• East Asian mathematical journal
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• v.26 no.1
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• pp.105-113
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• 2010

In the spectral analysis, Fourier coeffcients are very important to give informations for the original signal f on a finite domain, because they recover f. Also Fourier analysis has extension to wavelet analysis for the whole space R. Various kinds of reconstruction theorems are main subject to analyze signal function f in the field of wavelet analysis. In this paper, we will present a new reconstruction theorem of functions in $L^1(R)$ using a nonharmonic Fourier series. When we construct this series, we have used dyadic subdivision schemes.

• Journal of Magnetics
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• v.18 no.2
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• pp.130-134
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• 2013

Most electrical machines like motor, generator and transformer are symmetric in terms of magnetic field distribution and mechanical structure. In order to analyze these problems effectively, many coupling techniques have been introduced. This paper deals with a coupling scheme for open boundary problem of symmetric and periodic structure. It couples an analytical solution of Fourier series expansion with the standard finite element method. The analytical solution is derived for the magnetic field in the outside of the boundary, and the finite element method is for the magnetic field in the inside with source current and magnetic materials. The main advantage of the proposed method is that it retains sparsity and symmetry of system matrix like the standard FEM and it can also be easily applied to symmetric and periodic problems. Also, unknowns of finite elements at the boundary are coupled with Fourier series coefficients. The boundary conditions are used to derive a coupled system equation expressed in matrix form. The proposed algorithm is validated using a test model of a bush bar for the power supply. And the each result is compared with analytical solution respectively.

• Structural Engineering and Mechanics
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• v.16 no.6
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• pp.655-674
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• 2003

Investigated in this study are the natural vibration characteristics of the coaxial cylindrical shells coupled with a fluid. Theoretical method is developed to find the natural frequencies of the shell using the finite Fourier series expansion, and their results are compared with those of finite element method to verify the validation of the method developed. The effect of the fluid-filled annulus and the boundary conditions on the modal characteristics of the coaxial shells is investigated using a finite element modeling.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.9
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• pp.439-453
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• 2001

This study deals with the free vibration of two identical circular plates coupled with a bounded fluid. An analytical method based on the finite Fourier-Bessel series expansion and Rayleigh-Ritz method is suggested. In the theory, it is assumed that the ideal fluid in a rigid cylindrical container and the two plates are clamped along the plate edges. The proposed method is verified by the finite element analysis using commercial program with a good accuracy. Two transverse vibration modes, namely in-phase and out-of-phase, are observed alternately in the fluid-coupled system when the number of nodal circles increases for the fixed nodal diameter. The effect of gap between the plates on the fluid-coupled natural frequencies sis also investigated.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.406-412
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• 1996

Optimal trajectory for a robot manipulator minimizing actuator torques or energy consumption in a fixed traveling time is obtained in the presence of obstacles. All joint displacements are represented in finite terms of Fourier cosine series and the coefficients of the series are obtained optimally by nonlinear programming. Thus, the geometric path need not be prespecified and the full dynamic model is employed. To avoid the obstacles, the concept of penalty area is newly introduced and this penalty area is included in the performance index with an appropriate weighting coefficient. This optimal trajectory will be useful as a geometric path in the minimum-time trajectory planning problem.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2002.11b
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• pp.908-913
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• 2002

An analytical study is presented on the hydroelastic vibration of two rectangular identical plates coupled with a bounded fluid by using the finite Fourier series expansion method. It is observed that the two contrastive modes, the so called the out-of-phase and in-phase modes appear. The proposed analytical method is verified by observing a good agreement to three dimensional finite element analysis results. All natural frequency of the in-phase modes can be predicted well by the combination of the dry beam modes. The theoretical prediction for the out-of-phase mode can be improved by using the polynomial functions satisfying the plate boundary conditions and fluid volume conservation instead of using dry beam modes.

• Proceedings of the KIEE Conference
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• 1998.07a
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• pp.64-66
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• 1998

This paper presents a new efficient method for transient analysis in magnetodynamic systems of linear eddy current problems. This mehtod employs the Fourier transform and the high-order frequency sensitivity of harmonic finite element method. By taking into account the time-constant of magnetodynamic system, the Fourier integral of continuous frequency is converted into the Fourier series of discrete frequency. And with the results of Fourier series expansion of converted input wave form, the responses of each sinusoids is superposed to give the total response of the magnetodynamic systems. But, if the frequency band of input wave form is broad, it takes long computational time since all responses for each sinusoids must be calculated. Therefore, the high-order frequency sensitivity method is employed to estimate the response variation to frequency. The proposed algorithm is applied to an induction heating system to validate its numerical efficiency.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.541-555
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• 1996

The Fourier transform plays a central role in the theory of distribution on Euclidean spaces. Although Lebesgue measure does not exist in infinite dimensional spaces, the Fourier transform can be introduced in the space $(S)^*$ of generalized white noise functionals. This has been done in the series of paper by H.-H. Kuo [1, 2, 3], [4] and [5]. The Fourier transform $F$ has many properties similar to the finite dimensional case; e.g., the Fourier transform carries coordinate differentiation into multiplication and vice versa. It plays an essential role in the theory of differential equations in infinite dimensional spaces.

• Journal of Electrical Engineering and Technology
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• v.10 no.3
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• pp.990-1001
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• 2015

This paper presents analysis of Switched Reluctance Machine (SRM) using Geometry Based Analytical Model (GBAM), Finite Element Analysis (FEA) and Fourier Series Model (FSM) with curve fitting technique. Further a Transient Analysis (TA) technique is proposed to corroborate the analysis. The main aim of this paper is to give in depth procedure in developing a Geometry Based Analytical Model of Switched Reluctance Machine which is very accurate and simple. The GBAM is developed for the specifications obtained from the manufacturer and magnetizing characteristic of the material used for the construction. Precise values of the parameters like Magneto Motive Force (MMF), flux linkage, inductance and torque are obtained for various rotor positions taking into account the Fringing Effect (FE). The FEA model is developed using MagNet7.1.1 for the same machine geometry used in GBAM and the results are compared with GBAM. Further another analytical model called Fourier Series Model is developed to justify the accuracy of the results obtained by the methods GBAM and FEA model. A prototype of microcontroller based SRM drive system is constructed for validating the analysis and the results are reported.

• The Journal of the Acoustical Society of Korea
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• v.18 no.7
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• pp.39-44
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• 1999

An analysis of the frequency parameters and vibrational modes is described for a rectangular plate. Double Fourier sine series is used as a modal displacement functions of a rectangular plate and applied to the free vibration analysis of a rectangular plate under various boundary conditions. The frequency parameters obtained by the double Fourier sine series method are compared with those obtained by the theory of finite element method and Ritz method. Frequency parameters are presented for the various aspect ratios for plate. The first four modal shapes for the rectangular plate under various boundary conditions are accurately described.