• 대한수학회논문집
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• 제27권4호
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• pp.721-732
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• 2012

The principal aim of the paper is to investigate new integral expression $${\int}_0^{\infty}x^{s+1}e^{-{\sigma}x^2}L_m^{(\gamma,\delta)}\;({\zeta};{\sigma}x^2)\;L_n^{(\alpha,\beta)}\;({\xi};{\sigma}x^2)\;J_s\;(xy)\;dx$$, where $y$ is a positive real number; $\sigma$, $\zeta$ and $\xi$ are complex numbers with positive real parts; $s$, $\alpha$, $\beta$, $\gamma$ and $\delta$ are complex numbers whose real parts are greater than -1; $J_n(x)$ is Bessel function and $L_n^{(\alpha,\beta)}$ (${\gamma};x$) is generalized Laguerre polynomials. Some integral formulas have been obtained. The Maple implementation has also been examined.

• 한국전기전자재료학회논문지
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• 제17권9호
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• pp.994-1000
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• 2004

We studied the characteristics of annular phase gratings as spatial frequency filters. We first calculated the Fraunhofer diffraction patterns of annular gratings and then got the modulation transfer function (MTF) from the zeroth order Hankel transform of the intensity distribution function. Binaryphase annular grating shows higher diffraction efficiency than binary phase rectangular grating. But the MTF decreases linearly in the low-frequency region as that of rectangular grating does. The diffraction pattern of 4-phase annular grating is similar to that of 2-phase grating and hence MTFs of the two are much alike. For 8-phase annular grating, the 7th order diffracted beam is the lowest one next to the first. Consequently, the diffraction efficiency is very high and the MTF graph is curved upward. The diffracted beams except the first order are negligible and hence the MTF characteristics are more improved in the case of 16-phase grating. But the degree of improvement becomes lowered c(Impaled with 8-phase grating. We made a 16-phase annular grating and measured its MTF. The experimental result agrees well with the calculated one.

• Structural Engineering and Mechanics
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• 제18권6호
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• pp.759-768
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• 2004

The torsion of a penny-shaped crack in a transversely isotropic strip is investigated in this paper. The shear moduli are functionally graded in such a way that the mathematics is tractable. Hankel transform is used to reduce the problem to solving a Fredholm integral equation. The crack tip stress field is obtained by taking the asymptotic behavior of Bessel function into account. The effects of material property parameters and geometry criterion on the stress intensity factor are investigated. Numerical results show that increasing the shear moduli's gradient and/or increasing the shear modulus in a direction perpendicular to the crack surface can suppress crack initiation and growth, and that the stress intensity factor varies little with the increasing of the strip's height.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2004년도 추계학술대회논문집
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• pp.1101-1106
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• 2004

This study presents the reconstruction of sound field radiated from an automotive engine using equivalent sources. Basic concept of the method presented is to replace the engine noise source with elementary sources of multipoles, e.g., monopoles and dipoles. The so-called Helmholtz equation least-squares (HELS) method can reconstruct the sound radiation fields from spherical geometries in a series expansion of spherical Hankel functions and spherical harmonics. In this paper, multi-Point, multipole equivalent sources are employed to reconstruct the sound field radiated from an automotive engine with a fixed rotation speed. To ensure and improve the accuracy of reconstruction, the spatial filters of multipole coefficients and wave-vectors are adopted for suppressing the adverse effect of high-order multipoles. Optimal filter shapes are designed with regularization parameters minimizing the generalized cross validation (GCV) function between actual and reproduced model. After regeneration of field pressures using the proposed method as many as necessary, the vibro-acoustic field of an engine could be reconstructed by using the BEM-based near-field acoustic holography (NAH) technique in a cost-effective manner.

• 한국지진공학회논문집
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• 제1권4호
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• pp.59-68
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• 1997

터널 등과 같은 지하구조계를 유한요소법 등의 수치적 방법으로 해석할 경우 인위적인 경제에서 파의 반사가 발생하게 되어 실제 결과의 큰 차이를 발생시킨다. 따라서 동역학적 하중을 받는 지하구조계는 실질적인 반무한 구조계로 고려되어야 한다. 특히 지하구조계는 실제 다층구조로 구성되어 있으므로 이러한 다층문제를 고려할 수 있어야 한다. 이를 위해 본 연구에서는 외부영역 경제적문제로 해석하기 위한 동적 수치기본해를 개발하였다. 주파수영역의 정적인 경우에 대한 엄밀 적분해와 Bessel 함수의 점근식을 이용한 적분을 통해 축대치문제를 2차원 문제로 보다 쉽게 적용할 수 있도록 하였다. 이와 같이 개발된 동적 수치기본해를 경제 적분 방정식에 적용하여 해석한 결과와 기존 해석결과와의 비교를 통해 그 효율성을 입증하였다. 또한 다층지반내 지하구조물에 대해 지반매체의 각 물성 및 공동의 깊이에 따른 민감도분석을 수해하여 지하구조계의 동적 거동특성 파악의 적용성을 다루었다.