• Structural Engineering and Mechanics
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• 제39권5호
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• pp.669-682
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• 2011

A Chebyshev spectral method (CSM) for the dynamic analysis of non-uniform Timoshenko beams under various boundary conditions and concentrated masses at their ends is proposed. The matrix-based Chebyshev spectral approach was used to construct the spectral differentiation matrix of the governing differential operator and its boundary conditions. A matrix condensation approach is crucially presented to impose boundary conditions involving the homogeneous Cauchy conditions and boundary conditions containing eigenvalues. By taking advantage of the standard powerful algorithms for solving matrix eigenvalue and generalized eigenvalue problems that are embodied in the MATLAB commands, chebfun and eigs, the modal parameters of non-uniform Timoshenko beams under various boundary conditions can be obtained from the eigensolutions of the corresponding linear differential operators. Some numerical examples are presented to compare the results herein with those obtained elsewhere, and to illustrate the accuracy and effectiveness of this method.

• 대한기계학회논문집A
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• 제41권5호
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• pp.345-352
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• 2017

본 논문은 스퀼 시험을 통해 압력 변화에 의해 발생하는 스퀼 소음을 계측하고, 발생된 스퀼 소음을 FEM 복소수 고유치 해석으로 모드연성 불안정성을 구현하였다. FEM 해석에서 압력 변화에 따른 스퀼주파수 변화를 근사하기 위해서 접촉강성 변화에 의한 스퀼 민감도를 예측하고, 잠재적인 스퀼 모드를 유추하였다. 스퀼 실험 결과 1 kHz, 2.5 kHz, 3.5 kHz, 4 kHz 근방에서 스퀼 소음이 발생하였으며, 압력이 증가함에 따라 스퀼 주파수가 다소 증가되었다. FEM 해석 결과 접촉강성 변화에 따른 유사한 스퀼모드 및 민감도를 예측하였고, 해석시 접촉강성 변화가 스퀼실험에서의 압력증가 효과를 근사할 수 있음을 보였다.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 Proceedings of the Korea Automatic Control Conference, 11th (KACC); Pohang, Korea; 24-26 Oct. 1996
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• pp.362-367
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• 1996

In this paper, the eigenstructure of a class of linear time varying systems, termed as linear quasi-time invariant(LQTI) systems, is investigated. A system composed of dynamic devices such as linear time varying capacitors and resistors can be an example of the class. To effectively describe and analyze the LQTI systems, a generalized differential operator G is introduced. Then the dynamic systems described by the operator G are studied in terms of eigenvalue, frequency characteristics, stability and an extended convolution. Some basic attributes of the operator G are compared with those of the differential operator D. Also the corresponding generalized Laplace transform pair is defined and relevant properties are derived for frequency domain analysis of the systems under consideration. As an application example, a LQTI circuit is examined by using the concept of eigenstructure of LQTI system. The LQTI filter processes the sinusoidal signals modulated by some functions.

• Journal of applied mathematics & informatics
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• 제38권1_2호
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• pp.175-187
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• 2020

Recently Salkuyeh and Rahimian in (Comput. Math. Appl. 74 (2017) 2940-2949) proposed a modification of the generalized shift-splitting (MGSS) method for solving singular saddle point problems. In this paper, we present the spectral analysis of the MGSS preconditioner when it is applied to precondition the singular saddle point problems with the (1, 1) block being symmetric. Some eigenvalue bounds for the spectrum of the preconditioned matrix are given. We show that all the real eigenvalues of the preconditioned matrix are in a positive interval and all nonzero eigenvalues having nonzero imaginary part are contained in an intersection of two circles.

• 한국생산제조학회지
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• 제22권1호
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• pp.63-69
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• 2013

In order to find the optimum design of structures that have characteristic natural frequency range, a numerical optimization method to solving eigenvalue problems is a widely used approach. However in the most cases, it is difficult to decide the accurate thickness and shape of structures that have allowable natural frequency in design constraints. Parallel analysis algorithm involving the feasible direction optimization method and Rayleigh-Ritz eigenvalue solving method is developed. The method is implemented by using finite element method. It calculates the optimal thickness and the thickness ratio of individual elements of the 2-D plane element through a parallel algorithm method which satisfy the design constraint of natural frequency. As a result this method of optimization for natural frequency by using finite element method can determine the optimal size or its ratio of geometrically complicated shape and large scale structure.

• 대한기계학회논문집A
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• 제33권10호
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• pp.1074-1080
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• 2009

A method for determining the geometric stability characteristics of a brake corner module (BCM) is presented. Since disc brake "squeal" noise typically occurs at unstable resonant frequencies of a system, the likelihood of disc brake squeal for a particular design can be determined. Finite element methods are used to derive complex eigenvalue for a brake corner module. Some unstable modes calculated by finite element methods correspond to squeal noise data. Through kinetic energy participation analysis for each part of BCM, we can efficiently predict squeal noise data.

• 한국자동차공학회논문집
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• 제10권4호
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• pp.216-222
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• 2002

Brake Moan is a laud and strong noise occurring at any vehicle speed over 2 mph as a low frequency in below 600Hz. In this study, we targeted to shift the unstable mode that causes the brake moan from the moats frequency range to sufficiently higher frequency range to avoid the moan phenomenon. We simulated the finite element model and found out the nodes in which the brake moan occurs the most and we regarded the boundary and its relationship between the brake pad and the rotor as a spring coefficient k. With the binary set of the spring coefficient k, we finally used genetic algorithm (GA) to get the optimal topology of the brake pad and its shape to avoid the brake moan. The final result remarkably shows that genetic algorithm can be used in topology optimization procedures requiring complex eigenvalue problems.

• 대한전기학회논문지:전기물성ㆍ응용부문C
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• 제48권2호
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• pp.141-146
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• 1999

The eigenvalue equations of multiple waveguides with step-index profile are derived by using the WKB theory. Phase changes unique to step-index discontinuity areintroduced when applying the WKB connection formula to turning points. The transfer matrix method is employed for the analysis of multiple structure and the derived eigenvalue equation are represented in the recursive form. The results by the WKB are compared with those by the FEM for a three-waveguide coupler.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2002년도 하계학술대회 논문집 A
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• pp.139-141
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• 2002

This paper describes a new contingency analysis methods for small signal security assessment based on the eigenvalue perturbation. The eigenvalue perturbation with respect to MW changes can be used to find possible sources of the low frequency oscillation, and to select contingency for small signal stability. The proposed algorithm has been successfully tested on the KEPCO systems.

• 한국공간구조학회:학술대회논문집
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• 한국공간구조학회 2005년도 춘계학술발표회 및 정기총회 2권1호(통권2호)
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• pp.147-153
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• 2005

The single layer latticed dome is very sensitive on the slenderness ratio and half open angle of the elements, load condition, and the connection type because it is originazed by a lot of thin elements, so we have to use the geometrically nonlinear buckling load when the buckling of the structures is analyzed. But, it is very difficult to design the single layer latticed domes considered all conditions. Therefore the purpose of this paper is to propose the appropriate design method of the single layer latticed dome considered the geometrically nonlinear buckling load in base of the linear buckling load by the eigenvalue analysis.