• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.569-582
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• 2010

The following "Periodic Jacobi Procrustes" problem is studied: find the Periodic Jacobi matrix X which minimizes the Frobenius (or Euclidean) norm of AX - B, with A and B as given rectangular matrices. The class of Procrustes problems has many application in the biological, physical and social sciences just as in the investigation of elastic structures. The different problems are obtained varying the structure of the matrices belonging to the feasible set. Higham has solved the orthogonal, the symmetric and the positive definite cases. Andersson and Elfving have studied the symmetric positive semidefinite case and the (symmetric) elementwise nonnegative case. In this contribution, we extend and develop these research, however, in a relatively simple way. Numerical difficulties are discussed and illustrated by examples.

• International Journal of Reliability and Applications
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• v.9 no.1
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• pp.113-122
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• 2008

In this paper, we consider a periodic preventive maintenance policy in which each preventive maintenance reduces the hazard rate of amount proportional to the failure intensity, which increases since the system started to operate. And the effect of preventive maintenance at each preventive maintenance epoch is different. The expected cost rate per unit time for the proposed model is obtained. We discuss the optimal number N of the periodic preventive maintenance and the optimal period x, which minimize the expected cost rate per unit time and obtain the optimal preventive maintenance schedule for given cost structures of the model. A numerical example is given for the purpose of illustrating our results when the failure time distribution is Weibull distribution.

• Journal of the Optical Society of Korea
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• v.12 no.3
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• pp.196-199
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• 2008

We have investigated spectral properties of the periodic arrays of aluminum rods and holes on papers using the terahertz time-domain spectroscopy. The size of a rod(hole) is $600{\mu}m{\times}100{\mu}m$ and the spacing is $300{\mu}m$. The samples were fabricated by a femtosecond laser micromachining system. The periodic arrays of aluminum rods exhibit high reflection around 0.25 THz when the polarization of the THz pulse is parallel to the long axis of the rod, whereas the periodic arrays of holes exhibit high transmission around 0.25 THz when the polarization of the THz pulse is perpendicular to the long axis of the hole.

• Journal of Korean Association for Spatial Structures
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• v.20 no.4
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• pp.149-158
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• 2020

The governing equation for a dome-type shallow spatial truss subjected to a transverse load is expressed in the form of the Duffing equation, and it can be derived by considering geometrical non-linearity. When this model under constant load exceeds the critical level, unstable behavior is appeared. This phenomenon changes sensitively as the number of free-nodes increases or depends on the imperfection of the system. When the load is a periodic function, more complex behavior and low critical levels can be expected. Thus, the dynamic unstable behavior and the change in the critical point of the 3-free-nodes space truss system were analyzed in this work. The 4-th order Runge-Kutta method was used in the system analysis, while the change in the frequency domain was analyzed through FFT. The sinusoidal wave and the beating wave were utilized as the periodic load function. This unstable situation was observed by the case when all nodes had same load vector as well as by the case that the load vector had slight difference. The results showed the critical buckling level of the periodic load was lower than that of the constant load. The value is greatly influenced by the period of the load, while a lower critical point was observed when it was closer to the natural frequency in the case of a linear system. The beating wave, which is attributed to the interference of the two frequencies, exhibits slightly more behavior than the sinusoidal wave. And the changing of critical level could be observed even with slight changes in the load vector.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.489-494
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• 2003

Vibration localization characteristics of open loop repeated structures with mistuning are investigated in this paper. Mistuning of a periodic structure often creates significant non-uniformity in vibration responses. As a result of the localization, critical fatigue problems often occur in repeated structures. Therefore, it is of great importance to predict the vibration response of the mistuned repeated structures accurately. In this paper, a simplified model for the open-loop repeated structure is introduced and dimensionless parameters which influence the localization characteristics are identified. The effects of the parameters on the localization characteristics are investigated through numerical study.

• Journal of Korean Association for Spatial Structures
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• v.4 no.2 s.12
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• pp.81-88
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• 2004

The dynamic instability of snapping phenomena has been studied by many researchers. Few papers deal with dynamic buckling under loads with periodic characteristics, and the behavior under periodic excitations is expected to be different from behavior under STEP excitations. We investigate the fundamental mechanisms of the dynamic instability when the sinusoidally shaped arch structures are subjected to sinusoidally distributed excitations with pin-ends. The mechanisms of dynamic indirect snapping of shallow arches are especially investigated under not only STEP function excitations but also under sinusoidal harmonic excitations, applied i the up-and-down direction. The dynamic nonlinear responses are obtained by the numerical integration of the geometrically nonlinear equation of motion. And using this analyze characteristics of the dynamic instability through the running response spectrum by FFT(Fast Fourier Transform).

• Journal of the Korea Academia-Industrial cooperation Society
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• v.11 no.7
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• pp.2541-2548
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• 2010

This paper describes the calculation for characteristic impedance of transmission line with periodic structures such as defected ground structure (DGS) and photonic bandgap (PBG). The previous method which uses the ${\lambda}$/4 transmission line model is reviewed and its disadvantage that the calculated characteristic impedance is strongly dependent on the frequency is discussed. The characteristic impedance of transmission lines with periodic structures are calculated using the ${\lambda}$/4 transmission line model and analytic method. The calculated characteristic impedance by the latter method is an almost constant value while that from the first method depends on the frequency strongly. In addition, the characteristic impedance of the transmission line with PBG is calculated and proposed, while it has been rarely studied ever. S-parameters are obtained from the measurement using the fabricated sample as well as simulation, and used for calculating the characteristic impedances and comparison. The characteristic impedances calculated from the measured S-parameters agree well with the simulated results. It is well described that the analytic method to calculate the characteristic impedance of transmission lines on uniform dielectric structures can be applied successfully to the transmission lines with periodic structures such as DGS and PBG.

• Smart Structures and Systems
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• v.23 no.6
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• pp.641-651
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• 2019

The stochastic stability control of the parameter-excited vibration of an inclined stay cable with multiple modes coupling under random and periodic combined support disturbances is studied by using the direct eigenvalue analysis approach based on the response moment stability, Floquet theorem, Fourier series and matrix eigenvalue analysis. The differential equation with time-varying parameters for the transverse vibration of the inclined cable with control under random and deterministic support disturbances is derived and converted into the randomly and deterministically parameter-excited multi-degree-of-freedom vibration equations. As the stochastic stability of the parameter-excited vibration is mainly determined by the characteristics of perturbation moment, the differential equation with only deterministic parameters for the perturbation second moment is derived based on the $It{\hat{o}}$ stochastic differential rule. The stochastically and deterministically parameter-excited vibration stability is then determined by the deterministic parameter-varying response moment stability. Based on the Floquet theorem, expanding the periodic parameters of the perturbation moment equation and the periodic component of the characteristic perturbation moment expression into the Fourier series yields the eigenvalue equation which determines the perturbation moment behavior. Thus the stochastic stability of the parameter-excited cable vibration under the random and periodic combined support disturbances is determined directly by the matrix eigenvalues. The direct eigenvalue analysis approach is applicable to the stochastic stability of the control cable with multiple modes coupling under various periodic and/or random support disturbances. Numerical results illustrate that the multiple cable modes need to be considered for the stochastic stability of the parameter-excited cable vibration under the random and periodic support disturbances, and the increase of the control damping rather than control stiffness can greatly enhance the stochastic stability of the parameter-excited cable vibration including the frequency width increase of the periodic disturbance and the critical value increase of the random disturbance amplitude.

• Journal of electromagnetic engineering and science
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• v.5 no.1
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• pp.43-47
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• 2005

Microwave or optical photonic band-gap(PBG) structures are conventionally realized by cascading distributive elements in a periodic pattern. However, the frequency bandwidth obtained through such plainly periodic arrangement is typically narrow, corporate with a relatively high rejection side-lobe band. To alleviate such problems, a design involving a chirping and tapering technique is hence introduced and employed. The design has been applied in both a planar stratified dielectric medium as well as a strip-line transmission line structure, and results are validated when compared with the corresponding conventional PBG structure.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.1089-1093
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• 2003

The moving least square (MLS) basis is implemented for the real-space band-structure calculation of 2D photonic crystals. The value-periodic MLS shape function is thus used in order to represent the periodicity of crystal lattice. Any periodic function can properly be reproduced using this shape function. Matrix eigenequations, derived from the macroscopic Maxwell equations, are then solved to obtain photonic band structures. Through numerical examples of several lattice structures, the MLS-based method is proved to be a promising scheme for predicting band gaps of photonic crystals.