• The Journal of the Acoustical Society of Korea
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• v.10 no.1
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• pp.12-19
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• 1991

A numerical analysis is carried out for the nonlinear phenomena of the bubble oscillator. The model is based on the Keller's formulation for the bubble dynamics. Interpretation of the bubble interior is based on the formulation by Prosperetti. His formulation adopts the energy equation for the analysis of the bubble interior. The numerical simulation Shows typical nonlinear phenomena in its frequency response. Among such nonlinear aspects are the jump phenomenon, the shift of natural frequency of the system, and the appearance of superharmonic resonances. It is deduced that the nonlinear frequency response is dependent upon the initial condition of the bubble oscillator and some multi-valued frequency region can appear in the response curve. Nonlinear phenomena appeared in the bubble oscillator is compared with those of the Duffing equation and it may be said that the bubble dynamic equation has similar nonlinear aspects to the Duffing equation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.10a
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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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• 1996.10b
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• pp.453-456
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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. In order to evaluate the performance of our controller design method, two direct adaptive control methods are applied to a Duffing's equation and a Lorenz equation which are continuous-time chaotic systems. Our simulation results show the effectiveness of the controllers.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10a
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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.

• Wind and Structures
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• v.5 no.5
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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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.1 no.3
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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.

• Steel and Composite Structures
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• v.17 no.1
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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.

• Proceedings of the KIEE Conference
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• 1996.07b
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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.

• Journal of Korean Association for Spatial Structures
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• v.19 no.4
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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.