• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.155-164
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• 2003

The existence and representations of some generalized inverses, including ${A_{T,*}}^{(2)},\;{A_{T,*}}^{(1,2)},\;{A_{T,*}}^{(2,3)},\;{A_{*,S}}^{(2)},\;{A_{*,S}}^{(1,2)}\;and\;{A_{*,S}}^{(2,4)}$, are showed. As applications, the perturbation theory for the generalized inverse {A_{T,S}}^{(2)} and the perturbation bound for unique solution of the general restricted system $A_{x}$ = b(dim(AT)=dimT, $b{\in}AT$ and $x{\in}T$) are studied. Moreover, a characterization and representation of the generalized inverse ${A_{T,*}}^{(2)}$ is obtained.

• Bulletin of the Korean Chemical Society
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• v.27 no.10
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• pp.1659-1663
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• 2006

A many-body master equation is constructed by incorporating stochastic terms responsible for chemical reactions into the many-body Smoluchowski equation. Two forms of Langevin-type of memory equations describing the time evolution of dynamical variables under the influence of time-independent perturbation with an arbitrary intensity are derived. One form is convenient in obtaining the dynamics approaching the steady-state attained by the perturbation and the other in describing the fluctuation dynamics at the steady-state and consequently in obtaining the linear response of the system at the steady-state to time-dependent perturbation. In both cases, the kinetics of statistical averages of variables is found to be obtained by analyzing the dynamics of time-correlation functions of the variables.

• Structural Engineering and Mechanics
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• v.69 no.2
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• pp.205-219
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• 2019

This paper analyzes nonlinear free vibration of the circular nano-tubes made of functionally graded materials in the framework of nonlocal strain gradient theory in conjunction with a refined higher order shear deformation beam model. The effective material properties of the tube related to the change of temperature are assumed to vary along the radius of tube based on the power law. The refined beam model is introduced which not only contains transverse shear deformation but also satisfies the stress boundary conditions where shear stress cancels each other out on the inner and outer surfaces. Moreover, it can degenerate the Euler beam model, the Timoshenko beam model and the Reddy beam model. By incorporating this model with Hamilton's principle, the nonlinear vibration equations are established. The equations, including a material length scale parameter as well as a nonlocal parameter, can describe the size-dependent in linear and nonlinear vibration of FGM nanotubes. Analytical solution is obtained by using a two-steps perturbation method. Several comparisons are performed to validate the present analysis. Eventually, the effects of various physical parameters on nonlinear and linear natural frequencies of FGM nanotubes are analyzed, such as inner radius, temperature, nonlocal parameter, strain gradient parameter, scale parameter ratio, slenderness ratio, volume indexes, different beam models.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.411-423
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• 2010

In this paper, a numerical method for singular perturbation problems arising in chemical reactor theory for general singularly perturbed two point boundary value problems with boundary layer at one end(left or right) of the underlying interval is presented. The original second order differential equation is replaced by an approximate first order differential equation with a small deviating argument. By using the trapezoidal formula we obtain a three term recurrence relation, which is solved using Thomas Algorithm. To demonstrate the applicability of the method, we have solved four linear (two left and two right end boundary layer) and one nonlinear problems. From the results, it is observed that the present method approximates the exact or the asymptotic expansion solution very well.

• Structural Engineering and Mechanics
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• v.9 no.2
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• pp.181-193
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• 2000

The objective of this research is to propose a new global damage detection parameter, termed as the static defect energy (SDE). This candidate parameter possesses the ability to detect, locate and quantify structural damage. To have a full understanding about this parameter and its applications, the scope of work can be divided into several tasks: theory and formulation, numerical simulation studies, experimental verification and feasibility studies. This paper only deals with the first part of the task. Brief introduction will be given to the dynamic defect energy (DDE) after systematically reviewing the previous works. Process of applying the perturbation method to the oscillatory system to obtain a static expression will be followed. Two implementation methods can be used to obtain SDE equations and the diagrams. Both results are equally good for damage detection.

• Proceedings of the KIEE Conference
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• 2001.07a
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• pp.112-115
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• 2001

Eigenvalue perturbation theory of augmented system matrix(AMEP) is a useful tool in the analysis and design of large scale power systems. This paper describes the application results of AMEP algorithm with respect to all controller parameter of KEPCO systems. AMEP for interarea and local mode can be used for turning controller parameter, and verifying system data and linear model of controller.

• Journal of Ocean Engineering and Technology
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• v.33 no.3
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• pp.229-235
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• 2019

In this study, a two-dimensional oscillating foil with forward speed in a propagating wave flow field was considered. The time-mean power to maintain the heaving and pitching motions of the foil was analyzed using the perturbation theory in an ideal fluid. The power, which was a non-linear quantity of the second-order, was expressed in terms of the quadratic transfer functions related to the mutual product of the heaving and pitching motions and incoming vertical flow. The effects of the pivot point and phase difference among the disturbances were studied. The negative power, which indicates energy extraction from the fluid, is shown as an example calculation.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.4
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• pp.411-418
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• 1999

Generally PI controller is used in the servo system, But the time response of the system which is designed by the PI control scheme is deviated from the desired time response by the system parameter variation or the perturbation like the torque disturbance. LMFC(Linear Model Following Controller) is used to make the response of the system follow that of the model even though the parameter variation or the perturbation exists. In this paper, the design method which uses auxiliary model to construct the robustness enhancer in LMFC is proposed. And this robustness enhancer is designed by robust control theory. The proposed method has facter convergence time against low frequency torque disturbance than LMFC. The results are verified by SIMULINK simulation and experiments.

• Journal of KSNVE
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• v.7 no.3
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• pp.387-392
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• 1997

This paper concerns a SCARA robot with the flexible forearm linked to the rigid upper arm. The equations of motion are derived by the Lagrangian mechanics. For controller design, the perturbation approach is taken to separate the original equations of motion into linear equations describing small perturbed motions and nonlinear equations describing purely rigid motion of the robot. To effect the desired payload motion, open loop control inputs are determined based on the inverse dynamics of the latter. In order to reduce the positional error during maneuver, an active vibration suppression is done. To this end, a feedback control is designed for robustness against disturbance on the basis of the linear equations and the LQR theory modified to have a prescribed degree of stability. The proposed control scheme shows satisfactory performances in experiments as well as in numerical simulations.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.225-228
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• 1996

This paper concerns a SCARA type robot with the second arm flexible. Its equations of motion are derived by the Lagrangian mechanics. For controller design, the perturbation approach is taken to separate the original equations of motion into linear equations describing small perturbed motions and nonlinear equations describing purely rigid motion of the robot. To effect the desired payload motion, open loop control inputs are first determined based on the inverse dynamics of the latter. Next, in order to reduce the positional error during maneuver, an active vibration suppression is done. To this end, a feedback control is designed for robustness against disturbance on the basis of the linear equations and the LQR theory modified with a prescribed degree of stability. The numerical simulations results show the satisfactory control performance.