• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.10
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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.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.11
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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.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.10
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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 the Korean Society for Precision Engineering
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• v.29 no.10
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• pp.1056-1061
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• 2012

FEM analysis is essential to shorten the development time and reduce the cost for developing high-performance machine tools. Mount joint parts play important role to ensure static and dynamic stability of machine tools. This paper suggests a computational modeling of mount joint part of machine tools. MATRIX27 element of ANSYS is adopted to model mount joint parts. MATRIX27 allows the definition of stiffness and damping matrices in matrix form. The matrix is assumed to relate two nodes, each with six degrees of freedom per node. Stiffness and damping values of commercial mount products are measured to build a database for FEM analysis. Jack mounts with rubber pad are exemplified in this paper. The database extracted from the experiments is also used to estimate of stiffness and damping of untested mounts. FEM analysis of machine tools system with the suggested mount computational model is performed. Static and dynamic results prove the feasibility of the suggested mount model.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.10 no.3
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• pp.57-65
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• 1990

The finite element menthod for the investigation of the static and dynamic stability of the plane framed structures subjected to non-conservative forces is presented. By using the Hermitian polynomial as the shape function, the geometric stiffness matrix, the load correction stiffness matrix for non-conservative forces, and the matrix equation of internal and external damping are derived. Then, a matrix equation of the motion for the non-conservative system is formulated and the critical divergence and flutter loads are determined from this equation.

• Structural Engineering and Mechanics
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• v.55 no.6
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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.

• Journal of the Earthquake Engineering Society of Korea
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• v.8 no.2
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• pp.45-53
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• 2004

In this paper, the stiffness and damping matrix are experimentally constructed using the structural modal information on frequencies, damping ratio and modal vectors, which are obtained by shaking table tests. Free vibration, harmonic and white noise vibration tests are performed. The acceleration of the shaking table was used as the input signal, and the corresponding accelerations of each floor were measured as output signals. The characteristics and limitations of modal information from each test are compared. The results of this study would be a basic resource of the analytical and experimental studies on the system identification of structures.

• Smart Structures and Systems
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• v.19 no.1
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• pp.57-66
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• 2017

Nanocomposites reinforced with carbon nanotube fibers exhibit greater stiffness, strength and damping properties in comparison to conventional composites reinforced with carbon/glass fibers. Consequently, most of the nanocomposite research is focused in understanding the dynamic characteristics, which are highly useful in applications such as vibration control and energy harvesting. It has been observed that those nanocomposites show better stiffness when the geometry of nanotubes is straight as compared to curvilinear although nanotube agglomeration may exist. In this work the damping behavior of the nanocomposite is characterized in terms of loss factor under the presence of nanotube agglomerations. A micro stick-slip damping model is used to compute the damping properties of the nanocomposites with multiwall carbon nanotubes. The present formulation considers the slippage between the interface of the matrix and the nanotubes as well as the slippage between the interlayers in the nanotubes. The nanotube agglomerations model is also presented. Results are computed based on the loss factor expressed in terms of strain amplitude and nanotube agglomerations. The results show that although-among the various factors such as the material properties (moduli of nanotubes and polymer matrix) and the geometric properties (number of nanotubes, volume fraction of nanotubes, and critical interfacial shear stresses), the agglomeration of nanotubes significantly influences the damping properties of the nanocomposites. Therefore the full potential of nanocomposites to be used for damping applications needs to be analyzed under the influence of nanotube agglomerations.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.12
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• pp.3109-3117
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• 1994

To operate a flexible mechanism in high speed its weight must be reduced as far as the structural strength does not decrease too much, but a light-weighted mechanism causes undesirable elastodynamic responses deteriorating the system performance. Besides, clearance within the connections of mechanisms causes rapid wear, increased noise and vibration. Even if the problems described above must be considered in the initial design stage, there has been no effective design process which takes account of the correlation between dynamic characteristics of flexible mechanism and the clearance effect at the joint. In this study, the generalized elastodynamic governing equations which include dynamic characteristics and boundary conditions of flexible mechanism are derived by variational calculus and solved by using FFM theory. To take the clearance effect at joint into account a new dynamic model is presented and also the method of modified stiffness/damping matrix is proposed to activate the dynamic clearance model, which cooperates with the developed governing equation very easily. As the results of this study, the proposed method(modified stiffness/damping matrix) to calculate clearance effect was proved to be superior to the existing one(force reaction method) in solution convergency and calculation performance. Besides this method can be easily adopted to the complex shape joint without calculation of reaction force direction.

• Journal of Advanced Marine Engineering and Technology
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• v.35 no.2
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• pp.271-277
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• 2011

An identification method of the structural damping matrix for a steel bar by the genetic algorithm is proposed. Supposing the damping matrix were in proportion to the stiffness matrix, the proportional factors can be identified from the curve fitting of the experimental frequency response function(FRF) by the genetic algorithm. Applying the identified damping matrix to FEM of a beam model, the values of the objective function could be reduced to about 1/60 in comparison with conventional FEM model without damping. The damping matrices of some sub-structures which have large damping partly could be identified by the algorithm, and they could be used as some parts of the FEM model for a whole structure.