• 지구물리와물리탐사
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• 제5권2호
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• pp.99-107
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• 2002

표면파 기법(SASW, Spectral Analysis of Surface Waves)을 지반공학 분야에 효율적으로 적용하기 위해 모형 응답 알고리듬을 해석적으로 도출하였다. 이 논문에서는 이론적인 분산 곡선 응답 반응을 Aki and Richard에 의해 제안된 운동 응력 벡터(motion stress vector)를 이용하여 미분 방정식을 구성한 후 차분 전개를 통하여 구함으로서 동적 강성도 법이나 전파 행렬법에 비해 간단하고 빠르게 구할 수 있었다. 차분 전개를 통한 이론 분산 곡선 응답 반응 알고리즘으로 2개의 지구 모형에 대해 이론 분산 곡선을 구하여 타당성을 검증하였다. 또한 모형 응답 계산 과정에서 고려하여야 할 주파수 대역에 따른 적절한 모형의 크기에 대하여 고찰한 결과 각 파장의 $1.5\~2$배 이내로 모형의 크기를 결정할 때 경제적이고 안정적인 결과를 얻을 수 있었다.

• Structural Engineering and Mechanics
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• 제28권2호
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• pp.129-152
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• 2008

This paper considers the solution of the stochastic differential equations (SDEs) with random operator and/or random excitation using the spectral SFEM. The random system parameters (involved in the operator) and the random excitations are modeled as second order stochastic processes defined only by their means and covariance functions. All random fields dealt with in this paper are continuous and do not have known explicit forms dependent on the spatial dimension. This fact makes the usage of the finite element (FE) analysis be difficult. Relying on the spectral properties of the covariance function, the Karhunen-Loeve expansion is used to represent these processes to overcome this difficulty. Then, a spectral approximation for the stochastic response (solution) of the SDE is obtained based on the implementation of the concept of generalized inverse defined by the Neumann expansion. This leads to an explicit expression for the solution process as a multivariate polynomial functional of a set of uncorrelated random variables that enables us to compute the statistical moments of the solution vector. To check the validity of this method, two applications are introduced which are, randomly loaded simply supported reinforced concrete beam and reinforced concrete cantilever beam with random bending rigidity. Finally, a more general application, randomly loaded simply supported reinforced concrete beam with random bending rigidity, is presented to illustrate the method.

• 전기의세계
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• 제31권3호
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• pp.209-217
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• 1982

This paper considers a finite spectrum assignment Problem for a functional retarded linear differential system with delays in control only. In this problem, by generalizing from an abstract linear system characterized by Semigroups on a Hilbert space to a finite dimensional linear system, we unify the relationship between a control-delayed system and its non-delayed system, and then by using the spectrum of the generator-decomposition of Semigroup, we try to get a feedback law which yields a finite spectrum of the closed-loop system, located at an arbitrarily preassigned sets of n points in the complex plane. The comparative examinations between the standard spectrum assignment method and the method of spectral projection for the feedback law which consists of proportional and finite interval terms over present and past values of control variables are also considered. The analysis is carry down to the elementary spectral projection level because, in spite of all the research efforts, so far there has been no significant attempt to obtain the feedback implementation directly from the abstract representation forms in the case of multivariables.

• 한국음향학회지
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• 제33권3호
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• pp.191-199
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• 2014

파이프, 평판과 같이 단면의 형상이 길이 방향으로 일정한 도파관 구조물을 따라 전파되는 진동의 반사 및 투과 특성은 여러 공학 분야에서 응용되는 중요한 주제이다. 도파관에 조인트 또는 균열 등의 국부적 불연속이 있는 경우, 스펙트럴 요소(spectral element)와 유한 요소(finite elment)를 결합한 SE/FE 방법이 주로 사용되고 있다. 그러나 이 방법은 보 이론에 기반한 스펙트럴 요소가 사용되므로 저주파수 대역 해석에 국한되는 단점이 있다. 고주파수 대역 해석에는 스펙트럴 수퍼 요소(spectral super element)와 유한 요소를 결합한 SSE/FE 방법이 제안되었으나 유한요소와 스펙트럼 요소의 연성으로 인해 많은 연산 시간이 요구된다. 이러한 문제점을 개선하고자, 본 연구에서는 국부적 불연속 구간의 단면이 일정한 경우에 대해 국부적 불연속 구간을 스펙트럴 수퍼 요소로 대체한 SSE/SSE 연성 해석을 시도하였다. 적용 모델로는 국부적 결함을 가진 레일의 파동 반사 및 투과, 그리고 주기적 보강재를 가진 평판의 진동전파에 대해 적용하였다. 결함을 가진 레일의 해석 예를 통해, 본 논문에서 사용한 SSE/SSE 방법과 기존의 SSE/FE 방법의 성능을 비교하였다. 보강재를 가진 평판의 예를 통해서는 반복 구조를 가진 도파관의 파동 전파 특성 해석에 SSE/SSE 방법이 유용함을 확인하였다.

• 대한기계학회논문집A
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• 제27권2호
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• pp.294-301
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• 2003

It is of often important to accurately predict the flow-induced vibration or dynamic instability of a pipeline conveying internal high speed flow in advance, which requires a very accurate solution method. In this study, first the dynamic equations for the axial and transverse vibrations of a pipeline are reduced from a set of pipe-dynamic equations derived in the previous study and then the spectral element model is formulated. The accuracy of the spectral element method (SEM) is then verified by comparing its results with the results obtained by finite element method (FEM). It is shown that the present spectral element model provides very accurate solutions by using an extremely small number of degrees-of-freedom when compared with FEM. The dynamics of a sample pipeline is investigated with varying the axial tension and the speed of internal flow.

• 한국방재학회:학술대회논문집
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• 한국방재학회 2007년도 정기총회 및 학술발표대회
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• pp.137-139
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• 2007

한반도의 지각에 대한 지진파의 파형들을 피킹하기 위하여 한반도의 남동부지역에서 시행된 폭파로부터 각 관측소에서 관측된 지진자료를 2 차원 수치 순산모델링으로 계산된 이론적인 신호와 비교하였다. 실제 지진자료와 같은 완전한 파형을 얻기 위해서는 실체파뿐만 아니라 표면파를 포함한 모든 파형을 이론적으로 생성하여야 한다. 또한, 각 파형의 Q 값을 고려하여 그 감쇄 정도를 파악하여야 실제 파형과 똑 같은 이론적인 파형을 만들 수 있다. 본 연구에서는 FEM(Finite Element Method)과 FDM(Finite Difference Method) 같은 전형적인 수치 모델링 기법 대신에 수도스펙트럼기법(pseudo-spectral method)을 사용하여 이론적인 파형을 계산하였다. Q 값을 고려하지 않았기 때문에 완전한 파형을 얻기에는 어려움이 있었다. 그러나 각 관측소에 도달하는 실체파의 초기 파형들의 주시를 실제 파형과 맞추었다는 데에 그 성과가 있다고 할 수 있다. 본 연구의 궁극적인 목표는 수치 모델링을 통하여 지진원의 위치와 종류를 밝혀 내는데 그 정확성을 높이는 것이다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2001년도 ICCAS
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• pp.33.5-33
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• 2001

We consider here the problem of spectral estimation of multidimensional wide sense stationary (WSS) random process. A method, employing a special difference equation of correlation function, is proposed to solve the problem of multidimensional spectral estimation. In this approach, the special difference equation of correlation function is derived by modal decomposition method. Maximum likelihood estimator and Kalman filter are used to estimate the model parameters of the difference equation and the decomposed spectral residues. An algorithm is presented to estimate the multidimensional spectral density. According to the result of the simulation, these methods are feasible to estimate the spectral density of WSS process, which is realized by finite dimensional multivariable lineal system driven by white noise.

• Smart Structures and Systems
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• 제13권4호
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• pp.587-614
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• 2014

In recent years the interest in online monitoring of lightweight structures with ultrasonic guided waves is steadily growing. Especially the aircraft industry is a driving force in the development of structural health monitoring (SHM) systems. In order to optimally design SHM systems powerful and efficient numerical simulation tools to predict the behaviour of ultrasonic elastic waves in thin-walled structures are required. It has been shown that in real industrial applications, such as airplane wings or fuselages, conventional linear and quadratic pure displacement finite elements commonly used to model ultrasonic elastic waves quickly reach their limits. The required mesh density, to obtain good quality solutions, results in enormous computational costs when solving the wave propagation problem in the time domain. To resolve this problem different possibilities are available. Analytical methods and higher order finite element method approaches (HO-FEM), like p-FEM, spectral elements, spectral analysis and isogeometric analysis, are among them. Although analytical approaches offer fast and accurate results, they are limited to rather simple geometries. On the other hand, the application of higher order finite element schemes is a computationally demanding task. The drawbacks of both methods can be circumvented if regions of complex geometry are modelled using a HO-FEM approach while the response of the remaining structure is computed utilizing an analytical approach. The objective of the paper is to present an efficient method to couple different HO-FEM schemes with an analytical description of an undisturbed region. Using this hybrid formulation the numerical effort can be drastically reduced. The functionality of the proposed scheme is demonstrated by studying the propagation of ultrasonic guided waves in plates, excited by a piezoelectric patch actuator. The actuator is modelled utilizing higher order coupled field finite elements, whereas the homogenous, isotropic plate is described analytically. The results of this "semi-analytical" approach highlight the opportunities to reduce the numerical effort if closed-form solutions are partially available.

• East Asian mathematical journal
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• 제39권1호
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• pp.75-85
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• 2023

In this paper, a non-overlapping rectangular domain decomposition method is presented in order to numerically solve two-dimensional telegraph equations. The method is unconditionally stable and efficient. Spectral radius of the iteration matrix and convergence rate of the method are provided theoretically and confirmed numerically by MATLAB. Numerical experiments of examples are compared with several methods.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1996년도 춘계학술대회논문집; 부산수산대학교, 10 May 1996
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• pp.328-334
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• 1996

Finite Element Method(FEM) is the most popularly used method in analyzing the dynamic behaviors of structures. But unless the number of finite elements is large enough, the results from FEM are somewhat different from exact analytical solutions, especially at high frequency range. On the other hand, as the Spectral Element Method(SEM) deals directly with the governing equations of structures, the results from this method cannot but be exact regardless of any frequency range. However, despite two dimensional structures are more general, the SEM has been applied only to the analysis of one dimensional structures so far. In this paper, therefore, new methodologies are introduced to analyze the two dimensional plate using SEM. The results from this new method are compared with the exact analytical solutions by letting the two dimensional plate be one dimensional one and showed the dynamic responses of two dimensional plate by including various waves propagated into x-direction.