• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1996년도 추계학술대회논문집; 한국과학기술회관, 8 Nov. 1996
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• pp.282-287
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• 1996

The non-linear torsional vibrations of the propulsion shafting system with viscous damper are considered. The motion is modeled by non-linear differential equations of second order. the equivalent system is modeled by two mass softening system with Duffing's oscillator. The steady state response of a equivalent system is analyzed for primary resonance only. Harmonic balance method as a non-linear vibration analysis technique is used. Jump phenomena are explained. The primary unstable region obtained by the Mathieu equation is investigated. Both theoretical and measured results of the propulsion shafting system are compared with and evaluated. As a result of comparisons with both data, it was confirmed that Duffing's oscillator can be used as a analysis method in the modeling of the propulsion shafting system attached viscous damper with non-linear stiffness.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국내학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.1234-1239
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• 1993

We study how to design conventional feedback controllers to drive chaotic trajectories of the well-known systems to their equilibrium points or any of their inherent periodic orbits. The well-known chaotic systems are Heon map and Duffing's equation, which are used as illustrative examples. The proposed feedback controller forces the chaotic trajectory to the stable manifold as OGY method does. Simulation results are presented to show the effectiveness of the proposed design method.

• 대한의용생체공학회:학술대회논문집
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• 대한의용생체공학회 1994년도 추계학술대회
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• pp.142-146
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• 1994

This paper proposes an fill-factor algorithm that determines embedding parameters which are needed in optimal attractor reconstruction. For reliability test, using this algorithm, we reconstructs the attractor of numerical chaotic data such as Duffing equation, Lorenz equation and Rossler equation whose embedding parameters are known. Also we reconstructs the attractor of experimental data and evaluates correlation dimension. Experimental data used in this paper are 38 ECG data of AHA(American Heart Association) ECG database. For numerical chaotic data, correlation dimension and Lyapunov exponent of reconstructed attractor are very close to those of attractor using original coordinate system.

• Structural Engineering and Mechanics
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• 제66권1호
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• pp.139-149
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• 2018

Many practical engineering problems are associated with nonlinear systems subjected to nonstationary random excitations. Equivalent linearization methods are commonly used to seek for approximate solutions to this kind of problems. Compared to various approaches developed in the frequency and mixed time-frequency domains, though directly solving the system equation of motion in the time domain would improve computation efficiency, only limited studies are available. Considering the fact that the orthogonal functions have been widely used to effectively improve the accuracy of the approximated responses and reduce the computational cost in various engineering applications, an orthogonal-function-based equivalent linearization method in the time domain has been proposed in the current paper for nonlinear systems subjected to nonstationary random excitations. In the numerical examples, the proposed approach is applied to a SDOF system with a set-up spring and a SDOF Duffing oscillator subjected to stationary and nonstationary excitations. In addition, its applicability to nonlinear MDOF systems is examined by a 3DOF Duffing system subjected to nonstationary excitation. Results show that the proposed method can accurately predict the nonlinear system response and the formulation of the proposed approach allows it to be capable of handling any general type of nonstationary random excitations, such as the seismic load.

• 전자공학회논문지SC
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• 제39권1호
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• pp.51-65
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• 2002

본 논문에서는 혼돈 비선형 시스템의 지능 제어를 위해 간접 적응 제어 방식에 기초한 신경 회로망 제어기 설계 방법을 제안하였다. 제안된 제어 방법은 혼돈 비선형 시스템의 동정을 위해 다층 신경 회로망과 간단한 상태 공간 신경 회로망을 사용한 직-병렬 동정 구조를 이용하여 오프 라인으로 동정 과정을 수행하였으며, 학습된 혼돈 비선형 시스템에 대한 신경 회로망 모델을 사용하여 온 라인으로 제어를 수행하였다. 이때 혼돈 비선형 시스템의 동정 및 제어를 위한 학습 방법은 오차 역전파 방법을 사용하였다. 한편 본 논문에서 제안된 제어 방법을 연속 시간 혼돈 비선형 시스템인 Duffing 방정식과 Lorenz 방정식에 각각 적용하여 신경 회로망을 사용한 기존의 제어 방법과 컴퓨터 모의 실험을 통해 제어 성능을 비교 및 고찰하였다.

• 대한기계학회논문집
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• 제1권3호
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• pp.141-145
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• 1977

In this paper, approximate solutions of the von Karman equations for the free flexural vibration of a transversely isotropic thin rectangular plate with two simply supported edges and two clamped edges are obtained. Applying one term Ritz-Galerkin procedure, the spatial dependent part of the equation is separated and time dependent function is found to be the Duffing's equation. Then the relation between nonlinear period and amplitude of the vibration is obtained by using averaging method which is a method of the perturbation procedure. It can be seen that averaging method is easy and agrees well with prior results.

• Wind and Structures
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• 제5권5호
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• pp.423-440
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• 2002

The effects of the nonlinear (quadratic) term in wind pressure have been analyzed in many papers with reference to linear structural models. The present paper addresses the problem of the response of nonlinear structures to stochastic nonlinear wind pressure. Adopting a single-degree-of-freedom structural model with polynomial nonlinearity, the solution is obtained by means of the moment equation approach in the context of It$\hat{o}$'s stochastic differential calculus. To do so, wind turbulence is idealized as the output of a linear filter excited by a Gaussian white noise. Response statistical moments are computed for both the equivalent linear system and the actual nonlinear one. In the second case, since the moment equations form an infinite hierarchy, a suitable iterative procedure is used to close it. The numerical analyses regard a Duffing oscillator, and the results compare well with Monte Carlo simulation.

• Steel and Composite Structures
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• 제17권1호
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• pp.123-131
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• 2014

In this paper we have considered the vibration of parametrically excited oscillator with strong cubic positive nonlinearity of complex variable in nonlinear dynamic systems with forcing based on Mathieu-Duffing equation. A new analytical approach called homotopy perturbation has been utilized to obtain the analytical solution for the problem. Runge-Kutta's algorithm is also presented as our numerical solution. Some comparisons between the results obtained by the homotopy perturbation method and Runge-Kutta algorithm are shown to show the accuracy of the proposed method. In has been indicated that the homotopy perturbation shows an excellent approximations comparing the numerical one.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1996년도 하계학술대회 논문집 B
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• pp.1155-1157
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• 1996

In this paper, the direct adaptive control using neural networks is presented for the control of chaotic nonlinear systems. The direct adaptive control method has an advantage that the additional system identification procedure is not necessary. Two direct adaptive control methods are applied to a Duffing's equation and the simulation results show the effectiveness of the controllers.

• 한국공간구조학회논문집
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• 제19권4호
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• pp.69-76
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• 2019

A stadium roof that uses the pin-jointed spatial truss system has to be designed by taking into account the unstable phenomenon due to the geometrical non-linearity of the long span. This phenomenon is mainly studied in the single-free-node model (SFN) or double-free-node model (DFN). Unlike the simple SFN model, the more complex DFN model has a higher order of characteristic equations, making analysis of the system's stability complicated. However, various symmetric conditions can allow limited analysis of these problems. Thus, this research looks at the stability of the DFN model which is assumed to be symmetric in shape, and its load and equilibrium state. Its governing system is expressed by nonlinear differential equations to show the double Duffing effect. To investigate the dynamic behavior and characteristics, we normalize the system of the model in terms of space and time. The equilibrium points of the system unloaded or symmetrically loaded are calculated exactly. Furthermore, the stability of these points via the roots of the characteristic equation of a Jacobian matrix are classified.