• Smart Structures and Systems
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• v.15 no.1
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• pp.81-97
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• 2015

Recently, a new output-only modal identification method based on time-frequency independent component analysis (ICA) has been developed by the authors and shown to be useful for even highly-damped structures. In many cases, it is of interest to identify the complex modes of structures with non-proportional damping. This study extends the time-frequency ICA based method to a complex ICA formulation for output-only modal identification of non-proportionally-damped structures. The connection is established between complex ICA model and the complex-valued modal expansion with sparse time-frequency representation, thereby blindly separating the measured structural responses into the complex mode matrix and complex-valued modal responses. Numerical simulation on a non-proportionally-damped system, laboratory experiment on a highly-damped three-story frame, and a real-world highly-damped base-isolated structure identification example demonstrate the capability of the time-frequency complex ICA method for identification of structures with complex modes in a straightforward and efficient manner.

• KIEE International Transactions on Electrophysics and Applications
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• v.3C no.5
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• pp.199-206
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• 2003

Numerical solutions to complex characteristic equations are quite often required to solve electromagnetic wave problems. In general, two traditional complex root search algorithms, the Newton-Raphson method and the Muller method, are used to produce such solutions. However, when utilizing these two methods, the choice of the initial iteration value is very sensitive, otherwise, the iteration can fail to converge into a solution. Thus, as an alternative approach, where the selection of the initial iteration value is more relaxed and the computation speed is high, Davidenko's method is used to determine accurate complex propagation constants for leaky circular symmetric modes in circular dielectric rod waveguides. Based on a precise determination of the complex propagation constants, the leaky mode characteristics of several lower-order circular symmetric modes are then numerically analyzed. In addition, no modification of the characteristic equation is required for the application of Davidenko's method.

• Steel and Composite Structures
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• v.22 no.5
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• pp.1039-1054
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• 2016

This paper presents the dynamic characteristics analysis of the purlin-sheet roofs by the random vibration theories. Results show that the natural vibration frequency of the purlin-sheet roof is low, while the frequencies and mode distributions are very intensive. The random vibration theory should be used for the dynamic characteristics of the roof structures due to complex vibration response. Among the first 20th vibration modes, the first vibration mode is mainly the deformations of purlins, while the rest modes are the overall deformations of the roof. In the following 30th modes, it mainly performs unilateral local deformations of the roof. The frequency distribution of the first 20th modes varies significantly while those of the following 30th modes are relatively sensitive. For different parts, the contributions of vibration modes on the vibration response are different. For the part far from the roof ridge, only considering the first 5th modes can reflect the wind-induced vibration response. For the part near the ridge, at least the first 12 modes should be considered, due to complex vibration response. The wind vibration coefficients of the upwind side are slightly higher than that of the leeward side. Finally, the corresponding wind vibration coefficient for the purlin-sheet roof is proposed.

• Advances in aircraft and spacecraft science
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• v.2 no.1
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• pp.57-76
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• 2015

We investigated complex damped modes in beams in the presence of a viscoelastic layer sandwiched between two elastic layers. The problem was solved using two approaches, (1) Rayleigh beam theory and analyzed using the Ritz method, and (2) by using 2D plane stress elasticity based finite-element method. The damping in the layers was modeled using the complex modulus. Simply-supported, cantilever, and viscously supported boundary conditions were considered in this study. Simple trigonometric functions were used as admissible functions in the Ritz method. The key idea behind sandwich structure is to increase damping in a beam as affected by the presence of a highly-damped core layer vibrating mainly in shear. Different assumptions are utilized in the literature, to model shear deformation in the core layer. In this manuscript, we used FEM without any kinematic assumptions for the transverse shear in both the core and elastic layers. Moreover, numerical examples were studied, where the base and constraining layers were also damped. The loss factor was calculated by modal strain energy method, and by solving a complex eigenvalue problem. The efficiency of the modal strain energy method was tested for different loss factors in the core layer. Complex mode shapes of the beam were also examined in the study, and a comparison was made between viscoelastically and viscously damped structures. The numerical results were compared with those available in the literature, and the results were found to be satisfactory.

• Journal of Mechanical Science and Technology
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• v.14 no.9
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• pp.968-977
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• 2000

The motion of an aircraft landing gear over a rough runway can be modeled by a nonclassically damped system subject to nonstationary random excitations. In this paper, the approximate analysis methods based on either the real or complex normal modes for the computation of nonstationary response covariances are proposed. It has been found by simulation involving a realistic example that, for the nonclassically damped random vibrational systems, the approximate solution method based on the complex normal mode is superior to other approaches with respect to the accuracy and computation time.

• Journal of KSNVE
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• v.10 no.1
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• pp.138-143
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• 2000

Longitudinal vibration of an axially moving material is investigated by using the assumed modes method. To circumvent a difficulty in choosing the comparison functions which satisfy the boundary conditions, the assumed modes method is adopted by which equations of motion are discretized. Based on the discretized equations, the complex eigenvalue problem is solved and then the effects of the translating velocity on the natural frequencies and modes are analyzed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.1513-1520
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• 2000

Complex modal testing method for rotating disks with support motion is introduced which handles the pairs of two point excitation and responses of the disk as complex input and output, respectively. This method utilizes the directivity information and the separation over the rotational speed of forward and backward traveling wave modes or bending coupled modes in the directional frequency response functions(dFRFs). This method synthesizes the normal/reverse dFRFs and complex wave dFRF, which were originally applied to rotating shaft and rotating disk, respectively, and is applied to complex system with dynamically coupled rotating disks and shaft. Experiments with a commercial hard disk drive spindle system demonstrate the validity of this method.

• YAKHAK HOEJI
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• v.46 no.6
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• pp.416-425
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• 2002

A comparative study to validate the reliability of a fully automated docking program, FlexiDock, was carried out to predict the binding modes of DHFR-inhibitor complex. The inhibitors were extracted from the crystallographically determined DHFR-NADP$^{+}$(H)-inhibitor ternary complexes of human, Escherichia coli and Candida albicans and then docked back into the remaining DHFR-NADP$^{+}$(H) binary complexes using FlexiDock. The resulting conformations and orientations were compared to the original crystal complex structures for reproducibility. Then, folate, the substrate, and known inhibitors such as methotrexate, piritrexim and trimethoprim were docked into the wild-type human DHFR and their binding modes were compared with X-ray crystallographic or other modeling data. The root mean square deviations (RMSDs) for ligands ranged from 1.14 to 1.57$\AA$, and the protein backbone RMSDs from 0.94 to 1.26$\AA$. FlexiDock reproduced the orientations and binding modes of all seven ligands in good agreement with the crystal structures. It proved to be a reliable and efficient program in studying binding modes of DHFR-inhibitor complexes of different species, and the information obtained from this work may provide additional insight into the design of new agents with improved activity.ity.

• Structural Engineering and Mechanics
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• v.14 no.4
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• pp.491-504
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• 2002

A state-space method is proposed to analyze the aerodynamically coupled flutter problems of long-span bridges based on the modal coordinates of structure. The theory about complex modes is applied in this paper. The general governing equation of the system is converted into a complex standard characteristic equation in a state space format, which contains only two variables. The proposed method is a single-parameter searching method about reduced velocity, and it need not choose the participating modes beforehand and has no requirement for the form of structure damping matrix. The information about variations of system characteristics with reduced velocity and wind velocity can be provided. The method is able to find automatically the lowest critical flutter velocity and give relative amplitudes, phases and energy ratios of the participating modes in the flutter motion. Moreover, the flutter analysis of Jiangyin Yangtse suspension bridge with 1385 m main span is performed. The proposed method has proved reliable in its methodology and efficient in its use.

• Journal of the Korean Society for Railway
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• v.16 no.4
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• pp.253-261
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• 2013

According to the measured results of KTX brake squeal noise in this study, high level brake noise occurred in a wide frequency range, 100~18,000Hz. To identify the sources of the brake squeal noise, unstable vibration modes due to brake disc/pad interaction were analyzed under various conditions by the finite element method. Complex eigenvalues for a brake unit with a disc and four pads were obtained. It was found that the real parts of the complex eigenvalues, that is, unstable vibration modes, were closely related to friction coefficients, pressure on the brake cylinders, elastic moduli of the components, and other conditions.