• 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 KSR Conference
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• 2008.06a
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• pp.841-848
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• 2008

This paper examined dynamic characteristics of high speed trains using a time varying frequency transform. Fourier transform based methods are frequently used for the calculation of the dynamic characteristics of trains in the frequency domain, but they cannot represent the time-varying characteristics. Therefore it is necessary to examine their characteristics using a time-varying frequency transform. For the examination, the non-stationary vibration of wheelset, bogie, and carbody are measured using accelerometers and stored in a data aquisition system. They are processed with localization of the data by modulating with a window function, and Fourier transform is taken to each localized data, called the short-time Fourier transform. From the processed results, time varying auto-spectral density, cross-spectral density, frequency response, and coherence functions have been calculated. From the analysis, it is confirmed that the time varying frequency transform is a useful method for analyzing the dynamic characteristics of high speed trains.

• Structural Engineering and Mechanics
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• v.87 no.2
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• pp.165-172
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• 2023

This paper presents a novel method for modeling elastic wave propagation in long beams. The proposed method derives a solution for the transient transverse displacement of the beam's neutral axis without assuming the separation of variables (SV). By mapping the governing equation from the space domain to the frequency domain using Fourier transformation (FT), the transverse displacement function is determined as a convolution integral of external loading functions and a combination of trigonometric and Fresnel functions. This method determines the beam's response to general loading conditions as a linear combination of the analytical response of a beam subjected to an abrupt localized loading. The proposed solution method is verified through finite element analysis (FEA) and wave propagation patterns are derived for tone burst loading with specific frequency contents. The results demonstrate that the proposed solution method accurately models wave dispersion, reduces computational cost, and yields accurate results even for high-frequency loading.

• The Bulletin of The Korean Astronomical Society
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• v.32 no.1
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• pp.36.2-36.2
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• 2007

• Journal of the Chungcheong Mathematical Society
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• v.29 no.2
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• pp.283-286
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• 2016

In this paper, we find a new recurrence formula of the Euler zeta functions.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.569-579
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• 1997

We investigate the existence of the operator-valued Feynman integral when a Wiener functional is given by a Fourier transform of complex Borel measure.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1321-1322
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• 2014

• Proceedings of the KIEE Conference
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• 1979.08a
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• pp.155-157
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• 1979

The Fourier convolution algorithms are used to reconstruct a 3-D density function from the projection data sets. The convolved data are then back projected to obtain a density function. There are several choices of the weighting function for the design of the reconstruction(deblurring) filter. Present paper reviews the design of reconstruction filter considering the problems such as the effects of sampling rate, aliasing, and noise.

• Interaction and multiscale mechanics
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• v.6 no.3
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• pp.287-300
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• 2013

In this paper, the effect of impulsive line on the propagation of shear waves in non-homogeneous elastic layer is investigated. The rigidity and density in the intermediate layer is assumed to vary quadratic as functions of depth. The dispersion equation is obtained by using the Fourier transform and Green's function technique. The study ends with the mathematical calculations for transmitted wave in the layer. These equations are in complete agreement with the classical results when the non-homogeneity parameters are neglected. Various curves are plotted to show the effects of non-homogeneities on shear waves in the intermediate layer.

• Economic and Environmental Geology
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• v.25 no.1
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• pp.73-77
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• 1992

This paper compares numerical quadrature techniques for computing an inverse Fourier transform integral in two-dimensional resistivity modeling. The quadrature techniques using exponential and cubic spline interpolations are examined for the case of a homogeneous earth model. In both methods the integral over the interval from 0 to ${\lambda}_{min}$, where ${\lambda}_{min}$, is the minimum sampling spatial wavenumber, is calculated by approximating Fourier transformed potentials to a logarithmic function. This scheme greatly reduces the inverse Fourier transform error associated with the logarithmic discontinuity at ${\lambda}=0$. Numrical results show that, if the sampling intervals are adequate, the cubic spline interpolation method is more accurate than the exponential interpolation method.