• Structural Engineering and Mechanics
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• v.44 no.3
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• pp.267-288
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• 2012

Free vibration analysis of arbitrary quadrilateral thick plates with internal columns and elastic edge supports is presented by using the powerful pb-2 Ritz method and Reddy's third order shear deformation plate theory. The computing domain of arbitrary quadrilateral planform is mapped onto a standard square form by coordinate transformation. The versatile pb-2 Ritz functions defined by the product of a two-dimensional polynomial and a basic function are taken to be the admissible functions. Substituting these displacement functions into the energy functional and minimizing the total energy by differentiation, leads to a typical eigenvalue problem, which is solved by a standard eigenvalue solver. Stiffness and mass matrices are numerically integrated over the plate by using Gaussian quadrature. The accuracy and efficiency of the proposed method are demonstrated through several numerical examples by comparison and convergency studies. A lot of numerical results for reasonable natural frequency parameters of quadrilateral plates with different combinations of elastic boundary conditions and column supports at any locations are presented, which can be used as a benchmark for future studies in this area.

• Computational Structural Engineering
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• v.4 no.4
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• pp.97-106
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• 1991

The frequency window method has been extended to include strong coupling and multiple connections between the primary structure and the secondary structures. The rational polynomial expansion of the eigenvalue problem and the analytical methods for its solution are novel and distinguish this work from other eigenvalue analysis methods. The key results are the identification of parameters which quantify the resonance and coupling characteristics; the derivation of analytical closed-form expressions describing the fundamental modal properties in the frequency windows; and the development of an iterative procedure which yields accurate convergent results for strongly-coupled primary-secondary structures.

• 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.

• Wind and Structures
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• v.14 no.4
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• pp.359-381
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• 2011

This paper deals with the flutter instability problem of flexible bridge decks in the framework of bimodal-coupled aeroelastic bridge system analysis. Based on the analysis of coefficients of the polynomials deduced from the singularity conditions of an integral wind-structure impedance matrix, a set of simplified formulations for calculating the critical wind velocity and coupled frequency are presented. Several case studies are discussed and comparisons with available approximated approaches are made and presented, along with a conventional complex eigenvalue analysis and numerical results. From the results, it is found that the formulas that are presented in this study are applicable to a variety of bridge cross sections that are not only prone to coupled-mode but also to single-mode-dominated flutter.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2003.03a
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• pp.481-490
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• 2003

This paper presents an efficient eigensolution method for non-proportionally damped systems. The proposed method is obtained by applying the accelerated Newton-Raphson technique and the orthonormal condition of the eigenvectors to the linearized form of the quadratic eigenproblem. A step length and a selective scheme are introduced to increase the convergence of the solution. The step length can be evaluated by minimizing the norm of the residual vector using the least square method. While the singularity may occur during factorizing process in other iteration methods such as the inverse iteration method and the subspace iteration method if the shift value is close to an exact eigenvalue, the proposed method guarantees the nonsingularity by introducing the orthonormal condition of the eigenvectors, which can be proved analytically. A numerical example is presented to demonstrate the effectiveness of the proposed method.

• Structural Engineering and Mechanics
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• v.5 no.2
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• pp.137-148
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• 1997

In computing eigenvalues for a large finite element system it has been observed that the eigenvalue extractors produce eigenvectors that are in some sense more accurate than their corresponding eigenvalues. From this observation the paper uses a patch type technique based on the eigenvector for one mesh quality to provide an eigenvalue error indicator. Tests show this indicator to be both accurate and reliable. This technique was first observed by Stephen and Steven for an error estimation for buckling and natural frequency of beams and two dimensional in-plane and out-of-plane structures. This paper produces and error indicator for the more difficult problem of three dimensional brick elements.

• Nuclear Engineering and Technology
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• v.55 no.4
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• pp.1350-1364
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• 2023

2D/1D coupling method is an important neutron transport calculation method due to its high accuracy and relatively low computation cost. However, 2D/1D coupling method may diverge especially in small axial mesh size. To analyze the convergence behavior of 2D/1D coupling method, a Fourier analysis for k-eigenvalue neutron transport problems is implemented. The analysis results present the divergence problem of 2D/1D coupling method in small axial mesh size. Several common attempts are made to solve the divergence problem, which are to increase the number of inner iterations of the 2D or 1D calculation, and two times 1D calculations per outer iteration. However, these attempts only could improve the convergence rate but cannot deal with the divergence problem of 2D/1D coupling method thoroughly. Moreover, the choice of axial solvers, such as DGFEM SN and traditional SN, and its effect on the convergence behavior are also discussed. The results show that the choice of axial solver is a key point for the convergence of 2D/1D method. The DGFEM SN based 2D/1D method could converge within a wide range of optical thickness region, which is superior to that of traditional SN method.

• The Journal of Engineering Geology
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• v.18 no.4
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• pp.381-391
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• 2008

The eigenvalue technique is introduced to overcome the problem of truncation errors caused by temporal discretization of numerical analysis. The eigenvalue technique is different from simulation in that only the space is discretized. The spatially discretized equation is diagonized and the linear dynamic system is then decoupled. The time integration can be done independently and continuously for any nodal point at any time. The results of eigenvalue technique are compared with the exact solution and FEM numerical solution. The eigenvalue technique is more efficient than the FEM to the computation time and the computer storage in the same conditions. This technique is applied to the solute transport analysis in nonuniform flow fields around underground storage caverns. This method can be very useful for time consuming simulations. So, a sensitivity analysis is carried out by using this method to analyze the safety of caverns from nearly located contaminant sources. According to the simulations, the reaching time from source to the nearest cavern may takes 50 years with longitudinal dispersivity of 50 m and transversal dispersivity of 5 m, respectively.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.197-202
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• 1992

In this paper, we consider the synthesis of mixed H$_{2}$/H$_{\infty}$ controllers such that the closed-loop poles are located in a specified region in the complex plane. Using solution to a generalized Riccati equation and a change of variable technique, it is shown that this synthesis problem can be reduced to a convex optimization problem over a bounded subset of matrices. This convex programming can be further reduced to Generalized Eigenvalue Minimization Problem where Interior Point method has been recently developed to efficiently solve this problem..

• 제어로봇시스템학회:학술대회논문집
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• 1992.10b
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• pp.575-580
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• 1992

Mixed H$_{2}$/H$_{\infty}$ robust control synthesis is considered for finite dimensional linear time-invariant systems under the presence of diagonal structured uncertainties. Such uncertainties arise for instance when there is real perturbation in the nominal model of the state space system or when modeling multiple (unstructured) uncertainty at different locations in the feedback loop. This synthesis problem is reduced to convex optimization problem over a bounded subset of matrices as well as diagonal matrix having certain structure. For computational purpose, this convex optimization problem is further reduced into Generalized Eigenvalue Minimization Problem where a powerful algorithm based on interior point method has been recently developed..