• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.4
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• pp.427-436
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• 2000

This study presents the nonlinear responses of a hinged-clamped beam under broadband random excitation. By using Galerkin's method the governing equation is reduced to a system or nonautonomous nonlinear ordinary differential equations. The Fokker-Planck equation is used to generate a general first-order differential equation in the joint moments of response coordinates. Gaussian and non-Gaussian closure schemes are used to close the infinite coupled moment equations. The closed equations are then solved for response statistics in terms of system and excitation parameters. The case of two mode interaction is considered in order to compare it with the case of three mode interaction. Monte Carlo simulation is used for numerical verification.

• Journal of the Korean Society of Industry Convergence
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• v.3 no.1
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• pp.43-51
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• 2000

The response statistics of a hinged-clamped beam under broad-band random excitation is investigated. The random excitation is applied at the nodal point of the second mode. By using Galerkin's method the governing equation is reduced to a system of nonautonomous nonlinear ordinary differential equations. A method based upon the Markov vector approach is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian and non-Gaussian closure methods the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. The case of two mode interaction is considered in order to compare it with the case of three mode interaction. The analytical results for two and three mode interactions are also compared with results obtained by Monte Carlo simulation.

• Journal of the Korean Society of Industry Convergence
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• v.4 no.2
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• pp.133-139
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• 2001

The nonlinear response statistics of an spring-pendulum system with internal resonance under narrow band random excitation is investigated analytically- The center frequency of the filtered excitation is selected to be close to natural frequency of directly excited spring mode. The Fokker-Planck equations is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian closure method the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. The nonlinear phenomena, such as jump and multiple solutions, under narrow band random excitation were found by Gaussian closure method.

• Journal of the Earthquake Engineering Society of Korea
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• v.14 no.1
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• pp.25-34
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• 2010

A method is presented for evaluating the seismic failure probability of bridge structures which show a nonlinear hysteretic dynamic behavior. Bridge structures are modeled as a bilinear dynamic system with a single degree of freedom. We regarded that the failure of bridges will occur when the displacement response of a deck level firstly crosses the predefined limit state during a duration of strong motion. For the estimation of the first-crossing probability of a nonlinear structural system excited by earthquake motion, we computed the average frequency of crossings of the limit state. We presented the non-Gaussian closure method for the approximation of the joint probability density function of response and its derivative, which is required for the estimation of the average frequency of crossings. The failure probabilities are estimated according to the various artificial earthquake acceleration sets representing specific seismic characteristics. For the verification of the accuracy and efficiency of presented method, we compared the estimated failure probabilities with the results evaluated from previous methods and the exact values estimated with the crude Monte-Carlo simulation method.

• Journal of the Korean Society of Industry Convergence
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• v.3 no.2
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• pp.141-147
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• 2000

The nonlinear response statistics of an autoparameteric system under broad-band random excitation is investigated. The specific system examined is a vibration absorber system with internal resonance, which is known to be a good model for a variety of engineering systems, including ship motions with nonlinear coupling between pitching and rolling motions. The Fokker-Planck equations is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian closure method the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. The jump phenomenon was found by Gaussian closure method under random excitation.

• Journal of KSNVE
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• v.8 no.3
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• pp.399-407
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• 1998

An investigation into the modal interaction of an autoparameteric systemunder broad-band random excitation is made. The specific system examined is a spring-pendulum system with internal resonance, which is known to be a good model for a variety of engineering systems, including ship motions with nonlinear coupling between pitching and rolling motions. By means of the Gaussian closure method the dynamic moment equations explaining the random responses of the system are reduced to a system of autonomous ordinanary differential equations of the first and second moments. In view of equilibrium solutions of this system and their stability we examine the system responses. The stabilizing effect of system damping is also examined.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.892-896
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• 2001

Investigation is performed on the stability of nonlinear system under turbulent fluid motion modelled as white noise random process, which is a preliminary result in the course of research on the characteristic and nonlinear control of the stochastic system. Adopted physical model is beam-type structure with tip-mass and main base mass. The governing equation is derived via F-P-K approach in stochastic sense. By means of Gaussian Closure method infinite dynamic moment equations due to system nonlinearity is closed to finite one. At the best of authors' knowledge, it is the first trial to design nonlinear controller by using of sliding mode technique in stochastic domain and control performance and effect in stochastic domain is studied.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1997.04a
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• pp.86-94
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• 1997

An investigation into the modal interaction of an autoparametric system under broad-band random excitation is made. The specific system examined is a spring-pendulum system with internal resonance, which is known to be a good model for a variety of engineering systems, including ship motions with nonlinear coupling between pitching and rolling motions. By means of the Gaussian closure method the dynamic moment equations explaining the random response of the system are reduced to a system of autonomous ordinanary differential equations of the first and second moments. In view of equilibrium solutions of this system and their stability we examine the system responses. The stabilizing effect of system damping is also examined.

• 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.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.4 no.4
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• pp.201-207
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• 1992

The averaged non-linear term in the turbulence equations, suggested by Yeo (1987), is analyzed theoretically and experimentally. It was formulated by applying the filtering concepts to the convolution integral average definition with the Gaussian response function. This filtering approach seems to be superior to the conventional averaging methods in which all four terms at the doubly average vol must be defined separately, and it also gives a very useful tool in understanding the turbulence structures. By theoretically analyzing the newly derived description for the averaged non-linear terms, it is found that the vortex stretching can be explicitly accounted for. Furthermore, comparisons of the correlation coefficients based on the experimental data show that the vortex stretching acts most significantly on the turbulence residual stress. Thus, it strongly supports the claim that the vortex stretching is essential in the transfer of turbulence. In addition. a general form of turbulent energy models in LES is derived, by which it is recognized that the Smagorinsky, the vorticity and the SGS energy models are not distinctive.