• Structural Engineering and Mechanics
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• 제8권4호
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• pp.343-360
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• 1999

This work applies a structural analysis method based on an analytical solution from the Fourier series which transforms a half-range cosine expansion into a static solution involving plated structures. Two sub-matrices of in-plane and plate-bending problems are also formulated and coupled with the prescribed boundary conditions for these variables, thereby providing a convenient basis for a numerical solution. In addition, the plate connection are introduced by describing the connection between common boundary continuity and equilibrium. Moreover, a simple computation scheme is proposed. Numerical results are then compared with finite element results, demonstrating the numerical scheme's versatility and accuracy.

• Journal of Advanced Marine Engineering and Technology
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• 제14권4호
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• pp.46-56
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• 1990

Stress analysis of axi-symetric body with non-symetric loading and non-symetric given displacements is investigated in this paper using the finite element method. As the non-symetric load and non-symetric given displacements of axi-symetric body are generally periodic functions of angle .theta., the nodal forces and nodal displacements can be expanded in cosine and sine series, that is, Fourier series. Furthermore, using Euler's formula, the cosine and sine series can be converted into exponential series and it is prooved that the related calculus become more clear. Substituting the nodal displacements expanded in Fourier series into the strain components of cylindrical coordinates system, the element strains are expressed in series form and by the principal of virtual work, the element stiffness martix and element load vector are obtained for each order. It is also showed that if the non-symetric loads are even or odd functions of angle ${\theta}$ the stiffness matrix and load vector of the system are composed with only real numbers and relatively small capacity fo computer memory is enough for calculation.

• Journal of applied mathematics & informatics
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• 제26권5_6호
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• pp.1101-1121
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• 2008

One proposes an approach to fractional Fourier's transform, or Fourier's transform of fractional order, which applies to functions which are fractional differentiable but are not necessarily differentiable, in such a manner that they cannot be analyzed by using the so-called Caputo-Djrbashian fractional derivative. Firstly, as a preliminary, one defines fractional sine and cosine functions, therefore one obtains Fourier's series of fractional order. Then one defines the fractional Fourier's transform. The main properties of this fractal transformation are exhibited, the Parseval equation is obtained as well as the fractional Fourier inversion theorem. The prospect of application for this new tool is the spectral density analysis of signals, in signal processing, and the analysis of some partial differential equations of fractional order.

• Kyungpook Mathematical Journal
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• 제60권4호
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• pp.781-795
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• 2020

In this paper, we obtain an analytical solution for an unsolved definite integral RC (m, n) from a 1915 paper of Srinivasa Ramanujan. We obtain our solution using the hypergeometric approach and an infinite series decomposition identity. Also, we give some generalizations of Ramanujan's integral RC (m, n) defined in terms of the ordinary hypergeometric function 2F3 with suitable convergence conditions. Moreover as applications of our result we obtain nine new infinite summation formulas associated with the hypergeometric functions 0F1, 1F2 and 2F3.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1996년도 추계학술대회 논문집
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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.

• Structural Engineering and Mechanics
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• 제24권1호
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• pp.63-89
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• 2006

Geometric imperfections have an important influence on the buckling response of structural components. This paper describes an experimental technique for determining imperfections in long (5.7 m) structural members using a series of overlapping measurements. Measurements were performed on 31 austenitic stainless steel sections formed from three different production routes: hot-rolling, cold-rolling and press-braking. Spectral analysis was carried out on the imperfections to obtain information on the periodic nature of the profiles. Two series were used to model the profile firstly the orthogonal cosine and sine functions in a classic Fourier transform and secondly a half sine series. Results were compared to the relevant tolerance standards. Simple predictive tools for both local and global imperfections have been developed to enable representative geometric imperfections to be incorporated into numerical models and design methods.

• 한국통신학회논문지
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• 제31권3A호
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• pp.321-327
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• 2006

본 논문은 접지된 유전체 평면 위에 균일한 저항율을 갖는 저항띠 격자구조로 임의의 방향으로 입사되는 H-분극 전자파산란 문제를 모멘트 법으로 해석하였다. 기존의 논문에서는 전류밀도의 분포에 따라 기저함수를 다양한 직교다항식으로 변경하여 I-분극의 경우만 수치해석 하였다. 반면에, 본 연구에서는 각 저항띠의 양끝에서 유도 전류밀도가 0 이 되도록 cosine 함수와 sine 함수로 구성된 다항식의 급수로 나타내었다. 산란 전자계는 주기적인 구조에 대응시킬 수 있는 Floquet 모드함수의 급수로 전재하였으며, 미지의 계수를 구하기 위하여 경계조건을 적용하였다. 또한, Fourier-Galerkin 모멘트 법을 적용함으로서 접지된 유전체 위에 여러 가지 저항율을 갖는 저항띠에 대하여 기하광학적인 정규화 된 반사전력에 관한 스트립 폭 및 주기, 입사각의 영향을 수치해석 하였다.

• Journal of Electrical Engineering and Technology
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• 제7권2호
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• pp.163-170
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• 2012

This paper presents a DFT (Discrete Fourier Transform) based estimation algorithm for the parameters of a low-frequency oscillating signal. The proposed method estimates the parameters, i.e., the frequency, the damping factor, the mode amplitude, and the phase, by fitting a discrete Fourier spectrum with an exponentially damped cosine function. Parameter estimation algorithms that consider the spectrum leakage of the discrete Fourier spectrum are introduced. The multi-domain mode test functions are tested in order to verify the accuracy and efficiency of the proposed method. The results show that the proposed algorithms are highly applicable to the practical computation of low-frequency parameter estimations based on DFTs.

• JSTS:Journal of Semiconductor Technology and Science
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• 제1권4호
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• pp.209-215
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• 2001

In this paper a method for analysis and modelling of coplanar transmission interconnect lines that are placed on top of silicon-silicon oxide substrates is presented. The potential function is expressed by series expansions in terms of solutions of the Laplace equation for each homogeneous region of layered structure. The expansion coefficients of different series are related to each other and to potentials applied to the conductors via boundary conditions. In the plane of conductors, boundary conditions are satisfied at $N_d$ discrete points with $N_d$ being equal to the number of terms in the series expansions. The resulting system of inhomogeneous linear equations is solved by matrix inversion. No iterations are required. A discussion of the calculated line admittance parameters as functions of width of conductors, thickness of the layers, and frequency is given. The interconnect capacitance and conductance per unit length results are given and compared with those obtained using full wave solutions, and good agreement have been obtained in all the cases treated

• Kyungpook Mathematical Journal
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• 제45권1호
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• pp.73-85
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• 2005

In this paper a criterion for $L^1-convergence$ of a new modified sine sums is obtained by using $Ces{\grave{a}}ro$ means of integral and non-integral orders.