• Steel and Composite Structures
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• v.28 no.6
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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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• v.49 no.6
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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.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2005.11a
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• pp.422-425
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• 2005

In an transversely isotropic composite laminates, the velocities, the particle directions and the amplitudes of reflected and transmitted waves were obtained using the equation of motion, the constitutive equation, and the displacement equation expressed by wave number and frequency Eigenvalue problem involving a velocity was solved by Snell's law. Finally, the results were confirmed by T300 Carbon fiber/5208 Epoxy materials. This approach could be applied to the detection of flaws in a transversely isotropic composite laminates by the water immersion C-scan procedure.

• Structural Engineering and Mechanics
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• v.3 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.33 no.4
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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.

• Journal of the Korean Society of Propulsion Engineers
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• v.10 no.2
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• pp.62-69
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• 2006

In transversely isotropic composite laminates, the velocities, the particle directions and the amplitudes of reflected and transmitted waves were obtained using the equation of motion, the constitutive equation, and the displacement equation expressed by wave number and frequency. Eigenvalue problem involving a velocity was solved by Snell's law. Finally, the results were confirmed by 7300 Carbon fiber/5208 Epoxy materials. This approach could be applied to the detection of flaws in transversely isotropic composite laminates by the water immersion C-scan procedure.

• Bulletin of the Korean Mathematical Society
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• v.30 no.2
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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.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.3
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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.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.26 no.5
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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.

• Convergence Security Journal
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• v.8 no.4
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• pp.153-159
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• 2008

Graded-Index Multimode Optical fibers have recently received a lot of attention as regards their application and lightwave behavior in relation to broadband communication links. Accordingly, this aticle presents a novel lightwave mode analysis that solves the wave equation using a numerical analysis based on an eigenvalue problem method, thereby avoiding the typical complicated Bessel function method. Angular depedences and number of modes were observed as well. Future research implications will be possibly noticed such areas as bending effects and mode coupling analyses thru this research.