• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1055-1071
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• 2010

Recently, a number of algorithms have been proposed for numerical evaluation of Hankel transforms as these transforms arise naturally in many areas of science and technology. All these algorithms depend on separating the integrand $rf(r)J_{\upsilon}(pr)$ into two components; the slowly varying component rf(r) and the rapidly oscillating component $J_{\upsilon}(pr)$. Then the slowly varying component rf(r) is expanded either into a Fourier Bessel series or various wavelet series using different orthonormal bases like Haar wavelets, rationalized Haar wavelets, linear Legendre multiwavelets, Legendre wavelets and truncating the series at an optimal level; or approximating rf(r) by a quadratic over the subinterval using the Filon quadrature philosophy. The purpose of this communication is to take a different approach and replace rapidly oscillating component $J_{\upsilon}(pr)$ in the integrand by its Bernstein series approximation, thus avoiding the complexity of evaluating integrals involving Bessel functions. This leads to a very simple efficient and stable algorithm for numerical evaluation of Hankel transform.

• 한국음향학회지
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• 제37권4호
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• pp.181-187
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• 2018

본 논문은 원형 단면 임피던스 튜브내에 고정된 미세천공 탄성판의 흡음을 해석적으로 구하는 방법을 다루었다. 판의 진동과 덕트 내부 음장을 모드 함수의 무한 급수의 합으로 전개하였는데 반경방향으로는 Bessel 함수를 포함한다. 평면파 가정하에서 저주파수 대역의 근사식을 판의 처음 몇 개의 모드만 고려하여 흡음율을 유도하였으며 등가 임피던스를 갖는 단일 표면의 형태로 제시하였다. 본 논문에서 제안한 공식과 FEM(Finite Element Method)을 이용한 결과는 잘 일치 하였는데 탄성의 효과는 판의 고유진동수에 해당하는 골 또는 피크의 형태로 나타난다. 천공율이 매우 작으면 진동의 영향이 지배적이나 천공율이 어느 한계이상 되면 박판의 탄성거동은 매우 작게 나타나고 강체 MPP(Micro-Perforated Plate)의 흡음 특성이 지배적이 된다.

• Structural Engineering and Mechanics
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• 제10권5호
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• pp.441-449
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• 2000

In this study, the state equation for axisymmetric bending of laminated transversely isotropic circular plates on elastic foundation is established on the basis of three-dimensional elasticity. By using the expansions of Bessel functions, an analytical solution of the problem is presented. As a result, all the fundamental equations of three-dimensional elasticity can be satisfied exactly and all the independent elastic constants can be fully taken into account. Furthermore, the continuity conditions at the interfaces of plies can also be satisfied.

• 대한수학회지
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• 제54권2호
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• pp.575-598
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• 2017

This paper introduces and studies a generalization of the classical Struve function of order p given by $$_aS_{p,c}(x):=\sum\limits_{k=0}^{\infty}\frac{(-c)^k}{{\Gamma}(ak+p+\frac{3}{2}){\Gamma}(k+\frac{3}{2})}(\frac{x}{2})^{2k+p+1}$$. Representation formulae are derived for $_aS_{p,c}$. Further the function $_aS_{p,c}$ is shown to be a solution of an (a + 1)-order differential equation. Monotonicity and log-convexity properties for the generalized Struve function $_aS_{p,c}$ are investigated, particulary for the case c = -1. As a consequence, $Tur{\acute{a}}n$-type inequalities are established. For a = 2 and c = -1, dominant and subordinant functions are obtained for the Struve function $_2S_{p,-1}$.

• Geomechanics and Engineering
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• 제6권3호
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• pp.213-233
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• 2014

The present paper is dealing with the investigation of the stress field around the infinitely long cylindrical cavity, of a circular cross section, contained in the transversally isotropic elastic continuum. Investigation is based upon the determination of the stress function that satisfies the biharmonic equation, for the given boundary conditions and for rotationaly symmetric loading. The solution of the partial differential equation of the problem is given in the form of infinite series of Bessel's functions. Determination of the stress-strain field around cavities is a common requirement for estimation of safety of underground rock excavations.

• 한국수산과학회지
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• 제25권6호
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• pp.443-456
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• 1992

황해에서와 같은 선형의 양향성 대륙붕 해저 지형에서 저주파의 분산관계가 단주기$\cdot$단파까지 포함하는 장주기$\cdot$장파 경우에 대해 유도되었다. 선형의 양향성 대륙붕에서 장주기$\cdot$장파일 경우 Bessel 방정식이 유도되는데 비해 일반적인 경우에는 Hummer 방정식이 유도된다. Hummer 방정식의 해로 유도되는 confluent Hypergeometric 함수는 극한 경우에 여러 형태로 바뀐다. 단일한 대륙붕에서는 해안선과 수직한 방향의 대륵붕 규모가 Rossby deformation radius에 비해 많이 작을 때는 수평흐름의 수렴$\cdot$발산효과가 무시되지만 양향성 대륙붕에서는 수평흐름의 수린$\cdot$발산효과가 해안선과 수직한 방향의 대륙붕규모가 관계없이 파동역학에 결정적으로 중요하다. 수렴$\cdot$발산효과는 Kelvin 파를 포함시키며 대륙붕파의 파속을 감소시킨다. 끝으로 양향성 대륙붕의 비마찰 eigenfunction들의 직교가 증명되었다.

• Structural Engineering and Mechanics
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• 제12권1호
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• pp.85-100
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• 2001

In this paper, an analytical procedure for solving several static and dynamic problems of non-uniform beams is proposed. It is shown that the governing differential equations for several stability, free vibration and static problems of non-uniform beams can be written in the from of a unified self-conjugate differential equation of the second-order. There are two functions in the unified equation, unlike most previous researches dealing with this problem, one of the functions is selected as an arbitrary expression in this paper, while the other one is expressed as a functional relation with the arbitrary function. Using appropriate functional transformation, the self-conjugate equation is reduced to Bessel's equation or to other solvable ordinary differential equations for several cases that are important in engineering practice. Thus, classes of exact solutions of the self-conjugate equation for several static and dynamic problems are derived. Numerical examples demonstrate that the results calculated by the proposed method and solutions are in good agreement with the corresponding experimental data, and the proposed procedure is a simple, efficient and exact method.

• Structural Engineering and Mechanics
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• 제8권3호
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• pp.243-256
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• 1999

Using appropriate transformations, the differential equation for flexural free vibration of a cantilever bar with variably distributed mass and stiffness is reduced to a Bessel's equation or an ordinary differential equation with constant coefficients by selecting suitable expressions, such as power functions and exponential functions, for the distributions of stiffness and mass. The general solutions for flexural free vibration of one-step bar with variable cross-section are derived and used to obtain the frequency equation of multi-step cantilever bars. The new exact approach is presented which combines the transfer matrix method and closed form solutions of one step bars. Two numerical examples demonstrate that the calculated natural frequencies and mode shapes of a 27-storey building and a television transmission tower are in good agreement with the corresponding experimental data. It is also shown through the numerical examples that the selected expressions are suitable for describing the distributions of stiffness and mass of typical tall buildings and high-rise structures.

• Structural Engineering and Mechanics
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• 제54권4호
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• pp.623-648
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• 2015

A numerical approach is presented for the analysis of the forced vibration of a rigid surface foundation with arbitrary shape. In the analysis, the foundation is discretized into a number of sub squaree-lements. The dynamic response within each sub-element is described by the Green's function, which is obtained by the Fourier-Bessel transform and Precise Integration Method (PIM). Incorporating the displacement boundary condition and force equilibrium of the foundation, it obtains a system of linear algebraic equation in terms of the contact forces within each sub-element. Solving the equation leads to the desired dynamic impedance functions of the foundation. Numerical results are obtained for foundation not only with simple geometrical configurations, such as rectangular and circular foundation, but also the case of irregularly shaped foundation. Several comparisons between the proposed approach and other methods are made. Very good agreement is reached. Also, parametric studies are carried out on the dynamic response of foundation. Addressed in this study are the effects of Poisson's ratio, material damping and contact condition of soil-foundation interface. Several conclusions are drawn the significance of the factors.

• 지구물리와물리탐사
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• 제9권1호
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• pp.73-85
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• 2006

상시진동의 수직 성분에 대한 배열 관측은 상시진동이 대부분 레일리파의 기본 모드로 이루어졌다는 가정하에 지하 층서구조를 추정하기 위해 자주 수행된다. 자료획득, 처리 및 분석의 유용한 도구로서 공간 자기상관(SPAC) 방법이 많이 사용되는데 이는 실제로 M개의 원형 수진기 배열과 중앙의 하나 측점으로 이루어진다 (M 측점 원형 배열). 이 논문에서는 분석 효율 및 현장 노력의 관점에서 효율적인 자료획득을 위한 원형 배열에 필요한 측점의 최소 수에 대해 연구하였다. 이 연구에서는 먼저 M 무한대의 원형 배열을 위한 SPAC 계수들이 단지 Bessel 함수 J0(rk)(r은 반지름, k는 파수)로서 표현되는 SPAC 알고리듬의 이론적 배경을 재정리하였다. 두번째로 M 측점 원형 배열에 대해 상시진동 에너지장과 무관한 오차항을 포함하는 SPAC 계수들을 배열을 가로지르는 파의 방향에 한해 해석적으로 유도해 내고 수치적으로 이들 오차항들에 대해서 평가하였다. 주요 평가 결과들은: 1) 만약 SPAC 계수들이, 계수가 첫번째 최소값을 갖는 주파수까지 이용되면 다른 4-, 5-, 9-측점 배열들에 비교했을 때 3-측점 원형배열이 상시진동의 관측에 효율적이고 유리하다. 2) 나이퀴스트 파수가 유효한 SPAC 계수가 평가될 수 있는 주파수의 상한선을 결정하는데 가장 영향을 끼치는 요소이다.