• 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 Society for Precision Engineering
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• v.23 no.9 s.186
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• pp.76-83
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• 2006

Machining accuracy is closely related with tool deflection induced by cutting forces. In this research, cutting forces and tool deflection in end milling are expressed as a closed form of tool rotational angle and cutting conditions. The discrete cutting fores caused by periodic tool entry and exit are represented as a continuous function using the Fourier series expansion. Tool deflection is predicted by direct integration of the distributed loads on cutting edges. Cutting conditions, tool geometry, run-outs and the stiffness of tool clamping part are considered together far cutting forces and tool deflection estimation. Compared with numerical methods, the presented method has advantages in prediction time reduction and the effects of feeding and run-outs on cutting forces and tool deflection can be analyzed quantitatively. This research can be effectively used in real time machining error estimation and cutting condition selection for error minimization since the form accuracy is easily predicted from tool deflection curve.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2005.10a
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• pp.781-785
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• 2005

Cutting forces and tool deflection in end milling are represented as the closed form of tool rotational angle and cutting conditions. The discrete cutting forces caused by tool entry and exit are continued using the Fourier series expansion. Tool deflection is predicted by direct integration of the distributed loads on cutting edges. Cutting conditions, tool geometry, run-outs and the stiffness of tool clamping pan are considered for cutting forces and tool deflection estimation. Compared to numerical methods, the presented method has advantages in short prediction time and the effects of feeding and run-outs on cutting forces and tool deflection can be analyzed quantitatively. This research can be effectively used in real time machining error estimation and cutting condition selection for error minimization since the ferm accuracy is easily predicted by tool deflect ion curve.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1330-1333
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• 1997

In this paper, the optimal torque shaping is obtained for 3-axis rotation of a spacecraft. The true optimal 3-axis rotation of rigid spaeraft is first investigated via parameter optimization method with prescribed switching times. Input torque shape of the troque generating device mounted on the central hub is optimized using fourier Series expansion so that the spacecraft may slew while minimizing the vibration energy of flexible modes. Numerical results show that proposed method suggests a reference trahectory for open-loop control, and also verify that it can minimize the vibratory modes of the spacecraft during/after the rest-to-rest maneuver.

• Proceedings of the KIPE Conference
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• 2001.10a
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• pp.556-560
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• 2001

In this paper, a soft-switching discontinuous mode (DCM) power factor corrected (PFC) converter is analyzed by applying the double Fourier series expansion. It is found that the fundamental component and higher-order harmonics included in the input current waveform are obtained by the Fourier series expansion of the mean value of the inductor current. From the theoretical analysis, a new method removing the distortion of the input current waveform is proposed. In spite of an open loop system, the proposed method makes a great improvement of the total harmonic distortion even if the ratio of output voltage to input voltage is very low.

• 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.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.2
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• pp.150-160
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• 2002

The free vibration characteristics of the triple cylindrical shells filled with fluid are investigated. The triple cylindrical shells are filled with compressible fluid. The boundary condition is clamped at both ends. Analytical method is developed to evaluate natural frequencies of triple cylindrical shells using Sanders' shell theory and courier series expansion by Stokes' transformation. Their results are compared with those of finite element method to verify the validation of the method developed. The modal characteristics of shells filled with fluid at region 1, 2 and 3 are evaluated.

• Geophysics and Geophysical Exploration
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• v.24 no.4
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• pp.158-163
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• 2021

The frequency-domain induced polarization (IP) response based on Cole-Cole model is expressed as a simple equation in close form. However, it is difficult to compute the time-domain IP response based on Cole-Cole model or any other relaxation model because it cannot be written in closed form. In this study, using numerical experiments, we compared three numerical methods for calculating the time-domain IP response of the Cole-Cole model asymptotically: series expansion, digital linear filtering and Fourier transform. The series expansion method is inadequately accurate for certain time values and converges very slowly. A digital linear filter specially designed to calculate the time-domain IP response does not present the desired accuracy, especially at later times. The Fourier transform method can overcome the abovementioned problems and present the time-domain IP response with adequate accuracy for all time values, even though more computing time is required.

• Journal of KSNVE
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• v.4 no.2
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• pp.163-175
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• 1994

An analytical method for nautral frequencies of a partially liquid- filled circular cylindrical shell with various boundary conditions is developed by means of the Stokes's transformation and Fourier series expansion on the basis of Sanders' shell equation. The liquid-shell coupled system is divided into two regions for convenient formulation. One is the empty shell region in which the Sanders' shell equations are formulated without the lipuid effect, the other is wetted shell region in which the shell equations are formulated with consideration of the liquid dynamic effect. The shell equations for each regions are combined by the geometry and the force continuities at the junction of the two regions. For the vibration relevant to the liquid motion, the velocity potential of liquid is assumed as a sum of linear combination of suitable harmonic functions in axial direction. The unknown parameters are selected to satisfy the boundary condition along the wetted shell surface. The natural frequencies of the liquid filled cylindraical shells with the clamped- free and the clamped-clamped boundary conditions examined in the previous works, are obtained by this analytical method. The results are compared with the previous works, and excllent agreement is found for the natural frequencies of the shells.

• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.333-347
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• 2015

In this paper, by using the modular forms of weight nk ($2{\leq}n{\in}\mathbb{N}$ and $k{\in}\mathbb{Z}$), we construct a formula which generates modular forms of weight 2nk+4. This formula consist of some known results in [14] and [4]. Moreover, we obtain Fourier expansion of these modular forms. We also give some properties of an operator related to the derivative formula. Finally, by using the function $j_4$, we obtain the Fourier coefficients of modular forms with weight 4.