• 한국소음진동공학회논문집
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• 제19권10호
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• pp.1021-1027
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• 2009

Finite element models of dynamic systems can be updated in two stages. In the first stage, mass and stiffness matrices are updated neglecting damping. In the second stage, a damping matrix is estimated with the mass and stiffness matrices fixed. Methods to estimate a damping matrix for this purpose are proposed in this paper. For a system with proportional damping, a damping matrix is estimated using the modal parameters extracted from the measured responses and the modal matrix calculated from the mass and stiffness matrices from the first stage. For a system with non-proportional damping, a damping matrix is estimated from the impedance matrix which is the inverse of the FRF matrix. Only one low or one column of the FRF matrix is measured, and the remaining FRFs are synthesized to obtain a full FRF matrix. This procedure to obtain a full FRF matrix saves time and effort to measure FRFs.

• 대한기계학회논문집
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• 제17권8호
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• pp.1963-1970
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• 1993

A simple technique to decouple the modal equations of motion of a linear nonclassically damped system is to neglect the off-diagonal elements of the modal damping matrix. This is called the decoupling approximation. It has generally been conceived that smallness of off-diagonal elements relative to the diagonal ones would validate its use. In this study, the relationship between elements of the modal damping matrix and the error arising from the decoupling approximation is explored. It is shown that the enhanced diagonal dominance of the modal damping matrix need not diminish the error. In fact, the error may even increase. Moreover, the error is found to be strongly dependent on the exitation. Therefore, within the practical range of engineering applications, diagonal dominance of the modal damping matrix would not be sufficient to supress the effect of modal coupling.

• 한국소음진동공학회논문집
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• 제20권10호
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• pp.923-930
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• 2010

Finite element models of dynamic systems can be updated in two stages. In the first stage, mass and stiffness matrices are updated neglecting damping, and in the second stage, damping matrices are estimated with the mass and stiffness matrices fixed. Three methods to estimate damping matrices for this purpose are proposed in this paper. The methods include one for proportional damping systems and two for non-proportional damping systems. Method 1 utilizes orthogonality of normal modes and estimates damping matrices using the modal parameters extracted from the measured responses. Method 2 estimates damping matrices from impedance matrices which are the inverse of FRF matrices. Method 3 estimates damping using the equation which relates a damping matrix to the difference between the analytical and measured FRFs. The characteristics of the three methods are investigated by applying them to simulated discrete system data and experimental cantilever beam data.

• Journal of Advanced Marine Engineering and Technology
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• 제35권2호
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• pp.271-277
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• 2011

이 연구에서는 유전알고리즘을 이용하여 강봉의 감쇠행렬을 산출하는 방법을 제안하다. 감쇠행렬이 강성행렬과 비례한다는 가정을 전제로 각 요소강성행렬에 임의의 정수를 곱하여 감쇠행렬을 구성하여 주파수응답함수를 구성하고, 이를 실험 주파수응답함수와 비교한 값을 목적함수로 하여 목적함수가 가장 작은 정수의 감쇠행렬을 구한다. 비감쇠 해석의 경우보다 목적함수의 값이 약 1/60로 작아지는 것을 알 수 있었다. 이를 이용하면 큰 구조물의 감쇠가 큰 일부 부분구조물을 떼어내어 감쇠행렬을 구할 수 있어 구조물의 감쇠진동해석을 하는데 도움이 될 것으로 사료된다.

• 한국정밀공학회지
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• 제12권7호
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• pp.99-106
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• 1995

Frequency response functions are of great use in dynamic analysis of structural systems. The present paper proposes an efficient method for computation of the frequency rewponse functions of linear structural dynamic models with a sparse, non-proportional damping matrix. An exact condensation procedure is proposed which enables the present method to condense the matrices without resulting in any errors. Also, an iterative scheme is proposed to be able to avoid matrix inversion in computing frequency response matrix. The proposed method is illustrated through a numerical example.

• Advanced Composite Materials
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• 제17권2호
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• pp.111-124
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• 2008

The effect of temperature on natural frequency and damping is investigated in two different composite materials, Kevlar 29 fiber woven and polyethylene cloth, used especially to design ballistic armor. A damping monitoring method is used experimentally to measure the frequency response curve and it is also modeled numerically using a finite element program. The natural frequencies of a material, or a system, are a function of its elastic properties, dimensions and mass. This concept is used to calculate theoretical vibration modes of the composites. The damping properties in terms of the damping factor are determined by the half-power bandwidth technique. Numerically analyzed and experimentally measured time response curves are compared. It is seen that polymer matrix composites have temperature dependent mechanical properties. This relationship is functional and they have different effects against temperature.

• 한국소음진동공학회논문집
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• 제22권11호
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• pp.1144-1151
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• 2012

A damage in structure alters its dynamic characteristics. The change is characterized by changes in the modal parameter, i.e., modal frequencies, modal damping value and mode shape associated with each modal frequency. Changes also occur in some of the structural parameters; namely, the mass, damping, stiffness matrices of the structure. In this paper, evaluation of changes in stiffness matrix of a structure is presented as a method not only for identifying the presence of the damage but also locating the damage. It is shown that changed stiffness matrix can be accurately estimated a sensitivity coefficient matrix derived from modifying mode shapes, First, with 4 story shear structure models, the effect of presence of damage in a structure on its stiffness matrix is studied. By using these analytical model, the effectiveness of using change of stiffness matrix in detecting and locating damages is demonstrated. To validate the predicted changing stiffness and its location, the obtained results are compared to the reanalysis result which shows good agreement.

• Journal of Advanced Marine Engineering and Technology
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• 제40권4호
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• pp.369-373
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• 2016

감쇠구조물의 해석을 위해서는 정확한 감쇠모델을 구성하는 것이 중요하지만, 감쇠특성을 모델링 하는 것은 매우 어려운 일이다. 부정확한 감쇠 모델링에서 기인하는 오차는 진동 소음 문제 및 구조물 안전 평가 등에 많은 어려움을 주고 있다. 본 연구에서는 주파수 응답함수를 이용한 비비례 점성감쇠행렬 추정기법을 제시하였다. 복소 주파수 응답함수는 구조물의 실험데이터로부터 계측되며, 정상상태 주파수 응답함수는 계측된 복소 주파수 응답함수로부터 추정된다. 제안된 기법을 통해 비비례 점성감쇠 행렬을 추정하였으며, 두 가지 수치 예제(집중질량 모델과 외팔보)를 통해 제시된 기법을 검토하였다. 결과적으로 두 가지 예제 모두에서 비비례 점성감쇠 행렬을 정확히 추정할 수 있었다.

• Structural Engineering and Mechanics
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• 제55권6호
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• pp.1241-1260
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• 2015

Any rational approach to define the configuration and size of viscous fluid dampers in a structure should be based on the dynamic properties of the system with the dampers. In this paper we propose an alternative representation of the complex eigenvalues of multi degree of freedom systems with dampers to calculate new equivalent natural frequencies. Analytical expressions for the dynamic properties of a two-story building model with a linear viscous damper in the first floor (i.e. with a non-proportional damping matrix) are derived. The formulas permit to obtain the equivalent damping ratios and equivalent natural frequencies for all the modes as a function of the mass, stiffness and damping coefficient for underdamped and overdamped systems. It is shown that the commonly used formula to define the equivalent natural frequency is not applicable for this type of system and for others where the damping matrix is not proportional to the mass matrix, stiffness matrix or both. Moreover, the new expressions for the equivalent natural frequencies expose a novel phenomenon; the use of viscous fluid dampers can modify the vibration frequencies of the structure. The significance of the new equivalent natural frequencies is expounded by means of a simulated free vibration test. The proposed approach may offer a new perspective to study the effect of viscous dampers on the dynamic properties of a structure.

• 한국해양공학회지
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• 제26권4호
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• pp.86-91
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• 2012

A new identification method for a nonproportional damping matrix using the finite element (FE) model updating technique is proposed. Mass and stiffness matrices of the undamped system are identified by FE model updating method. Sensitivity analysis is used to update the FE model, and zero frequencies are considered as design parameters to supplement the information of vibration characteristics. The nonproportional damping matrix is identified through the proposed method. A numerical example is considered to verify the performance of the proposed method. As a result, the damping matrix of the nonproportional system is estimated accurately.