• Structural Engineering and Mechanics
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• 제73권3호
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• pp.271-286
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• 2020

Passive control technologies are commonly used in several areas to suppress structural vibrations by the addition of supplementary damping, and some modal damping may be heavy beyond critical damping even for regular structures with energy dissipation devices. The design of passive control structures is typically based on (complex) mode superposition approaches. However, the conventional mode superposition approach is predominantly applied to cases of under-critical damping. Moreover, when any modal damping ratio is equal or close to 1.0, the system becomes defective, i.e., a complete set of eigenvectors cannot be obtained such that some well-known algorithms for the quadratic eigenvalue problem are invalid. In this paper, a generalized complex mode superposition method that is suitable for under-critical, critical and over-critical damping is proposed and expressed in a unified form for structural displacement, velocity and acceleration responses. In the new method, the conventional algorithm for the eigenvalue problem is still valid, even though the system becomes defective due to critical modal damping. Based on the modal truncation error analysis, modal corrected methods for displacement and acceleration responses are developed to approximately consider the contribution of the truncated higher modes. Finally, the implementation of the proposed methods is presented through two numerical examples, and the effectiveness is investigated. The results also show that over-critically damped modes have a significant impact on structural responses. This study is a development of the original complex mode superposition method and can be applied well to dynamic analyses of non-classically damped systems.

• Earthquakes and Structures
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• 제4권4호
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• pp.341-363
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• 2013

Earthquake response calculation, parametric analysis and seismic parameter optimization of base-isolated structures are some critical issues for seismic design of base-isolated structures. To calculate the earthquake responses for such non-symmetric and non-classical damping linear systems and to implement the earthquake resistant design codes, a modified complex mode superposition design response spectrum method is put forward. Furthermore, to do parameter optimization for base-isolation structures, a graphical approach is proposed by analyzing the relationship between the base shear ratio of a seismic base-isolation floor to non-seismic base-isolation one and frequency ratio-damping ratio, as well as the relationship between the seismic base-isolation floor displacement and frequency ratio-damping ratio. In addition, the influences of mode number and site classification on the seismic base-isolation structure and corresponding optimum parameters are investigated. It is demonstrated that the modified complex mode superposition design response spectrum method is more precise and more convenient to engineering applications for utilizing the damping reduction factors and the design response spectrum, and the proposed graphical approach for parameter optimization of seismic base-isolation structures is compendious and feasible.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1993년도 봄 학술발표회논문집
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• pp.37-44
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• 1993

There are a lot of linear dynamic analysis methods for complex structures. Each method has advantages and shortcomings. Method of dynamic analysis for complex structure is selected considering characteristics of dynamic loading, computer facility available number of degree of freedem and accuracy of results. It is a main point of view to get economical results rather then accurate ones for analysis of general complex structures, Mode superposition method and direct integration method are generally used. However, the characteristics of load is not considered in mode superpositon method, the personal computer cannot be used in direct integration methods. To over-come these shortcomings, the component mode method incorporating Ritz algorithm updated is proposed to solve economically dynamic behavior of the structures. The purpose of study is a formulation of algorithm, and computer programing suitable for dynamic analysis of the complex structure in personal computer environment.

• 대한토목학회논문집
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• 제14권1호
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• pp.13-20
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• 1994

동적(動的) 해석(解析)에 널리 사용되는 Mode Superposition Method(MSM)에 있어서 몇개의 모우드를 포함하여 해석(解析) 하느냐 하는 문제는 공학적(工學的) 판단에 의지할 수 밖에 없는 문제이다. 합리적(合理的)이고 알맞은 모우드수를 결정(決定)하기란 어려운 과제이고, 또 대단히 중요(重要)한 문제이다. 이러한 문제점을 보완할 수 있는 한 방법으로 Mode Acceleration Method(MAM)가 발표(發表)되었으나 주파수(周波數) 영역(領域)에서는 그 수식(數式)이 너무 복잡(複雜)하고, 까다로와서 또 다른 단점(短點)이 대두되었다. 본(本) 연구(硏究)에서는 이 단점을 극복할 수 있는 실용적(實用的)으로 간편화된 Advanced Mode Acceleration Method(AMAM)을 유도하였다. 예제(例題) 해석(解析)을 통하여 AMAM이 MSM 및 MAM보다 우수한 해법(解法)이 됨을 입증할 수 있었다.

• 한국전산구조공학회논문집
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• 제12권4호
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• pp.671-679
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• 1999

건물의 진동에너지 소산능력을 향상하기 위하여 점탄성감쇠를 설치하게 되면 이른바 비비례 감쇠시스템이 되어 구조물은 복소수형태의 고유모드와 고유치를 가진다. 복소모드중첩법은 이러한 복소모드를 이용하여 중첩함으로써 비비례 감쇠시스템 구조물의 정확한 동적 거동을 얻을 수 있는 방법이다. 그러나 건물이 고층화되면 많은 자유도로 인하여 고유치해석 및 모드중첩과정에서 많은 시간과 노력이 필요하게 된다. 본 논문에서는 효율적인 구조물의 모형화를 위하여 강막가정과 행렬응축기법을 적용하였다. 또한 몇 개의 주요 모드만을 선택하여 중첩하는 방법에 대하여 연구하였으며 구조물의 진동에 영향을 주는 모드의 선택을 위한 복소모드 응답참여계수를 제안하였다. 제안된 해석방법의 정확성과 효율성을 검토하기 위하여 예제 구조물을 대상으로 해석한 결과, 응답의 정확성을 유지하면서 해석에 필요한 시간을 대폭 절감할 수 있었다.

• 한국전산구조공학회논문집
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• 제18권4호통권70호
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• pp.373-383
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• 2005

다양한 분야에서 방사선물질을 수송하기 위해 사용되고 있는 수송용기(cask)는 국내 원자력안전규정 및 IAEA 운반규정에서 정한 9m 자유낙하충격의 가상사고조건을 만족시켜야 된다. 현재까지 수송용기의 낙하충격력은 주로 복잡한 계산과정을 갖는 유한요소해석에 의해 수행되어 왔다. 본 논문에서는 수송용기 본체의 동적충격응답에 대해 모드중첩기법을 이용하여 해석하고 그 해법방법을 제시하였다. 해석결과는 이전에 실시되었던 시험결과와 유한요소해석과 비교를 통하여 그 타당성을 입증하였다. 본 해석방법은 유한요소 해석과 비교하여 간단한 방법으로서 수송용기에 대한 대체적인 동적응답을 예측할 수 있다.

• Structural Engineering and Mechanics
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• 제64권4호
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• pp.473-485
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• 2017

An isolated building, composed of superstructure and isolation system which have very different damping properties, is typically non-classical damping system. This results in inapplicability of traditional response spectrum method for isolated buildings. A multidimensional response spectrum method based on complex mode superposition is herein introduced, which properly takes into account the non-classical damping feature in the structure and a new method is developed to estimate velocity spectra from the commonly used displacement or pseudo-acceleration spectra based on random vibration theory. The error of forced decoupling method, an approximated approach, is discussed in the viewpoint of energy transfer. From the base-isolated benchmark model, as a numerical example, application of the procedure is illustrated companying with comparison study of time-history method, forced decoupling method and the proposed method. The results show that the proposed method is valid, while forced decoupling approach can't reflect the characteristics of isolated buildings and may lead to insecurity of structures.

• 소음진동
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• 제10권1호
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• pp.64-73
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• 2000

We present finite element equations in the Laplace-domain for linear viscoelastic and viscoelstically damped structures governed by a constitutive equation involving factional order derivative opeartors. These equations yield a nonstandard eigenproblem consisted of frequency dependent stiffness matrix. To solve this nonstandard eigenproblem we suggest an eigenvalue iteration procedure in the Laplace-domain. Improved Zenor and GHM material function type constitutive equations in the Laplace-domain are also available for this procedure. From above equations, complex eigenvalues and complex eigenvectors are obtained. Using obtained eigenvalues and eigenvectors, time domain analysis is performed by means of mode superposition. Finally, finite element solutions of viscoelastic and viscoeleastically damped sandwich beam are presented as an example.

• 한국지진공학회논문집
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• 제14권2호
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• pp.75-84
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• 2010

원자력발전소에 설치되는 주요 전기기기들의 내부 부품을 내진검증하기 위해서는 캐비닛내부응답스펙트럼이 필요하고, 이는 캐비닛의 각 위치에서 정확한 지진응답을 구한 후에 생성이 가능하다. 반면에 대부분의 전기기기는 질량과 강성 분포가 복잡하기 때문에 해석적 방법에 의해 동적 분석을 수행하는 것이 어렵다. 이러한 여건을 감안하여 이 연구에서는 해석과 시험을 조합하여 기기의 지진응답을 예측하는 간편한 절차를 제안하였다. 제안된 절차는 먼저 충격시험을 통하여 규명된 실험모드특성을 이용하여 독립된 모드방정식을 구성하고, 이로부터 모드응답을 계산한 다음, 각 모드응답을 중첩함으로써 구조물의 지진응답을 예측한다. 제안된 절차의 신뢰성을 검증하기 위해서, 별도로 제작된 단순 강재 프레임 시편에 제안된 절차를 적용하여 지진응답을 예측하고, 이를 실제 진동대시험을 통하여 계측한 결과와 비교하였다. 이 연구를 통하여 충격시험에 의해 얻어진 실험모드특성을 이용하여 구조물의 지진응답을 비교적 정확하게 예측할 수 있음을 확인하였다.

• 한국구조물진단유지관리공학회 논문집
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• 제5권4호
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• pp.197-203
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• 2001

This study presents the results of shaking table test of scaled model structures with added viscoelastic dampers, which are considered to be one of the most efficient means of upgrading existing structures against seismic loads. The experimental results were compared with those from analysis based on the linear modeling of viscoelastic dampers. The parameters obtained from free vibration test were utilized in the analysis. According to the results the added viscoelastic dampers turned out to be effective in reducing the responses of the model structures. It was also found that the analysis with linear modeling of viscoelastic dampers could simulate the test results accurately.