• 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.

• 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.

• Transactions of Materials Processing
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• v.8 no.5
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• pp.507-519
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• 1999

An approach using the energy method has veen proposed for the analysis of cone spinning having the complicated deformation modes mixed by shear and normal deformation. In the proposed method, the corresponding solution is found through optimization of the total energy dissipation with respect to the parameters assumed by the velocity field defined as the variation of the length in longitudinal direction. The sheet blank is divided into three layers to consider the bending effect and the energy dissipated by shear deformation is superposed to the energy consumption due to normal deformation related with the shrinking deformation is superposed to the energy consumption due to normal deformation related with the shrinking deformation of axi-symmetric sheet element for the evaluation of total deformation energy. In order to check the validity of the proposed method, the complex spinning for making the conical cup is analyzed and the computed results are compared with the experimental results. In comparison of the computed results with existing experimental results,, the good agreement is obtained for the variation of outer radius and the distribution of thickness, and it has thus been shown that the present approach is applicable to the analysis of complex spinning.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2007.05a
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• pp.379-382
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• 2007

The proper orthogonal decomposition(POD) is used to the modal analysis of microcantilever of dynamic mode atomic force microscopy(AFM). The proper orthogonal modes(POM) are extracted from vibrating signals of microcantilever when it resonates and taps the sample. The POMs resemble the linear normal modes(LNM) of cantilever vibrating at each resonance frequency. Some of POMs in tapping microcantilever show quite different shapes from the POMs of the resonating microcantilever. Also this POMs can be applied to model for the complex nonlinear behavior of the dynamic mode AFM microcantilevers.

• Journal of Electrical Engineering and Technology
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• v.3 no.1
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• pp.8-13
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• 2008

Because of the robust nonlinear characteristics appearing in today's modern power system, a strong interaction exists between the angle stability and the voltage stability, which were conventionally studied insularly. However, as the power system is a complex unified system, angle instability always happens in conjunction with voltage instability. The authors propose a novel method to analyze this type of stability problem. In the proposed method, the theory of normal forms of vector fields is utilized to treat the auxiliary dynamic system. By use of this method, the interaction between response modes caused by the nonlinearity of the power system can be analyzed. Consequently, the eigenvalue analysis method is extended to cope with performance analysis of the power system with heavy nonlinearity. The effectiveness of the proposed methodology is verified on a 3-bus power system.

• Structural Engineering and Mechanics
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• v.14 no.6
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• pp.679-698
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• 2002

In this paper some techniques for the dynamic analysis of non-classically damped linear systems are reviewed and compared. All these methods are based on a transformation of the governing equations using a basis of complex or real vectors. Complex and real vector bases are presented and compared. The complex vector basis is represented by the eigenvectors of the complex eigenproblem obtained considering the non-classical damping matrix of the system. The real vector basis is a set of Ritz vectors derived either as the undamped normal modes of vibration of the system, or by the load dependent vector algorithm (Lanczos vectors). In this latter case the vector basis includes the static correction concept. The rate of convergence of these bases, with reference to a parametric structural system subjected to a fixed spatial distribution of forces, is evaluated. To this aim two error norms are considered, the first based on the spatial distribution of the load and the second on the shear force at the base due to impulsive loading. It is shown that both error norms point out that the rate of convergence is strongly influenced by the spatial distribution of the applied forces.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1995.10a
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• pp.185-190
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• 1995

In recent years, many researcher have been interested in the stability of a thin beam. Among them, Pai and Nayfeh[1] had investigated the nonplanar motion of the cantilever beam under lateral base excitation and chaotic motion, but this study is associated with internal resonance, i.e. one to one resonance. Also Cusumano[2] had made an experiment on a thin beam, called Elastica, under bending loads. In this experiment, he had shown that there exists out-of-plane motion, involving the bending and the torsional mode. Pak et al.[3] verified the validity of Cusumano's experimental works theoretically and defined the existence of Non-Local Mode(NLM), which is came out due to the instability of torsional mode and the corresponding aspect of motions by using the Normal Modes. Lee[4] studied on a thin beam under bending loads and investigated the routes to chaos by using forcing amplitude as a control parameter. In this paper, we are interested in the motion of a thin beam under torsional loads. Here the form of force based on the natural forcing function is used. Consequently, it is found that small torsional loads result in instability and in case that the forcing amplitude is increasing gradually, the motion appears in the form of dynamic double potential well, finally leads to complex motion. This phenomenon is investigated through the poincare map and time response. We also check that Harmonic Balance Method(H.B.M.) is a suitable tool to calculate the bifurcated modes.

• Bulletin of the Korean Chemical Society
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• v.31 no.6
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• pp.1615-1620
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• 2010

Bis-[dipyrido[3,2-$\alpha$:2',3'-c]phenazine)$_2$(1,10-phenanthroline)$_2Ru_2$]$^{2+}$ complexes (bis-Ru(II) complexes) tethered by linkers of various lengths were synthesized and their binding properties to DNA investigated by normal absorption and linear dichroism spectra, and fluorescence techniques in this study. Upon binding to DNA, the bis-Ru(II) complex with the longest linker (1,3-bis-(4-pyridyl)-propane), exhibited a negative $LD^r$ signal whose intensity was as large as that in the DNA absorption region, followed by a complicate $LD^r$ signal in the metal-to-ligand charge transfer region. The luminescence intensity of this bis-Ru(II) complex was enhanced. The observed $LD^r$ and luminescence results resembled that of the [Ru(1,10-phenanthroline)$_2$ dipyrido[3,2-$\alpha$:2',3'-c]phenazine]$^{2+}$ complex, whose dipyrido[3,2-$\alpha$:2',3'-c]phenazine (dppz) ligand has been known to intercalate between DNA bases. Hence, it is conclusive that both dppz ligands of the bis-Ru(II) complex intercalate. The binding stoichiometry, however, was a single intercalated dppz per ~ 2.3 bases, which violates the "nearest binding site exclusion" model for intercalation. The length between the two Ru(II) complexes may be barely long enough to accommodate one DNA base between the two dppz ligands, but not for two DNA bases. When the linker was shorter (4,4'-bipyridine or 1,2-bis-(4-pyridyl)-ethane), the magnitude of the LD in the dppz absorption region, as well as the luminescence intensity of both bis-Ru(II) complexes, was half that of the bis-Ru(II) complex bearing a long linker. This observation can be elucidated by a model whereby one of the dppz ligands intercalates while the other is exposed to the aqueous environment.

• Tribology and Lubricants
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• v.39 no.6
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• pp.221-227
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• 2023

A rotordynamic system consists of components that undergo rotational motion. These components include shafts, impellers, thrust collars, and components that support rotation, such as bearings and seals. The motion of this type of rotating system can be modeled as two-dimensional motion and, accordingly, the equation of motion for the rotordynamic system can be represented using complex coordinates. The directional frequency response function (dFRF) can be derived from this complex coordinate system and used as an effective analytical tool for rotating machinery. However, the dFRF is not widely used in the field because most previous studies and commercial software are based on real coordinate systems. The objective of the current study is to introduce the dFRF and show that it can be an effective tool in rotordynamic analysis. In this study, the normal frequency response function (nFRF) and dFRF are compared under rotordynamic analysis for isotropic and unisotropic rotors. Results show that in the nFRF, the magnitude of the response is the same for both positive and negative frequencies, and the response is similar under all modes. Consequently, the severity of the mode cannot be identified. However, in the dFRF, the forward and backward modes are clearly distinguishable in the frequency domain of the isotropic rotor, and the severity of the mode can be identified for the unisotropic rotor.