• The Journal of the Korea institute of electronic communication sciences
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• v.10 no.12
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• pp.1389-1394
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• 2015

Recently many effort appears applying the concept of fractional calculus that can be represented by fractional differential equation in the control engineering, physics and mathematics. This paper describes the fractional order with real order for Duffing equation which can be represented by integer order. This paper also confirms the existence of chaotic behaviors by using time series and phase portrait with varying the parameter of real order.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.12 no.4
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• pp.62-69
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• 1998

The harmonics caused b th nonlinear operation of transmission equipments are not identified yet and have been seldom studied. Sources of harmonics in nonlinear circuit, especially caused by the nonlinear operation of transmission equipments, can be approximately modeled with Duffing's Equation which is often referred in nonlinear mechanical oscillation problem. In this study, a new analytic technique is proposed for the analysis of harmonics n nonlinear circuits using Duffing's Equation and compared with some conventional methods. Finally some case studies were performed to evaluate the performance of proposed method and conventional methods.

• 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.

• The Journal of the Korea institute of electronic communication sciences
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• v.7 no.5
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• pp.1073-1078
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• 2012

In this paper, we propose the MEMS system with Duffing equation to confirm nonlinear features in MEMS system. We also analyze nonlinear phenomena when adding the nonlinear term of another type. As a verification, we confirm chaotic motion by parameter variation through the time series, phase portrait and power spectrum.

• 한국항공운항학회:학술대회논문집
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• 2015.11a
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• pp.20-24
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• 2015

미분변환법은 미분방정식의 해를 구하기 위한 방법으로 다양한 분야에서 적용에 관한 연구를 수행 중이다. 항공우주분야의 동역학 모델링의 경우 미분방정식은 비선형성을 포함하게 되며 일반적으로 수치해석을 이용해 근사해를 구하게 된다. 본 논문에서는 미분변환법을 이용해 구해진 근사해의 오차 추이를 분석한 내용을 다루고 있다. 이를 위한 예제로써 duffing equation을 사용하였으며, duffing equation에 포함된 비선형성을 증가시킴에 따라 미분변환법을 이용해 구한 근사해와 수치해석을 이용해 구한 수치해를 비교하였다.

• The Journal of the Korea institute of electronic communication sciences
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• v.9 no.6
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• pp.711-717
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• 2014

Happiness has been studied in sociology and psychology as a matter of grave concern. In this paper the happiness model that a new second -order systems can be organized equivalently with a Spring-Damper-Mass are proposed. This model is organized a 2-dimensional model of identically type with Duffing equation. We added a nonlinear term to Duffing equation and also applied Gaussian white noise and period sine wave as external stimulus that is able to cause of happiness. Then we confirm that there are random motion, periodic motion and chaotic motion according to parameter variation in the new happiness model.

• Journal of Advanced Marine Engineering and Technology
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• v.24 no.1
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• pp.18-24
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• 2000

As ship's propulsion shafting system has been complicated, many linear methods that have been used until now are not sufficient enough to produce proper solutions and these solutions are ofter unreasonable. So we need to solve nonlinear systems, and many methods for solving nonlinear vibration system have been developed. In this study, the propulsion shafting system was modeled with Duffing's nonlinear vibration system and multi-degree-of-freedom, and analyzed by using Quasi-Newton method. And for the purpose of confirming the reliability of the calculating results for nonlinear forced torsional vibration of the propulsion shafting system, the nonlinear calculated results were compared with the linear calculated ones for ship's propulsion shafting system. In the result, for analysis of the forced torsional vibration of the propulsion systems with nonlinear elements, the modified Newton's method is confirmed reasonable.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.7
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• pp.107-113
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• 1995

Using the mathematical model of the torsional vibration in spindle system with magnetic coupling, which was proposed in the paper of dynamic analysis of spindle system with magnetic coupling(l), we derive the equations of the motion and the form of the derived equations represents Duffing equation. Numerical analyses are executed in many conditions, namely the various types in magnetic coupling, changes of the gap between driver and follower. To verify the results of the therorectical analyses, a precision dynamic drive system is manufactured and methods of the test to measure the torsional vibration of the spindle system with magnetic coupling are presented ad thests in various conditions are carried out.

• Transactions of the Korean Society of Automotive Engineers
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• v.13 no.4
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• pp.105-112
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• 2005

Analyses of dynamic models which were one and two degrees of freedom, and had the nonlinear springs and dampings with certain polynomial functions were performed from SIMULINK in MATLAB. Those consisted of 12 programs and were built on the basis of the preceding programs fur the linear dynamic simulations. However the programs for the nonlinear simulations were quite different from those f3r the linear ones, and showed the results of the analyses in real time with animating. It was found that the programs would help us to solve any kind of nonlinear dynamic simulation with one and two degrees of freedom. Especially, the simulations for 1 DOF system with cubic nonlinear spring farce showed the results for Duffing's equation, of which phenomena were jump-up and jump-down. It will be applied to the dynamic simulation of the car seat vibration with a passenger, of which model has the equivalent nonlinear springs and is two degrees of freedom.

• Journal of the KSME
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• v.31 no.1
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• pp.68-79
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• 1991

이 글에서는 다음의 내용에 대하여 알아보았다. Duffing - holmes 방정식에서의 Chaos Logistic map에서의 Chaos 기타 시스템에서의 Chaos 1) Henon map 2) Bouncty bau map (standard map) 3) 진자에서의 Chaos 4) Taylor-Couette유동 5) Fluid drop Chaos 6) Surface wave Chaos Lyapunov 지수 (Exponent)