle and improve the transient response.

• Honam Mathematical Journal
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• v.30 no.3
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• pp.411-423
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• 2008

In the field of population dynamics and chemical reaction the possibility or the existence of spatially and temporally nonhomogeneous solutions is a very important problem. For last 50 years or so there have been many results on the pattern formation of chemical reaction systems studying reaction systems with or without diffusions to explain instabilities and nonhomogeneous states arising in biological situations. In this paper we study time-dependent properties of a predator-prey system with functional response and give sufficient conditions that guarantee the existence of stable limit cycles.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1864-1866
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• 1997

Uncertainties in the aerodynamic coefficients or time delay effects in implementing an autopilot algorithm can make a Flight Control System(FCS) unstable. When a FCS enters unstable state, the actuator or sensor limiters in FCS make the unstable system not diverge but be in the state of stable limit cycle. If an autopilot recognize the FCS to be in the stable limit cycle phenomenon, it woudl be better to adjust autopilot gains to stabilize the FCS. A novel method to stabilize a FCS using parameter estimation and maintenance of given phase margin is proposed. The method is applied to roll control loop and verified its performance.

• Journal of the Korean Society of Combustion
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• v.17 no.3
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• pp.9-16
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• 2012

Nonlinear dynamics of pulsating instability in radiating counterflow diffusion flames is numerically investigated by imposing Damk$\ddot{o}$hler number perturbation. Stable limit-cycle solutions occur in small ranges of Damk$\ddot{o}$hler numbers past bifurcation point of instability. Period doubling cascade and chaotic behaviors appear just before dynamic extinction occurs. Nonlinear dynamics is also studied when large disturbances are imposed to flames. For weak steady flames, the dynamic extinction range shrinks as the magnitudes of disturbances are increased. However, strong steady flames can overcome relatively large disturbances, thereby the dynamic extinction range extending. Stable limit-cycle behaviors reappears prior to dynamic extinction when the steady flames are strong enough.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.65 no.5
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• pp.878-882
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• 2016

These days, SFCLs are being developed in order to limit fault current. However, the superconducting elements that limit the fault current have such problems as capacity increase and require auxiliary devices including cooling device. If devices that comprise the current power network can withstand fault current for at least one cycle, it is possible to limit the fault current with current limiting elements by bypassing it on the fault line. In this study, the fault current limiter was configured with current transformer, vacuum interrupter, and current limiting element. Through the experience, it was confirmed that the fault current was limited within one cycle. The superconducting element, as a current limiting element, limited the fault current by 80 % within one cycle from fault occurrence, and the passive element limited it more than 95 %. Also, through the comparison between resistance curve and power consumption curve, it was confirmed that the current limiting element using a passive element was more stable than the superconducting element that required capacity increase and other auxiliary devices. It was considered that the FCL proposed in this study could limit fault current stably within one cycle from fault occurrence by using the existing power technologies such as fault current detection and solenoid valve operating circuit.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.6
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• pp.562-569
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• 2011

In this study linear and nonlinear dynamic stability characteristics of a medium-size high-speed turbocharger, whose rotor is supported by two 3-lobe journal bearings, are analyzed to evaluate and identify the effects of its bearing design variables. The rotor has the rated speed of 40,500 rpm and maximum continuous speed of 45,000 rpm. At first, utilizing the linear stability analysis method, bearing designs of yielding stable or unstable LogDecs as small as possible are searched by manipulating with machined bearing clearances and preloads. As next, utilizing the nonlinear analysis method, limit cycles of the rotor responses at the rated and maximum continuous speeds are simulated to check their acceptances. Results have shown that for the turbocharger rotor-bearing system considered, the 3-lobe journal bearing design with a smaller machined clearance and a larger preload are preferred for the stable rotor responses. More importantly, since there exists a good correlation between the linear and nonlinear stability analysis results, it is concluded that firstly the linear stability analysis method may be applied to screen quickly the ranges of bearing designs for stable or least unstable solutions and then, lastly the nonlinear stability analysis method may be deployed to check an absolute motion stability in terms of the limit cycle.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.30 no.7 s.250
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• pp.671-681
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• 2006

This study focuses on the development of numerical procedure to analyze the nonlinear combustion instabilities in liquid rocket engine. Nonlinear behaviors of acoustic instabilities are characterized by the existence of limit cycle in linearly unstable engines and nonlinear or triggering instability in linearly stable engines. To discretize convective fluxes with high accuracy and robustness, approximated Riemann solver based on characteristics and Euler-characteristic boundary conditions are employed. The present procedure predicts well the transition processes from initial harmonic pressure disturbance to N-like steep-fronted shock wave in a resonant pipe. Longitudinal pressure oscillations within the SSME(Space Shuttle Main Engine) engine have been analyzed using the pressure-sensitive time lag model to account for unsteady combustion response. It is observed that the pressure oscillations reach a limit cycle which is independent of the characteristics of the initial disturbances and depends only on combustion parameters and operating conditions.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.5
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• pp.1097-1103
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• 1988

This paper deals with surface crack behavior and the fatigue life prediction of notched specimens using the relation between surface crack length, a, and the cycle ratio, $N/N_{f}$. From the $a-N\;/\;N_{f}$ curves, UC(the upper limit curve), LC(the lower limit curve) and MC(the middle limit curve) were assumed and utilized to predict the fatigue life and crack growth rate. The data computed from the three assumed curves were compared with the experimental data. It has been found that in the stable crack growth region ($N/N_{f}=0.3-0.8$) fatigue life can be predicted within 20% errors. Using the characteristics of $a-N\;/\;N_{f}$ curve, it is possible to predict the $da/dN-K_{max}$ curve, the $da/dN-{\Delta}K_{{\varepsilon}_t}$ curve, and the $S-N_{f}$ curve.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1379-1393
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• 2010

In this paper, a stage-structured predator prey model (stage structure on prey) with two discrete time delays has been discussed. The two discrete time delays occur due to maturation delay and gestation delay. Linear stability analysis for both non-delay as well as with delays reveals that certain thresholds have to be maintained for coexistence. Numerical simulation shows that the system exhibits Hopf bifurcation, resulting in a stable limit cycle.