• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 1997년도 춘계학술대회 논문집
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• pp.508-512
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• 1997

Design sensitivity analysis of Eigen Problem give systematic design improvement information for noise and vibration of a system. Based on reliable results form commercial FE code(UAI/NASTRAN), three computational procedures for design sensitivity analysis of eigen problem are suggested. Those methods are finite difference,design sensitivity analysis using external module and design sensitivity analysis running with NASTRAN. To verify the suggested methods, a numerical example is given and these results are compared with the results from UAI/NASTRAN eigen sensitivity option. We can conclude that design sensitivity coefficient of eigen proplems can be computed outside of the FE code as easy as inside of the FE code.

• 대한수학회논문집
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• 제29권1호
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• pp.173-185
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• 2014

In the present paper, we consider an anomalous diffusion problem in two dimensional space involving Caputo time and Riesz-Feller fractional derivatives and then solve it by using a series involving bilateral eigen-functions. Also, we obtain a numerical approximation formula of this problem and discuss some of its particular cases.

• Journal of applied mathematics & informatics
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• 제3권2호
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• pp.193-204
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• 1996

Overflow queuing models are ofter analyzed by explicitly solving a large sparse singular linear systems arising from Kolmogorov balance equation. The system is often converted into an eigenvalue problem the dominant eigenvector of which is the desired null vector. In this paper we convert an overflow queuing problem the dominant eigenvector of which is the desired null vector. In this paper we convert an overflow queuing problem into an overflow queuing problem into an eigen-value problem into an eigen-value problem of size 1/2 of the original. Then we devise an orthogonal projector that enhances its convergence by removing unsanted eigen-components effectively. Numerical result with some suggestion is given at the end.

• 비파괴검사학회지
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• 제30권3호
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• pp.194-199
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• 2010

Based on the idea of eigen-mode expansion, a method to analyze the reflection of Lamb wave from a finite vertical discontinuity of plate is theoretically derived and verified by experiment. The theoretical prediction is in good agreement with the experimental result, and this strongly suggests that eigen-mode expansion method could be used for solution of inverse scattering problem for ultrasonic testing using Lamb wave.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 추계학술대회논문집 II
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• pp.1317-1322
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• 2001

What changes in the eigen values and eigen functions are produced if the boundary surface S is no longer rigid but has a specific acoustic admittance which may vary from point to point on S. In this paper, changes in eigen values and eigen functions are derived by using Kirchhoff-Helmholtz integral equation. And acoustic potential energy, which is representative measure describing the physical quantity in cavity, is defined. Acoustic potential energy can be divided into primary one and secondary one. Primary one is the acoustic potential energy through unchanged eigen functions, and secondary one is through changed eigen functions. Using these two term, we can find the eigenvalue problem, which gives the control performance when the boundary condition is changed.

• 소음진동
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• 제10권5호
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• pp.800-805
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• 2000

To determine the modal matrix and modal frequency of engine mount system, we most solve so-called eigen-value problem. However eigen-value problem of engine mount system with hydraulic mount can not be solved by general eigne-analysis algorithm because the properties of hydraulic mount vary with frequency. so in this paper the method for modal analysis of rigid body motions of an engine supported by hydraulic mount is proposed. Natural frequencies and mode shapes of this nonlinear system are obtained by using complex exponential method and Laplace transformation method. In time domain, impulse response functions are calculated by (two-sided) discrete inverse Fourier Transformation of forced frequency response functions achieved by Laplace transformation of the differential equation of motion. Considering the fact that frequency response functions synthesized by modal parameters form proposed method are in good agreement with original FRFs, it is proved that the proposed method is very efficient and useful for the analysis of eigne-value problem of hydraulic engine mount system.

• Coupled systems mechanics
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• 제13권3호
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• pp.231-245
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• 2024

In the present work, a microelogated thermoelastic model based on Lord-Shulman (1967) and Green-Lindsay (1972) theories of thermoelasticity has been constructed. The governing equations for the simulated model are converted into two-dimensional case and made dimensionless for further simplification. Laplace and Hankel transforms followed by eigen value approach has been employed to solve the problem. The use of eigen value approach hasthe advantage of finding the solution of governing equationsin matrix form notations. This approach is straight forward and convenient for numerical computation and avoids the complicate nature of the problem. The components of displacement,stress and temperature distribution are obtained in the transformed domain. Numerical inversion techniques have been used to invert the resulting quantities in the physical domain. Graphical representation of the resulting quantities for describing the effect of microelongation are presented. A special case is also deduced from the present investigation. The problem find application in many engineering problems like thick-walled pressure vesselsuch as a nuclear containment vessel, a cylindricalroller etc.

• Kyungpook Mathematical Journal
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• 제57권2호
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• pp.211-222
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• 2017

In this paper, we consider three inverse eigenvalue problems for a special type of acyclic matrices. The acyclic matrices considered in this paper are described by a graph called a broom on n + m vertices, which is obtained by joining m pendant edges to one of the terminal vertices of a path on n vertices. The problems require the reconstruction of such a matrix from given partial eigen data. The eigen data for the first problem consists of the largest eigenvalue of each of the leading principal submatrices of the required matrix, while for the second problem it consists of an eigenvalue of each of its trailing principal submatrices. The third problem has an eigenvalue and a corresponding eigenvector of the required matrix as the eigen data. The method of solution involves the use of recurrence relations among the leading/trailing principal minors of ${\lambda}I-A$, where A is the required matrix. We derive the necessary and sufficient conditions for the solutions of these problems. The constructive nature of the proofs also provides the algorithms for computing the required entries of the matrix. We also provide some numerical examples to show the applicability of our results.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 춘계학술대회논문집
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• pp.117-119
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• 2005

For large structural eigen-analysis, the whole structure is divided into some partitioned structures and through synthesis of partitioned structural model the eigen-data of structure can be obtained. In that case, eigenvalue problem consists of semidefinite mass matrix form because of displacement constraint condition. In this work the eigenvalue problem is considered by means of several method, determinant search and null space reduction method.

• 한국산학기술학회논문지
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• 제19권12호
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• pp.32-40
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• 2018

열 교환기/원자로의 과도한 진동을 방지 하려면 진동해석을 설계 단계에서 수행해야 한다. 진동 문제에서 고유 진동수의 정보는 열 교환기/원자로의 안전성을 평가하기 위하여 요구된다. 본 논문은 일단 지지보에 발생되는 고유치 문제를 해석하기 위하여 수치해석 방법인 Galerkin의 방법을 기술하였다. 일단 지지보는 자유단 끝점 또는 모드의 노드 포인트에 부가 질량과 스프링에 의하여 구속되어 있다. 수치해석으로 구한 고유진동수는 간단한 해석 방법과 간단한 테스트에 의하여 각각 구한 결과와 비교 되었다. Galerkin의 방법을 사용하여 논의된 일단 지지보의 고유 진동수를 구할 수 있음을 보였다. 부가 질량 증가함에 따라 고유 주파수는 감소하며 스프링 힘의 증가에 따라 고유 주파수는 상승함을 보였다. 무거운 부가 질량은 가연성 배관의 지지대 역할을 함을 보였다. 일단 지지보의 끝단에 설치된 부가 질량의 경우에 개발된 기존의 어림적 해석 방법으로도 일차 모두의 고유 진동수를 비교적 정확하게 구할 수 있음을 알 수 있었다.