• Journal of Ocean Engineering and Technology
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• v.6 no.2
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• pp.41-45
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• 1992

In this paper an application technique of moment equation method to solution of nonlinear rolling equation of motion of ships is investigated. The exciting moment in the equation of rolling motion of ships is described as non-white noise. This non-white exciting moment is generated through use of a shaping filter. These coupled equations are used to generate moment equations. The nonstationary responses of the nonlinear system are obtained. The results are compared with those of a linear system.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.3
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• pp.697-704
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• 1995

The dynamic characteristics of a system can be critically influenced by system uncertainty, so the dynamic system must be analyzed stochastically in consideration of system uncertainty. This study presents the stochastic model of a nonlinear dynamic system with uncertain parameters under nonstationary stochastic inputs. And this stochastic system is analyzed by a new stochastic process closure method and moment equation method. The first moment equation is numerically evaluated by Runge-Kutta method and the second moment equation is numerically evaluated by stochastic process closure method, 4th cumulant neglect closure method and Runge-Kutta method. But the first and the second moment equations are coupled each other, so this equations are approximately evaluated by a iterative method. Finally the accuracy of the present method is verified by Monte Carlo simulation.

• International Journal of CAD/CAM
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• v.8 no.1
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• pp.69-72
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• 2009

In this paper, we present a new shape descriptor, which is named Poisson equation-Fourier-Mellin moment Descriptor. We solve the Poisson equation in the shape area, and use the solution to get feature function, which are then integrated using Fourier-Mellin moment to represent the shape. This method develops the Poisson equation-geometric moment Descriptor proposed by Lena Gorelick, and keeps both advantages of Poisson equation-geometric moment and Fourier-Mellin moment. It is proved better than Poisson equation-geometric moment Descriptor in shape recognition and classification experiments.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.4
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• pp.127-134
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• 1995

The dynamic characteristics of a system can be critically influenced by system uncertainty, so the dynamic system must be analyzed stochastically in consideration of system uncertainty. This study presents a generalized stochastic model of dynamic system subjected to bot external and parametric nonstationary stochastic input. And this stochastic system is analyzed by a new stochastic process closure method and moment equation method. The first moment equation is numerically evaluated by Runge-Kutta method. But the second moment equation is founded to constitute an infinite coupled set of differential equations, so this equations are numerically evaluated by cumulant neglect closure method and Runge-Kutta method. Finally the accuracy of the present method is verified by Monte Carlo simulation.

• Structural Engineering and Mechanics
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• v.52 no.3
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• pp.525-540
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• 2014

The Lyapunov exponent and moment Lyapunov exponents of Hill's equation with frequency and damping coefficient fluctuated by correlated wideband random processes are studied in this paper. The method of stochastic averaging, both the first-order and the second-order, is applied. The averaged $It\hat{o}$ differential equation governing the pth norm is established and the pth moment Lyapunov exponents and Lyapunov exponent are then obtained. This method is applied to the study of the almost-sure and the moment stability of the stationary solution of the thin simply supported beam subjected to time-varying axial compressions and damping which are small intensity correlated stochastic excitations. The validity of the approximate results is checked by the numerical Monte Carlo simulation method for this stochastic system.

• Magazine of the Korean Society of Agricultural Engineers
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• v.42 no.2
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• pp.78-85
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• 2000

The moment equations of the concentration distribution for the multi-region model are derived using the method of moment. The method originally devised by Aris is to obtain the concentration moments satisfying a given PDE (Partial Differential Equation. The method of moment is used to obtain the first five moments (0th to 4to) that satisfy the model PDE. Each moment of the concentration distribution for the model equation is plotted for the dimensionless time and gave similar results except the skewness and the kurtosis. The results of the analysis show the physical meaning of each moment. The comparisons with the number of regions or the global interaction coefficient give a possibility to determine the parameters of the multi-region model with the analytical concepts.

• Structural Engineering and Mechanics
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• v.23 no.6
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• pp.599-613
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• 2006

A method for the dynamical analysis of FE discretized uncertain linear and nonlinear structures is presented. This method is based on the moment equation approach, for which the differential equations governing the response first and second-order statistical moments must be solved. It is shown that they require the cross-moments between the response and the random variables characterizing the structural uncertainties, whose governing equations determine an infinite hierarchy. As a consequence, a closure scheme must be applied even if the structure is linear. In this sense the proposed approach is approximated even for the linear system. For nonlinear systems the closure schemes are also necessary in order to treat the nonlinearities. The complete set of equations obtained by this procedure is shown to be linear if the structure is linear. The application of this procedure to some simple examples has shown its high level of accuracy, if compared with other classical approaches, such as the perturbation method, even for low levels of closures.

• Journal of Korean Society for Atmospheric Environment
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• v.18 no.5
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• pp.345-353
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• 2002

A study of polydispersed aerosol dynamics by Electrostatic Precipitator (ESP) was carried out. The log-normal particle size distribution was assumed and moment method was considered. In order to apply moment method in Deutsch-Anderson equation, Cunningham slip correction factor and Cochet's charge equation were simplified for certain range of particle size. The three parameters, which explain the particle size distribution, such as total number concentration, geometric mean diameter, and geometric standard deviation were considered to derive the analytic solution. The obtained solution was compared with available numerical results (Bai et al., 1995). The comparison of the numerical and analytic results showed a good agreement.

• Journal of Advanced Marine Engineering and Technology
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• v.2 no.1
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• pp.3-14
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• 1978

The authors have developed a calculating method of propeller shaft alignment by the finite element method. The propeller shaft is divided into finite elements which can be treated as uniform section bars. For each element, the nodal point equation is derived from the stiffness matrix, the external force vector and the section force vector. Then the overall nodal point equation is derived from the element nodal point equation. The deflection, offset, bending moment and shearing force of each nodal point are calculated from the overall nodal point equation by the digital computer. Reactions and deflections of supporting points of straight shaft are calculated and also the reaction influence number is derived. With the reaction influence number the optimum alignment condition that satisfies all conditions is calculated by the simplex method of linear programming. All results of calculation are compared with those of Det norske Veritas, which has developed a computor program based on the three-moment theorem of the strength of materials. The authors finite element method has shown good results and will be used effectively to design the propeller shaft alignment.

• Journal of KSNVE
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• v.9 no.3
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• pp.502-508
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• 1999

Newly developed control methodology applied to dynamic system under random disturbance is investigated and its performance is verified experimentall. Flexible cantilever beam sticked with piezofilm sensor and piezoceramic actuator is modelled in physical domain. Dynamic moment equation for the system is derived via Ito's stochastic differential equation and F-P-K equation. Also system's characteristics in stochastic domain is analyzed simultaneously. LQG controller is designed and used in physical and stochastic domain as wall. It is shown experimentally that randomly excited beam on the base is controlled effectively by designed LQG controller in physical domain. By comparing the result with that of LQG controller designed in stochastic domain, it is shown that new control method, what we called $\ulcorner$Heo-stochastic controller design technique$\lrcorner$, has better performance than conventional ones as a controller.