• Journal of applied mathematics & informatics
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• 제28권3_4호
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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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• 제9권1호
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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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• 제12권3호
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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.

• 한국공간구조학회논문집
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• 제20권4호
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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.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2003년도 춘계학술대회논문집
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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.

• 한국공간구조학회논문집
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• 제4권2호
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• pp.81-88
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• 2004

동적 불안정 좌굴현상에 관한 연구는 다소 발표되고 있으나, 주기성을 가진 하중하에서의 동적 좌굴을 다룬 연구는 그리 많지 않은 편이다. 주기성을 가진 하중하에서의 거동은 STEP 하중하에서의 거동과는 매우 다르리라 예상된다. 본 논문에서는 동적 불안정의 기본 메커니즘을 파악하기 위하여 양단 핀으로 고정된 정현형 아치가 정현형 조화하중을 받았을 때의 얕은 아치를 대상으로 한다. 얕은 아치의 동적 간접 좌굴 메커니즘을 파악하기 위하여 STEP 하중뿐만 아니라 정현형 조화하중일 때를 대상으로 한다. 동적 비선형 응답 특성을 알기 위하여 수치적분에 의해 기하학적 비선형 운동방정식을 유도한다. 여기서 얻어진 비선형 변위 응답으로 FFT(Fast Fourier Transform)에 의한 연속 응답 스펙트럼을 구해 동적 불안정 특성에 관해서 분석한다.

• 한국산학기술학회논문지
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• 제11권7호
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• pp.2541-2548
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• 2010

본 논문에서는 결함접지구조와 포토닉 밴드갭과 같은 주기구조가 삽입된 전송선로의 특성 임피던스 계산에 대하여 기술한다. ${\lambda}$/4 전송선로 이론을 이용한 계산하는 종래 방법을 고찰하고, 이 방법에 의한 계산 결과가 주파수 의존성이 커서 신뢰도가 낮다는 문제점을 제시한다. 균일한 유전체 기판에 구현된 전송선로의 특성 임피던스 계산에 적용되는 해석적인 방법을 주기구조가 결합된 전송선로에서도 적용될 수 있음을 보인다. ${\lambda}$/4 전송선로 방법과 대신 해석적 방법으로 특성 임피던스를 구하고, 후자의 결과가 주파수에 관계없이 비교적 고정된 값을 가짐을 제시한다. 또한 종래에 특성 임피던스 계산 사례가 없었던 PBG 구조를 지닌 전송선로에 대해서도 특성 임피던스를 계산한다. 시뮬레이션뿐만 아니라 직접 제작하여 측정한 S-파라미터로부터 각각 특성 임피던스를 계산하고 서로 비교하여 상당히 유사함을 보인다. 그리고 이를 통하여 해석적 방법에 의한 특성 임피던스의 결정 방법이 DGS와 PBG와 같은 주기구조가 결합된 전송선로의 특성 임피던스 계산에 잘 적용될 수 있음을 보인다.

• Smart Structures and Systems
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• 제23권6호
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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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• 제5권1호
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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.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2003년도 춘계학술대회
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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.