• Structural Engineering and Mechanics
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• 제43권2호
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• pp.211-223
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• 2012

This paper deals with large deformation post-buckling of a linear-elastic and hygrothermal beam with axially nonmovable pinned-pinned ends and subjected to a significant increase in swelling by an alternative method. Analytical approximate solutions for the geometrically nonlinear problem are presented. The solution for the limiting case of a string is also obtained. By coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials, the governing differential equation with sinusoidal nonlinearity can be reduced to form a cubic-nonlinear equation, and supplementary condition with cosinoidal nonlinearity can also be simplified to be a polynomial integral equation. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. Two approximate formulae for load along axis, potential strain for free hygrothermal expansion and periodic solution are established for small as well as large angle of rotation at the end of the beam. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.

• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.299-309
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• 2013

In this paper, we introduce a new numerical technique which we call fractional Chebyshev finite difference method (FChFD). The algorithm is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. We tested this technique to solve numerically fractional BVPs. The proposed technique is based on using matrix operator expressions which applies to the differential terms. The operational matrix method is derived in our approach in order to approximate the fractional derivatives. This operational matrix method can be regarded as a non-uniform finite difference scheme. The error bound for the fractional derivatives is introduced. The fractional derivatives are presented in terms of Caputo sense. The application of the method to fractional BVPs leads to algebraic systems which can be solved by an appropriate method. Several numerical examples are provided to confirm the accuracy and the effectiveness of the proposed method.

• 한국항공우주학회지
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• 제47권3호
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• pp.220-227
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• 2019

궤도상에 있는 인공위성은 천문력 기반 태양 모델을 사용하여 기준 벡터를 형성한다. 이를 위해 제트 추진 연구소(JPL)에서 개발한 천문력인 DE-Series, 또는 Vallado가 제안한 기준 벡터 생성식을 사용한다. DE-Series는 체비셰프 다항식의 수치 계수를 제공하는데 정밀도가 높다는 장점이 있지만 인공위성의 탑재 컴퓨터의 계산 부담이 있으며, Vallado 방식은 생성식을 통해 태양 벡터를 간단히 구할 수 있지만 낮은 정밀도를 제공한다. 본 논문에서는 DE-Series를 통해 얻은 태양의 위치를 체비셰프 다항식으로 Curve fitting하여, 관성좌표계에서의 태양 위치좌표를 구할 수 있는 체비셰프 다항식 계수를 제공하는 프로그램을 개발하였다. 기존 방식에 비해 정밀도를 향상시킬 수 있었으며, 제안된 방법은 고성능, 고정밀 초소형위성 임무에 활용될 수 있다.

• Nonlinear Functional Analysis and Applications
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• 제28권3호
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• pp.647-657
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• 2023

The aim of this paper is to study certain subclass ${\tilde{S^q_{\Sigma}}}({\lambda},\,{\alpha},\,t,\,s,\,p,\,b)$ of analytic and bi-univalent functions which are defined by using symmetric q-derivative operator. We estimate the second and third coefficients of the Taylor-Maclaurin series expansions belonging to the subclass and upper bounds for Feketo-Szegö inequality. Furthermore, some relevant connections of certain special cases of the main results with those in several earlier works are also pointed out.

• 한국항행학회논문지
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• 제15권3호
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• pp.349-354
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• 2011

본 논문에서는 스트립 폭과 격자주기, 유전체 층의 비유전율과 두께, 그리고 transverse electric (TE) 평면파의 입사각에 따른 접지된 유전체 평면위의 스트립 양끝에서 0 저항율을 갖는 저항띠 격자구조에 의한 H-분극산란 문제를 Fourier-Galerkin Moment Method (FGMM)를 이용하여 해석하였다. 저항띠의 변하는 저항율은 저항띠의 양끝에서 0으로 변하는 경우를 취급하였고, 이때 저항띠 위에서 유도되는 전류밀도는 직교다항식의 일종인 2종 Chebyshev 다항식의 급수로 전개하였다. 반사전력의 급변점들은 공진효과에 기인한 것으로 과거에 wood's anomallies라고 불리워지며, 반사전력에 대한 수치결과들은 기존 논문의 균일 저항율의 수치 결과들과 비교하였다.

• Coupled systems mechanics
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• 제1권2호
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• pp.155-163
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• 2012

This paper presents analytical approximate solutions for the initial post-buckling deformation of the pipes in oil and gas wells. The governing differential equation with sinusoidal nonlinearity can be reduced to form a third-order-polynomial nonlinear equation, by coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials. Analytical approximations to the resulting boundary condition problem are established by combining the Newton's method with the method of harmonic balance. The linearization is performed prior to proceeding with harmonic balancing thus resulting in a set of linear algebraic equations instead of one of non-linear algebraic equations, unlike the classical method of harmonic balance. We are hence able to establish analytical approximate solutions. The approximate formulae for load along axis, and periodic solution are established for derivative of the helix angle at the end of the pipe. Illustrative examples are selected and compared to "reference" solution obtained by the shooting method to substantiate the accuracy and correctness of the approximate analytical approach.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권1호
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• pp.1-11
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• 2007

A linear stability analysis applied to a system consist of a horizontal fluid layer overlying a layer of a porous medium affected by a vertical magnetic field on both layers. Flow in porous medium is assumed to be governed by Darcy's law. The Beavers-Joseph condition is applied at the interface between the two layers. Numerical solutions are obtained for stationary convection case using the method of expansion of Chebyshev polynomials. It is found that the spectral method has a strong ability to solve the multilayered problem and that the magnetic field has a strong effect in his model.

• Structural Engineering and Mechanics
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• 제68권2호
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• pp.171-182
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• 2018

For the first time, nonlocal damped vibration and buckling analyses of arbitrary tapered bidirectional functionally graded solid circular nano-plate (BDFGSCNP) are presented by employing modified spectral Ritz method. The energy method based on Love-Kirchhoff plate theory assumptions is applied to derive neutral equilibrium equation. The Eringen's nonlocal continuum theory is taken into account to capture small-scale effects. The characteristic equations and corresponding first mode shapes are calculated by using a novel modified basis in spectral Ritz method. The modified basis is in terms of orthogonal shifted Chebyshev polynomials of the first kind to avoid employing adhesive functions in the spectral Ritz method. The fast convergence and compatibility with various conditions are advantages of the modified spectral Ritz method. A more accurate multivariable function is used to model two-directional variations of elasticity modulus and mass density. The effects of nanoscale, in-plane pre-load, distributed dashpot, arbitrary tapering, pinned and clamped boundary conditions on natural frequencies and buckling loads are investigated. Observing an excellent agreement between results of current work and outcomes of previously published works in literature, indicates the results' accuracy in current work.

• 한국전자파학회논문지
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• 제8권2호
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• pp.161-172
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• 1997

본 논문에서는 다충 유전체 위의 주기적인 도체 스트립 구조에 의한 전자파산란 문제를 Fourier-Galerkin 모멘트법으로 수치해석하여 정규화된 반사 및 투과전력을 계산하였다. 도체띠에 유도되는 전류밀도는 적절한 모서리 경계조건을 만족하는 함수와 l종 Chebyshev 다항식의 곱의 급수로 전개하였으며, 각유전체층의 경계 면에 서는 전자계 연속조건을 적용하였다. 산란 전자파는 Floquet 모드 함수를 이용하여 무한개의 급수로 전개하였다. 본 논문에서 제안된 방법의 타당성을 입증하기 위하여 각 유전체층의 비유전율과 두께를 변화시켜 얻어진 정규화된 반사 및 투과전력은 기존의 수치방법 및 논문의 결과와 평가 및 비교하였으며, 이 때 본 논문의 수치결과들은 기존의 수치방볍 및 논문의 결과와 매우 잘 일치하였다. 기하광학적 정규화된 반사 및 투과전력의 급변점 의 위치는 입사각 및 격자 주기 그리고 유전체충의 비유전율 및 두께에 따라 주된 영향을 받음을 알수 있었고, Wood의 변칙이라고 불리우는 이러한 급변점은 고차 모드의 반사전력이 전파모드와 감쇠모드 사이에서 모드 전환이 주된 요인으로 관측되었으며, 국부적인 최소 위치들은 유전체층의 비 유전율이 증가함에 따라 격자주기가 작아지는 좌측방향으로 약간 이동함을 알 수 있었다.