• Steel and Composite Structures
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• 제28권6호
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• pp.655-670
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• 2018

A coupled method, that combines the Ritz method and the finite element (FE) method, is proposed to solve the vibration problem of rectangular thin and thick plates with general boundary conditions. The eigenvalue partial differential equation(s) of the plate is (are) first reduced to a set of eigenvalue ordinary differential equations by the application of the Ritz method. The resulting eigenvalue differential equations are then reduced to an eigenvalue algebraic equation system using the finite element method. The natural boundary conditions of the plate problem including the free edge and free corner boundary conditions are also implemented in a simple and accurate manner. Various boundary conditions including simply supported, clamped and free boundary conditions are considered. Comparisons with existing numerical and analytical solutions show that the proposed mixed method can produce highly accurate results for the problems considered using a small number of Ritz terms and finite elements. The proposed mixed Ritz-FE formulation is also compared with the mixed FE-Ritz formulation which has been recently proposed by the present author and his co-author. It is found that the proposed mixed Ritz-FE formulation is more efficient than the mixed FE-Ritz formulation for free vibration analysis of rectangular plates with Levy-type boundary conditions.

• Nuclear Engineering and Technology
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• 제49권6호
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• pp.1259-1268
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• 2017

The alpha eigenvalue problem in multigroup neutron diffusion is studied with particular attention to the theoretical analysis of the model. Contrary to previous literature results, the existence of eigenvalue and eigenflux clustering is investigated here without the simplification of a unique fissile isotope or a single emission spectrum. A discussion about the negative decay constants of the neutron precursors concentrations as potential eigenvalues is provided. An in-hour equation is derived by a perturbation approach recurring to the steady state adjoint and direct eigenvalue problems of the effective multiplication factor and is used to suggest proper detection criteria of flux clustering. In spite of the prior work, the in-hour equation results give a necessary and sufficient condition for the existence of the eigenvalue-eigenvector pair. A simplified asymptotic analysis is used to predict bands of accumulation of eigenvalues close to the negative decay constants of the precursors concentrations. The resolution of the problem in one-dimensional heterogeneous problems shows numerical evidence of the predicted clustering occurrences and also confirms previous theoretical analysis and numerical results.

• 한국추진공학회:학술대회논문집
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• 한국추진공학회 2005년도 제25회 추계학술대회논문집
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• pp.422-425
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• 2005

가로 등방성 복합재료에서 반사되거나 굴절된 파동의 속도와 입자방향, 그리고 진폭을 운동방정식과 구성방정식 그리고 파동수와 진동수로 표현된 변위식을 사용하여 구하였다. Snell 법칙을 사용하여 Eigenvalue 문제를 풀어 파동속도를 구하였으며 그 결과는 T300 Carbon fiber/5208 Epoxy 재료 성질을 이용하여 검증하였다. 이러한 분석은 수분 침수 C-scan을 이용하여 가로등방성 복합재료의 결점을 찾아내는데 응용될 수 있다.

• Structural Engineering and Mechanics
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• 제3권4호
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• pp.313-324
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• 1995

Flexible cantilever pipes conveying fluids with high velocity are analysed for their dynamic response and stability behaviour. The Young's modulus and mass per unit length of the pipe material have a stochastic distribution. The stochastic fields, that model the fluctuations of Young's modulus and mass density are characterized through their respective means, variances and autocorrelation functions or their equivalent power spectral density functions. The stochastic non self-adjoint partial differential equation is solved for the moments of characteristic values, by treating the point fluctuations to be stochastic perturbations. The second-order statistics of vibration frequencies and mode shapes are obtained. The critical flow velocity is first evaluated using the averaged eigenvalue equation. Through the eigenvalue equation, the statistics of vibration frequencies are transformed to yield critical flow velocity statistics. Expressions for the bounds of eigenvalues are obtained, which in turn yield the corresponding bounds for critical flow velocities.

• 대한수학회보
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• 제33권4호
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• pp.503-512
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• 1996

In this paper we investigate a relation between the multiplicity of solutions and source terms in a nonlinear suspension bridge equation in the interval $(-\frac{2}{\pi}, \frac{2}{\pi})$, under Dirichlet boundary condition $$ (0.1) u_{tt} + u_{xxxx} + bu^+ = f(x) in (-\frac{2}{\pi}, \frac{2}{\pi}) \times R, $$ $$ (0.2) u(\pm\frac{2}{\pi}, t) = u_{xx}(\pm\frac{2}{\pi}, t) = 0, $$ $$ (0.3) u is \pi - periodic in t and even in x and t, $$ where the nonlinearity - $(bu^+)$ crosses an eigenvalue $\lambda_{10}$. This equation represents a bending beam supported by cables under a load f. The constant b represents the restoring force if the cables stretch. The nonlinearity $u^+$ models the fact that cables expansion but do not resist compression.

• 한국추진공학회지
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• 제10권2호
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• pp.62-69
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• 2006

가로 등방성 복합재료에서 반사되거나 굴절된 파동의 속도와 입자방향, 그리고 진폭을 운동방정식과 구성방정식 그리고 파동수와 진동수로 표현된 변위식을 사용하여 구하였다. Snell 법칙을 사용하여 Eigenvalue 문제를 풀어 파동속도를 구하였으며 그 결과는 T300 Carbon fiber/5208 Epoxy 재료 성질을 이용하여 검증하였다. 이러한 분석은 수분 침수 C-scan을 이용하여 가로등방성 복합재료의 결점을 찾아내는데 응용될 수 있다.

• 대한수학회보
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• 제30권2호
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• pp.229-238
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• 1993

Let M be an n-dimensional compact Riemannian manifold with boundary .part.M. We consider the Neumann eigenvalue problem on M of the equation (Fig.) where .upsilon. is the unit outward normal vector to the boundary .part.M. due to the importance of Poincare inequality for analysis on manifolds, one wishes to obtain the lower bound of the first non-zero eigenvalue .eta.$_{1}$ of (1.1). For the purpose of applications, it is important to relax the dependency of the lower bound on the geometric quantities. For general compact manifolds with convex boundary, Li-Yau [3] obtained the lower bound of .eta.$_{1}$. Recently, Roger Chen [1] investigated the lower bound of the first Neumann eigenvalue .eta.$_{1}$ on compact manifold M with nonconvex boundary. We investigate the lower bound .eta.$_{1}$ with the same conditions as those of Roger chen. But, using the different auxiliary function, we have the following theorem.

• 전기학회논문지
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• 제57권3호
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• pp.363-368
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• 2008

In this paper, the Resistive Companion Form(RCF) analysis method is applied to analyze small signal stability of power systems including thyristor controlled FACTS equipments such as SVC. The eigenvalue sensitivity analysis algorithm in discrete systems based on the RCF analysis method is presented and applied to the power system including SVC. As a result of simulation, the RCF analysis method is proved very effective to precisely calculate the variations of eigenvalues or newly generated unstable oscillation modes after periodic switching operations of SVC. Also the eigenvalue sensitivity analysis method based on the RCF analysis method enabled to precisely calculate eigenvalue sensitivity coefficients of controller parameters about the dominant oscillation mode after periodic switching operations in discrete systems. These simulation results are different from those of the conventional continuous system analysis method such as the state space equation and proved that the RCF analysis method is very effective to analyze the discrete power systems including periodically operated switching equipments such as SVC.

• 한국소음진동공학회논문집
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• 제26권5호
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• pp.602-608
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• 2016

The paper proposes a practical meshless method for the free vibration analysis of clamped plates having arbitrary shapes by extending the non-dimensional dynamic influence function (NDIF) method, which was developed by the author in 1999. In the proposed method, the domain and boundary of the plate of interest are discretized using only nodes without elements unlike FEM and the system matrices are obtained by making domain nodes and boundary nodes satisfy the governing differential equation and boundary conditions, respectively. However, since the above system matrices are not square ones, the problem of free vibrations of clamped plates is not reduced to an algebraic eigenvalue problem. An additional theoretical treatment is considered to produce an algebraic eigenvalue problem. It is revealed from case studies that the proposed method is valid and accurate.

• 융합보안논문지
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• 제8권4호
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• pp.153-159
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• 2008

최근 GRIN 다중모드 광섬유는 광대역 통신선로로써 주목받아왔으며, 광섬유 내부에서 광파의 운동은 모드간 결합, 휨에 의한 손실 등 여러 다른 연구와 맞물려 큰 관심이 되고 있다. 본 논문에서는 기존의 복잡하고 난해한 Bessel 함수를 통한 파동방정식의 해석을 피하고 파동방정식을 고유치문제(Eigenvalue Problem)로 풀이한 수치해석을 통하여, GRIN 광섬유 내에서의 각 광파의 각 의존도와 모드수동을 관찰하였다. 이 연구는 GRIN 광섬유의 다른효과(휨, 모드간 결합) 등의 추후 연구에 유용하게 쓰이리라 생각된다.