• Structural Engineering and Mechanics
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• v.14 no.4
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• pp.417-434
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• 2002

This paper explores the possibility of using a combination of the empirical mode decomposition (EMD) and the Hilbert transform (HT), termed the Hilbert-Huang transform (HHT) method, to identify the modal damping ratios of the structure with closely spaced modal frequencies. The principle of the HHT method and the procedure of using the HHT method for modal damping ratio identification are briefly introduced first. The dynamic response of a two-degrees-of-freedom (2DOF) system under an impact load is then computed for a wide range of dynamic properties from well-separated modal frequencies to very closely spaced modal frequencies. The natural frequencies and modal damping ratios identified by the HHT method are compared with the theoretical values and those identified using the fast Fourier transform (FFT) method. The results show that the HHT method is superior to the FFT method in the identification of modal damping ratios of the structure with closely spaced modes of vibration. Finally, a 36-storey shear building with a 4-storey light appendage, having closely spaced modal frequencies and subjected to an ambient ground motion, is analyzed. The modal damping ratios identified by the HHT method in conjunction with the random decrement technique (RDT) are much better than those obtained by the FFT method. The HHT method performing in the frequency-time domain seems to be a promising tool for system identification of civil engineering structures.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.8
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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.

• Smart Structures and Systems
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• v.15 no.3
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• pp.523-541
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• 2015

Structural health monitoring of steel truss bridge based on changes in modal properties was investigated in this study. Vibration measurements with five sensors were conducted at an existing Warren truss bridge with partial fractures in diagonal members before and after an emergency repair work. Modal properties identified by the Eigensystem Realization Algorithm showed evidences of increases in modal damping due to the damage in diagonal member. In order to understand the dynamic behavior of the bridge and possible mechanism of those increases in modal damping, theoretical modal analysis was conducted with three dimensional frame models. It was found that vibrations of the main truss could be coupled internally with local vibrations of diagonal members and the degree of coupling could change with structural changes in diagonal members. Additional vibration measurements with fifteen sensors were then conducted so as to understand the consistency of those theoretical findings with the actual dynamic behavior. Modal properties experimentally identified showed that the damping change caused by the damage in diagonal member described above could have occurred in a diagonal-coupled mode. The results in this study imply that damages in diagonal members could be detected from changes in modal damping of diagonal-coupled modes.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.7 s.112
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• pp.690-696
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• 2006

Thickness of damping layer in sandwich plate needs to be optimized in order to make modal loss factor of the sandwich plate maximum. Since previous studies were interested in noise reductions over high frequency range, the modal properties were derived based on simply supported boundaries. This conventional formula is approximately applicable to other boundary conditions over high frequency range only. The purpose of this study is to propose a method to determine optimum damping layer thickness of sandwich plate for maximum modal damping in low frequency range when the boundary condition is not a simple support. The conventional RKU equation based on simply supported boundary is modified to reflect other boundary conditions and the modified RKU equation is subsequently applied to determine the optimum damping layer thickness for arbitrary conditions. In order to reflect frequency-dependent characteristics of elastic modulus of the damping layer, an iteration method is proposed in determining the modal properties. Test results on sandwich plates for optimum damping layer thickness are compared with predictions by the proposed method and conventional method.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.1025-1032
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• 2006

The PVRC(Pressure Vessel Research Council) damping is for the response spectrum analysis of the piping system. In this study, the possibility to apply it to the time history analysis is evaluated to reduce the higher conservatism for the structural integrity. The evaluation was performed for the surge line connecting the pressurizer to the hot-leg, and the whole mode includes the RCS and the building structures with the surge line. The analyses were performed using ANSYS code. The first modal analysis shows the modes of the surge line are isolated from those of the other structures. The composite modal damping was calculated with PVRC damping for the surge line and RG 1.60 damping for the other structures by using ANSYS routines. Of the calculated composite modal damping values, the composite modal damping values related to the modes of the surge line were replaced with the PVRC damping values with respect to its frequencies. With this replacement, the composite modal damping values of the other structures were not changed. Based on this decouple characteristics, the time history analyses for the seismic events with PVRC damping for the surge line were performed. And the results show the resultant loads can be reduced by up to 50%.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2001.09a
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• pp.200-207
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• 2001

This paper introduces a methodology of seismic fragility analysis and discusses the basic input variables, focusing on the conservatism and variability of reference response spectrum. The procedures to consider the composite modal damping in the seismic fragility analysis is presented and its effects on the seismic capacity of structure is evaluated through an example analysis of the nuclear power plant structure which has typical composite modal damping characteristics. Two seismic fragility analyses were performed to obtain the seismic capacities which evaluated by considering the composite modal damping and the single damping characteristics. The results showed that the seismic fragility analysis without considering the different values of composite modal damping may considerably overestimate the seismic capacity of coupled structures.

• Smart Structures and Systems
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• v.12 no.5
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• pp.547-577
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• 2013

To suppress vibration and noise of mechanical structures piezoelectric ceramics play an increasing role as effective, simple and light-weighted damping devices as they are suitable for sensing and actuating. Out of the various piezoelectric damping methods this paper compares mode based active control strategies to passive shunt damping for thin plates. Therefore, a new approach for the optimal placement of the piezoelectric sensors/actuators, or more general transducers, is proposed after intense theoretical investigations based on the Kirchhoff kinematical hypotheses of plates; in particular, modal and nilpotent transducers are discussed in detail. Based on the proposed distribution a discrete design for modal transducers is implemented, tested and verified on an experimental setup. For active control the modal sensors clearly identify the eigenmodes, whereas the modal actuators impose distributed eigenstrains in order to reduce the transverse plate vibrations. In contrast to the modal control, passive shunt damping works without requiring additional actuators or auxiliary power and can therefore act as an autonomous system, but it is less effective compensating the flexible vibrations. Exemplarily, an acryl glass plate disturbed by an arbitrary force initialized by a loudspeaker is investigated. Comparing the different methods their specific advantages are highlighted and a significant broadband reduction of the vibrations of up to -20dB is obtained.

• Structural Engineering and Mechanics
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• v.38 no.3
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• pp.349-359
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• 2011

Input excitation and output response of structure are needed in conventional modal analysis methods. However, input excitation is often difficult to be obtained in the dynamic load test of bridge structures. Therefore, what attracts engineers' attention is how to get dynamic parameters from the output response. In this paper, a structural experimental modal analysis method is introduced, which can be used to conveniently obtain dynamic parameters of the structure from the free decay response. With known damping coefficients, this analysis method can be used to identify the natural frequencies and the mode shapes of MDOF structures. Based on the modal analysis theory, the mathematical relationship of damping ratio and frequency is obtained. By using this mathematical relationship to improve the previous method, an improved experimental modal analysis method is proposed in this paper. This improved method can overcome the deficiencies of the previous method, which can not identify damping ratios and requires damping coefficients in advance. Additionally, this improved method can also identify the natural frequencies, mode shapes and damping ratios of the bridge only from the free decay response, and ensure the stability of identification process by using modern mathematical means. Finally, the feasibility and effectiveness of this method are demonstrated by a numerical example of a simply supported reinforced concrete beam.

• Structural Engineering and Mechanics
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• v.73 no.3
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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.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.984-989
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• 2008

An estimation of high-order damping in flexible multibody dynamic simulation is introduced in this paper. The suggested damping model based on the experimental modal analysis leads to more accurate correlation results comparing to the traditional linear damping model because it directly uses the modal parameters of each mode achieved from experiment even high frequency modes. The modal parameters until the 5th mode are extracted from the experimental modal testing of the flexible beam using a high speed camera. And using the measured damping ratio and natural frequency until the 5th mode, the generic damping model is constructed. Then, the ANCF (absolute Nodal Coordinate Formulation) simulation results are compared to experimental results until the 5th mode.