• Smart Structures and Systems
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• v.2 no.4
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• pp.313-320
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• 2006

The reliability analysis of structures subjected to stochastic loading involves evaluation of time and probability of the system's residence in a reference domain. In this paper, we derive an asymptotic estimate of exit time for multi-degrees-of-freedom structural systems. The system's dynamics is governed by the Lagrangian equations with linear dissipation and fast additive noise. The logarithmic asymptotic of exit time is found explicitly as a sum of two terms dependent on kinetic and potential energy of the system, respectively. As an example, we estimate exit time and an associated structural performance for a rocking structure.

• Korean Chemical Engineering Research
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• v.57 no.5
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• pp.723-729
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• 2019

A theoretical analysis was conducted of convective instability driven by buoyancy forces under transient temperature fields in an annular porous medium bounded by coaxial vertical cylinders. Darcy's law and Boussinesq approximation are used to explain the characteristics of fluid motion and linear stability theory is employed to predict the onset of buoyancy-driven motion. The linear stability equations are derived in a global domain, and then cast into in a self-similar domain. Using a spectral expansion method, the stability equations are reformed as a system of ordinary differential equations and solved analytically and numerically. The critical Darcy-Rayleigh number is founded as a function of the radius ratio. Also, the onset time and corresponding wavelength are obtained for the various cases. The critical time becomes smaller with increasing the Darcy-Rayleigh number and follows the asymptotic relation derived in the infinite horizontal porous layer.

• 전기의세계
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• v.22 no.2
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• pp.28-32
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• 1973

System modeling is applied in developing a probabilistic linear estimator for the load of an electric power system for the purpose of short term load forecasting. The model assumer that the load in given by the suns of a periodic discrete time serier with a period of 24 hour and a residual term such that the output of a discrete time dynamical linear system driven by a white random process and a deterministic input. And also we have established the main forecasting algorithms, which are essemtally the Kalman filter-predictor equations.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.9
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• pp.2312-2321
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• 1994

In this work the dynamics of an electromagnetic levitation system is described by a set of three first order nonlinear ordinary differential equations. The objective is to design a digital linear controller which takes the inherent instability of the uncontrolled system and the disturbing force into consideration. The controller is made by employing digital linear quadratic(LQ) design methodology and the unknown state variables are estimated by the kalman filter. The state estimation is performed using not only an air gap sensor but also both an air gap sensor and a piezoelectric accelerometer. The design scheme resulted in a digital linear controller having good stability and performance robustness in spite of various modelling errors. In case of using both a gap sensor and an accelerometer for the state estimation, the control input was rather stable than that in a system with gap sensor only and the controller dealt with the disturbing force more effectively.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.167-183
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• 2002

A modified discretization ABS algorithm for solving a class of singular nonlinear systems, F($\chi$)=0, where $\chi$, F $\in$ $R^n$, is presented, constructed by combining a discretization ABS algorithm arid a method of Hoy and Schwetlick (1990). The second order differential operation of F at a point is not required to be calculated directly in this algorithm. Q-quadratic convergence of this algorithm is given.

• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.309-318
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• 1994

The approach presented in this paper is based on the transformation of the Stefan problem in one space dimension to an initial-boundary value problem for the heat equation in a fixed domain. Of course, the problem is non-linear. The finite element approximation adopted here is the standared continuous Galerkin method in time. In this paper, only the regular case is discussed. This means the error analysis is based on the assumption that the solution is sufficiently smooth. The aim of this paper is the existence of the solution in a finite Galerkin system of ordinary equations.

• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.463-475
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• 2009

This paper deals with the regularity properties for a class of semilinear integrodifferential functional differential equations. It is shown the relation between the reachable set of the semilinear system and that of its corresponding linear system. We also show that the Lipschitz continuity and the uniform boundedness of the nonlinear term can be considerably weakened. Finally, a simple example to which our main result can be applied is given.

• 전기의세계
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• v.28 no.1
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• pp.53-58
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• 1979

In the microwave heating system, a ferroresonant transformer is used to regulate the magnetron power fluctuation. For the simplification, nonlinear characteristics of the transformer and the magnetron are idealized to be piecewise linear. Dipped peak shape of the magnetron current is explained qualitatively by considering the fundamental and third harmonic frequency components in the circuit. Design equations providing the values of the leakage inductance, turn ratio of the transformer and the capacitance are derived analytically by cosnidering the fundamental frequency component only. The ferroresonant transformer is designed to obtain a required regulation and high input power factor from the derived design equations, and analytical calculations are compared with experimental measurements.

• Journal of Institute of Control, Robotics and Systems
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• v.21 no.4
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• pp.342-348
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• 2015

This paper presents a two-wheel balancing mobile robot with linear workspace extension structures. The two-wheel mobile robot has two linear motions at the waist and shoulder to have extended workspace. The linear motion of the waist and shoulder provides some structural advantages. A dynamic equation of the simplified robot system is derived. Simulation studies of the position control of the robot system are performed based on the dynamic equations. The dynamic relationship between a two-wheel mobile system and linear extension mechanism is observed by simulation studies.

• Structural Engineering and Mechanics
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• v.72 no.2
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• pp.229-244
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• 2019

Weak form integral equations are developed to investigate the flapwise bending vibration of the rotating beams. Rayleigh and Eringen nonlocal elasticity theories are used to investigate the rotatory inertia and Size-dependency effects on the flapwise bending vibration of the rotating cantilever beams, respectively. Through repetitive integrations, the governing partial differential equations are converted into weak form integral equations. The novelty of the presented approach is the approximation of the mode shape function by a power series which converts the equations into solvable one. Substitution of the power series into weak form integral equations results in a system of linear algebraic equations. The natural frequencies are determined by calculation of the non-trivial solution for resulting system of equations. Accuracy of the proposed method is verified through several numerical examples, in which the influence of the geometry properties, rotatory inertia, rotational speed, taper ratio and size-dependency are investigated on the natural frequencies of the rotating beam. Application of the weak form integral equations has made the solution simpler and shorter in the mathematical process. Presented relations can be used to obtain a close-form solution for quick calculation of the first five natural frequencies of the beams with flapwise vibration and non-local effects. The analysis results are compared with those obtained from other available published references.