• Wind and Structures
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• 제16권6호
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• pp.561-577
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• 2013

Rational Functions are used to express the self-excited aerodynamic forces acting on a flexible structure for use in time-domain flutter analysis. The Rational Function Approximation (RFA) approach involves obtaining of these Rational Functions from the frequency-dependent flutter derivatives by using an approximation. In the past, an algorithm was developed to directly extract these Rational Functions from wind tunnel section model tests in free vibration. In this paper, an algorithm is presented for direct extraction of these Rational Functions from section model tests in forced vibration. The motivation for using forced-vibration method came from the potential use of these Rational Functions to predict aerodynamic loads and response of flexible structures at high wind speeds and in turbulent wind environment. Numerical tests were performed to verify the robustness and performance of the algorithm under different noise levels that are expected in wind tunnel data. Wind tunnel tests in one degree-of-freedom (vertical/torsional) forced vibration were performed on a streamlined bridge deck section model whose Rational Functions were compared with those obtained by free vibration for the same model.

• 대한수학회보
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• 제36권4호
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• pp.629-636
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• 1999

We introduce Lipschitz algebras of differentiable functions of a perfect compact plane set X and extend the definition to Lipschitz algebras of infinitely differentiable functions of X. Then we define the subalgebras generated by polynomials, rational functions, and analytic functions in some neighbourhood of X, and determine the maximal ideal spaces of some of these algebras. We investigate the polynomial and rational approximation problems on certain compact sets X.

• Wind and Structures
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• 제14권2호
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• pp.133-151
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• 2011

For a detailed investigation of the dynamic behaviour of slender bridges under wind action especially the motion-induced fluid forces should be available not only for harmonic motions but also for more general ones. If linear transfer behaviour is assumed, the force-displacement relation for almost arbitrary motions can be handled in the frequency domain using aerodynamic transfer functions. In aerospace engineering as well as in bridge engineering, these functions are usually approximated by special kinds of complex-valued rational functions which depend on complex frequencies. The quality of this approximation is evaluated for several bridge cross sections in this article. It is shown that rational functions are for some sections scarcely suitable to realistically represent the transfer behaviour of motion-induced aerodynamic forces for arbitrarily complex frequencies.

• Wind and Structures
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• 제10권3호
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• pp.215-232
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• 2007

This paper presents an aeroelastic analysis procedure to highlight the influence of wind velocity on the structural damping and frequency of a long span cable-stayed bridge. Frequency dependent self-excited forces in terms of flutter derivatives are expressed as continuous functions using rational function approximation technique. The aeroelastically modified structural equation of motion is expressed in terms of frequency independent modal state-space parameters. The modal logarithmic dampings and frequencies corresponding to a particular wind speed are then determined from the eigen solution of the state matrix.

• 한국전자파학회논문지
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• 제22권2호
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• pp.191-198
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• 2011

본 논문에서는 1차원 모드 방정식의 FDTD 해석 결과와 분수 함수 근사법을 이용하여 다층 구조의 Green 함수를 근사화 하는 방법을 제안한다. 파수 값에 따른 FDTD 해석 결과를 Fourier 변환 과정을 거쳐 spectral domain 상에서 Green 함수를 계산한다. FDTD 수치 해석 결과로 얻은 Green 함수에 분수 함수 근사법을 적용하여 pole과 residue를 계산하여 Green 함수를 분수 함수로 근사화 한다. 제안된 방법은 path-loss 계산 방법 중 하나인 정상 모드(normal mode)에 사용할 수 있다. 단일 주파수 해석에 유효한 기존의 정상 모드 방법과는 달리 본 논문에서 제안하는 FDTD 기반 방법은 광대역 해석을 할 수 있다. 제안된 방법의 유용성을 입증하기 위해 정상 모드 해석기반의 Kraken 시뮬레이터 결과와 공진 모드의 pole 값을 비교한다. 또 알려진 해석해를 갖는 문제에 제안된방법을 적용하여 정확도를 검증하였다.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1996년도 춘계학술대회 논문집
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• pp.299-304
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• 1996

This paper studies the rational approximation of multiple input delay systems using the Hankel singular values and vectors, which are the soultion of a transcendental equation. Rational approximatants are obtained from output normal realizations which are constructed by the Hankel singular values and vectors. Consequently, it is shown that rational approximants by output normal realization preserve intrinsic properties of time delay systems than Pade approximants.

• Korean Journal of Geomatics
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• 제4권1호
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• pp.31-37
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• 2004

The aim of this research is comparing the existing approximation models (e.g. Affine Transformation and Direct Linear Transformation) with Rational Function Model as a substitute of rigorous sensor model of linear array scanner, especially push-broom sensor. To do so, this research investigates the mathematical model of each approximation method. This is followed by the assessments of accuracy of transformation from object space to image space by using simulated data generated by collinearity equations which incorporate or depict the physical aspects of linear array sensor.

• 한국정밀공학회지
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• 제14권1호
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• pp.194-204
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• 1997

In this paper, we consider the rational approximation of multiple input delay systems. The method of computing Hankel singular values and vectors is firstly introduced, where explicitly shows the structure of the corresponding Hankel singular vectors. Secondly, rational approximants are obtained from output nor- mal relizations, which are constructed by Hankel singular values and vectors. As a result, it is shown that rational approximants by output normal realization preserve intrinsic properties of time delay systems than Pad'e approximants.

• 제어로봇시스템학회지
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• 제1권1호
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• pp.50-50
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• 1995

It has been pointed out in the literature that the Routh approximation method for order reduction has limitations in treating transfer functions with the denominator-numerator order difference not equal to one. The purpose of this paper is to present a new algorithm based on the Routh approximation method that can be applied to general rational transfer functions, yielding reduced models with arbitrary order.

• 대한원격탐사학회:학술대회논문집
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• 대한원격탐사학회 2003년도 Proceedings of ACRS 2003 ISRS
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• pp.750-752
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• 2003

The objective of this investigation is to compare the geometric precision of Rigorous Sensor Model and Rational Function Model for QuickBird images. In rigorous sensor model, we use the on-board data and ground control points to fit an orbit; then, a least squares filtering technique is applied to collocate the orbit. In rational function model, we first use the rational polynomial coefficients provided by the satellite company. Then the systematic bias of the coefficients is compensated by an affine transformation using ground control points. Experimental results indicate that, the RFM provides a good approximation in the position accuracy.