• 한국전산구조공학회:학술대회논문집
• /
• 한국전산구조공학회 1990년도 가을 학술발표회 논문집
• /
• pp.22-27
• /
• 1990

Since an eigenvalue problem in structural analysis has been recognized as an important process for the assessment of structural strength, it is usually to be carried out the eigenvalue analysis or buckling analysis of structures when the compression behabiour of the member is dorminant. In general, various variables involved in the eigenvalue problem have also shown their variability. So it is natural to apply the probabilistic analysis into such problem. Since the limit state equation for the eigenvalue analysis or buckling reliability analysis is expressed implicitly in terms of random variables involved, the probabilistic finite element method is combined with the conventional reliability method such as MVFOSM and AFOSM for the determination of probability of failure due to buckling. The accuracy of the results obtained by this method is compared with results from the Monte Carlo simulations. Importance sampling method is specially chosen for overcomming the difficulty in a large simulation number needed for appropriate accurate result. From the results of the case study, it is found that the method developed here has shown good performance for the calculation of probability of buckling failure and could be used for checking the safety of the calculation of probability of buckling failure and could be used for checking the safely of frame structure which might be collapsed by either yielding or buckling.

• 대한수학회보
• /
• 제46권5호
• /
• pp.949-966
• /
• 2009

We proved in [10] that Friedrich's estimate [5] for the first eigenvalue of the Dirac operator can be improved when a Codazzi tensor exists. In the paper we further prove that his estimate can be improved as well via a well-chosen divergencefree symmetric tensor. We study the geometric implication of the new first eigenvalue estimates over Sasakian spin manifolds and show that some particular types of spinors appear as the limiting case.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2013년도 추계학술대회 논문집
• /
• pp.658-663
• /
• 2013

A new formulation of the MNDIF method is introduced to extract highly accurate eigenvalues of concave acoustic cavities with arbitrary shapes. It is said that the MNDIF method cannot yield accurate eigenvalues for concave cavities. To overcome this weak point, a new approach of dividing a concave cavity into two convex domains is proposed. The validity of the proposed method is shown through a case study.

• 대한수학회보
• /
• 제49권4호
• /
• pp.669-684
• /
• 2012

Using the minimax methods in critical point theory, we study the multiplicity of solutions for a class of degenerate Dirichlet problem in the case near resonance.

• 제어로봇시스템학회논문지
• /
• 제5권7호
• /
• pp.794-799
• /
• 1999

This study deals with robustness bounds estimation for uncertain linear systems with structured perturbations where the eigenvalues of the perturbed systems are guaranteed to stay in a prescribed region. Based upon the Lyapunov approach, new theorems to estimate allowable perturbation parameter bounds are derived. The theorems are referred to as the zero-order or first-order asymmetric robustness measure depending on the order of the P matrix in the sense of Taylor series expansion of perturbed Lyapunov equation. It is proven that Gao's theorem for the estimation of stability robustness bounds is a special case of proposed zero-order asymmetric robustness measure for eigenvalue assignment. Robustness bounds of perturbed parameters measured by the proposed techniques are asymmetric around the origin and less conservative than those of conventional methods. Numerical examples are given to illustrate proposed methods.

• 대한기계학회논문집A
• /
• 제31권5호
• /
• pp.541-549
• /
• 2007

In the case of control for mechanical systems, it is highly useful to be able to provide a compact model of the mechanical system to control engineers using the smallest number of state variables, while still providing an accurate model. The reduced mechanical model can then be inserted into the complete system models and used for extended system-level dynamic simulation. In this paper, moment-matching based model order reductions (MOR) using Krylov subspaces, which reduce the number of degrees of freedom of an original finite element model via the Arnoldi process, are presented to study the eigenvalue and frequency response problems of a HDD actuator and suspension system.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제5권2호
• /
• pp.63-69
• /
• 2001

In this study, we shall be concerned with computing in parallel a few of the smallest eigenvalues and their corresponding eigenvectors of the eigenvalue problem, $Ax={\lambda}Bx$, where A is symmetric, and B is symmetric positive definite. Both A and B are large and sparse. Recently iterative algorithms based on the optimization of the Rayleigh quotient have been developed, and CG scheme for the optimization of the Rayleigh quotient has been proven a very attractive and promising technique for large sparse eigenproblems for small extreme eigenvalues. As in the case of a system of linear equations, successful application of the CG scheme to eigenproblems depends also upon the preconditioning techniques. A proper choice of the preconditioner significantly improves the convergence of the CG scheme. The idea underlying the present work is a parallel computation of the Multi-Color Block SSOR preconditioning for the CG optimization of the Rayleigh quotient together with deflation techniques. Multi-Coloring is a simple technique to obatin the parallelism of order n, where n is the dimension of the matrix. Block SSOR is a symmetric preconditioner which is expected to minimize the interprocessor communication due to the blocking. We implemented the results on the CRAY-T3E with 128 nodes. The MPI(Message Passing Interface) library was adopted for the interprocessor communications. The test problems were drawn from the discretizations of partial differential equations by finite difference methods.

• Structural Engineering and Mechanics
• /
• 제20권3호
• /
• pp.293-312
• /
• 2005

In this paper, free vibration of rotating beam with random properties is studied. The cross-sectional area, elasticity modulus, moment of inertia, shear modulus and density are modeled as random fields and the rotational speed as a random variable. To study uncertainty, stochastic finite element method based on second order perturbation method is applied. To discretize random fields, the three methods of midpoint, interpolation and local average are applied and compared. The effects of rotational speed, setting angle, random property variances, discretization scheme, number of elements, correlation of random fields, correlation function form and correlation length on "Coefficient of Variation" (C.O.V.) of first mode eigenvalue are investigated completely. To determine the significant random properties on the variation of first mode eigenvalue the sensitivity analysis is performed. The results are studied for both Timoshenko and Bernoulli-Euler rotating beam. It is shown that the C.O.V. of first mode eigenvalue of Timoshenko and Bernoulli-Euler rotating beams are approximately identical. Also, compared to uncorrelated random fields, the correlated case has larger C.O.V. value. Another important result is, where correlation length is small, the convergence rate is lower and more number of elements are necessary for convergence of final response.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2002년도 춘계학술대회논문집
• /
• pp.705-709
• /
• 2002

The spacer grids in nuclear fuel assembly locate and align the fuel rods with respect to each other. They provide axial and lateral restraint against an excessive rod motion mainly caused by coolant flow. It is understood that each rod Is supported by multiple spacer grid. In such a case, it is important to determine spacer grid span so as to avoid resonance between the natural frequency of the fuel rods and excitation frequency. Actually dynamic characteristics of the fuel rods can be improved by assigning adequate spacer grid locations. When a dynamic performance of the structure is to be improved, design sensitivity analysis plays an important role as like many structural redesign problems. In this work, a shape design concept, different from conventional design, was applied to the problem. According to the theory shape can be a design parameter and optimal shape design can be found. This study concentrates on eigenvalue design sensitivity of the fuel rod supported by multiple spacer grids to determine optimal spacer grids positions.

• Wind and Structures
• /
• 제14권4호
• /
• pp.359-381
• /
• 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.