• 대한전기학회논문지
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• 제43권3호
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• pp.372-380
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• 1994

A systematic procedure for the elements of system state matrix in multimachine systems with loads and eigenvalue technique which utilize stage matrix have widespread application in the analysis of small signal stability. Synchronous machines are represented by either a two-axis model or classical model. The interrelationship of submatrices of system matrix is investigated. Once elements of one submatrix are determined, they can be used to calculate the elements of the other submatrix. The approach is useful in the eigenvalue sensitivity analysis for various initial conditions and for the adjustment of generator controller parameters. It is illustrated for a three-machine and nine-bus multimachine system(WSCC system) with constant impedance loads.

• 한국소음진동공학회논문집
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• 제23권11호
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• pp.1003-1011
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• 2013

A new formulation of the MNDIF method is introduced to extract highly accurate eigenvalues of concave acoustic cavities. Since the MNDIF method, which was introduced by the author, can be applicable for only convex acoustic cavities, a new approach of dividing a concave cavity into two convex domains and formulating an algebraic eigenvalue problem is proposed in the paper. A system matrix equation, which gives eigenvalues, is obtained from boundary conditions for each domain and the condition of continuity in the interface between the two domains. The validity and accuracy of the proposed method are shown through example studies.

• 한국소음진동공학회논문집
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• 제25권10호
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• pp.653-659
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• 2015

A new formulation of the non-dimensional dynamic influence function method, which is a type of the meshless method, is introduced to extract highly accurate eigenvalues of clamped plates with arbitrary shape. Originally, the final system matrix equation of the method, which was introduced by the author in 1999, does not have a form of algebraic eigenvalue problem unlike FEM. As the result, the non-dimensional dynamic influence function method requires an inefficient process to extract eigenvalues. To overcome this weak point, a new approach for clamped plates is proposed in the paper and the validity and accuracy is shown in verification examples.

• 비파괴검사학회지
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• 제30권6호
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• pp.527-538
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• 2010

This paper presents a nondestructive evaluation approach for system identification (SID) of real railway bridges using field vibration test results. First, a multi-phase SID scheme designed on the basis of eigenvalue sensitivity concept is presented. Next, the proposed multi-phase approach is evaluated from field vibration tests on a real railway bridge (Wondongcheon bridge) located in Yangsan, Korea. On the steel girder bridge, a few natural frequencies and mode shapes are experimentally measured under the ambient vibration condition. The corresponding modal parameters are numerically calculated from a three-dimensional finite element (FE) model established for the target bridge. Eigenvalue sensitivities are analyzed for potential model-updating parameters of the FE model. Then, structural subsystems are identified phase-by-phase using the proposed model-updating procedure. Based on model-updating results, a baseline model and a nondestructive evaluation of test bridge are identified.

• Steel and Composite Structures
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• 제22권2호
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• pp.369-386
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• 2016

In this work, the two-dimensional generalized magneto-thermoelastic problem of a fiber-reinforced anisotropic material is investigated under Green and Naghdi theory of type III. The solution will be obtained for a certain model when the half space subjected to ramp-type heating and traction free surface. Laplace and exponential Fourier transform techniques are used to obtain the analytical solutions in the transformed domain by the eigenvalue approach. The inverses of Fourier transforms are obtained analytically. The results have been verified numerically and are represented graphically. Comparisons are made with the results predicted by the presence and absence of reinforcement and magnetic field.

• Steel and Composite Structures
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• 제21권4호
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• pp.791-803
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• 2016

In this article, the problem of a two-dimensional thermoelastic half-space are studied using mathematical methods under the purview of the generalized thermoelastic theory with one relaxation time is studied. The surface of the half-space is taken to be thermally insulated and traction free. Accordingly, the variations of physical quantities due to by laser pulse given by the heat input. The nonhomogeneous governing equations have been written in the form of a vector-matrix differential equation, which is then solved by the eigenvalue approach. The analytical solutions are obtained for the temperature, the components of displacement and stresses. The resulting quantities are depicted graphically for different values of thermal relaxation time. The result provides a motivation to investigate the effect of the thermal relaxation time on the physical quantities.

• Structural Engineering and Mechanics
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• 제29권6호
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• pp.673-687
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• 2008

In this paper, a thermo-viscoelastic problem in an infinite isotropic medium in two dimensions in the presence of a point heat source is considered. The fundamental equations of the problems of generalized thermoelasticity including heat sources in a thermo-viscoelastic media have been derived in the form of a vector matrix differential equation in the Laplace-Fourier transform domain for a two dimensional problem. These equations have been solved by the eigenvalue approach. The results have been compared to those available in the existing literature. The graphs have been drawn for different cases.

• International Journal of Aeronautical and Space Sciences
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• 제2권2호
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• pp.46-55
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• 2001

A Green's function approach based on the laminate theory is adopted to obtain the unsteady temperature distributions in a semi-infinite hollow circular cylinder made of functionally graded materials (FGMs). The transient heat conduction equation based on the laminate theory is formulated into an eigenvalue problem for each layer by using the eigenfunction expansion theory and the separation of variables. The eigenvalues and the corresponding eigenfunctions obtained by solving an eigenvalue problem for each layer constitute the Green's function solution for analyzing the unsteady temperature distributions. Numerical calculations are carried out for the semi-infinite hollow circular FGM cylinder subjected to partially heated loads, and the numerical results are shown in figures.

• Structural Engineering and Mechanics
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• 제53권6호
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• pp.1105-1126
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• 2015

Many vibrating mechanical systems from the real life are modeled as combined dynamical systems consisting of beams to which spring-mass secondary systems are attached. In most of the publications on this topic, masses of the helical springs are neglected. In a paper (Cha et al. 2008) published recently, the eigencharacteristics of an arbitrary supported Bernoulli-Euler beam with multiple in-span helical spring-mass systems were determined via the solution of the established eigenvalue problem, where the springs were modeled as axially vibrating rods. In the present article, the authors used the assumed modes method in the usual sense and obtained the equations of motion from Lagrange Equations and arrived at a generalized eigenvalue problem after applying a Galerkin procedure. The aim of the present paper is simply to show that one can arrive at the corresponding generalized eigenvalue problem by following a quite different way, namely, by using the so-called "characteristic force" method. Further, parametric investigations are carried out for two representative types of supporting conditions of the bending beam.

• 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.