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정규모드 동역학을 활용한 비선형 진동

  • 박철희
    • Journal of KSNVE
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    • v.7 no.1
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    • pp.6-12
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    • 1997
  • 물리계에서 일어나는 동적 현상들은 선형해석 만으로 설명하기에는 불충분한 점이 많이 있다. 이는 기계구조물과 같은 실제 계의 진동이 기하학적 비선형성, 강성 의 비선형성 또는 경계조건의 비선형성 등의 영향으로 비선형적인 거동을 하기 때문 이다. 비선형 진동을 하는 기계 계는 우리 주변에서 쉽게 찾아 볼 수 있는데, 그 예로써 진자운동을 포함하여 동흡진기, 회전체계, 공작기계의 절삭운동, 건마찰 (dry friction) 관련 기계장치, 치차 및 기차의 바퀴와 레일 간의 접촉에서 볼수 있는 구분적 선형(piecewise linear) 진동계, 충격 진동계 등을 들 수 있다. 비선형 진동 연구는 limit cycle, 준주기운동(quasiperiodic motion), 점프현상(jump phenomena) 등의 인식에서 시작되어, 과거에는 설명이 안되어 회피되 왔던 랜덤(random) 형태의 비주기운동에 대한 연구로 까지 발전하고 있다. 비선형 진동을 다루는데 있어서 정규모드(normal mode)를 이용하는 방법이 있다. 일반적으로 선형계는 선형 정규모드 (linear normal mode)가 존재하는 것과 같이 비선형계에도 이와 유사한 정규모드가 존재한다는 사실이 연구 보고된 바 있다. 비선형계에 존재하는 정규모드는 계의 매개 변수(system parameters)에 따라 그 안정성이 바뀔 수 있으며, 만일 안정한 정규모드 가 어떤 매개변수에서 그 안정성이 바뀐다면 선형이론으로는 설명될 수 없는 새로운 운동이 일어나고 이러한 운동을 분기모드(bifurcation mode)라고 한다. 안정한 정규 모드 및 분기모드를 포함하여 비선형계를 다류는 것을 "정규모드 동역학(normal mode dynamics)"이라고 한다. 정규모드 동역학은 앞에서 언급된 비선형 현상들의 원인규명, 예측, 안정성해석 및 강제진동 해석을 가능하게 한다. 또한 최근에 활발히 연구되고 있는 혼돈운동(chaotic motion)의 해석도 가능하다. 이 글에서는 비선형 진동해석을 위한 정규모드 동역학에 대한 연구동향 및 기본 이론을 살펴 보았고, 그 적용 예를 통하여 실험결과와 비교 고찰 함으로써 정규모드 동역학의 적용성을 서술하여 보았다. 선형이론으로 이해하기 어려운 현상들에 대하여는 비선형의 관점에서 새롭게 접근하 려는 노력이 필요하며 비선형 이론에 대한 연구가 지속적으로 진행되어야 한다. 진행되어야 한다.

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A Frequency Domain Analysis of Corneal Deformation by Air Puff (Air puff에 의한 각막 변형의 주파수 영역 분석)

  • Hwang, Ho-Sik;Lee, Byeong Ha;Lee, Chang Su
    • Journal of IKEEE
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    • v.18 no.2
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    • pp.240-247
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    • 2014
  • Intraocular pressure is measured after a cornea air puff by observing biomechanical properties such as thickness or displacement of the cornea. In this paper, we deal with a frequency domain analysis of corneal deformation in the air puff tonometry that is used to diagnose glaucoma or lasik. We distinguish the patient from the normal by measuring the oscillation frequency in the neighborhood of the central cornea section. A binary image was obtained from the video images, and cornea vertical oscillation profile was extracted from the difference between the vertical displacement data and the curve fitting. In terms of Fourier transform, a vibration frequency of 479.2Hz for the patient was obtained as well as more higher 702.8Hz for the normal due to stiffness. Hilbert-Huang transform's empirical mode decomposition generally describes local, nonlinear, and nonstationary data. After the data were decomposed into intrinsic mode functions, a spectrum and power were analysed. Finally, we confirm that the patient has 6 times more higher power ratio for the specific intrinsic mode function between the patient and the normal.

Development of Monitoring System for the LNG plant fractionation process based on Multi-mode Principal Component Analysis (다중모드 주성분분석에 기반한 천연가스 액화플랜트의 성분 분리공정 감시 시스템 개발)

  • Pyun, Hahyung;Lee, Chul-Jin;Lee, Won Bo
    • Journal of the Korean Institute of Gas
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    • v.23 no.4
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    • pp.19-27
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    • 2019
  • The consumption of liquefied natural gas (LNG) has increased annually due to the strengthening of international environmental regulations. In order to produce stable and efficient LNG, it is essential to divide the global (overall) operating condition and construct a quick and accurate monitoring system for each operation condition. In this study, multi-mode monitoring system is proposed to the LNG plant fractionation process. First, global normal operation data is divided to local (subdivide) normal operation data using global principal component analysis (PCA) and k-means clustering method. And then, the data to be analyzed were matched with the local normal mode. Finally, it is determined the state of process abnormality through the local PCA. The proposed method is applied to 45 fault case and it proved to be more than 5~10% efficient compared to the global PCA and univariate monitoring.

Interfacial Crack Propagation Under Various Mode-Mixes

  • Park, Byung-Sun;Chai, Young-Suck
    • Journal of Mechanical Science and Technology
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    • v.16 no.1
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    • pp.39-45
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    • 2002
  • Initiation and propagation of interfacial crack along bimaterial interface are considered in this study. A biaxial loading device for a single specimen is used for obtaining a wide range of mode-mixities. The specimen is an edge-cracked bimaterial strip of glass and epoxy; the biaxial loading device, being capable of controlling displacements in two perpendicular directions, is developed. A series of interfacial crack initiation and Propagation experiments are conducted using the biaxial loading device for various mixed modes. Normal crack opening displacement (NCOD) is measured near crack front by a crack opening interferometry and used for extracting fracture parameters. From mixed mode interfacial crack initiation experiments, large increase in toughness with shear components is observed. The behavior of interfacial crack propagation analyzed as a function of mode-mix shows that initial crack propagation is delayed with increase of mode-mixity, and its velocity is increased with positive mode-mixity but decreased with negative case. However, it is found that crack propagation is less accelerated with positive mode-mixity than the negative mode-mixity, which may be caused by contact and/or effects of friction between far field and near-tip Held along the interfacial crack.

Stress intensity factor in cracked plate reinforced with a plate under mixed mode loading (혼합형 하중항에 있는 판재로 보강된 균열판의 응력세기계수)

  • Lee, Kang-Yong;Kim, Ok-Whan
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.22 no.3
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    • pp.569-578
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    • 1998
  • The mode I and II stress intensity factors have been calculated theoretically for the cracked plate reinforced with a plate by symmetric spot welding under remote mixed mode loading. This is the extension of authors' previous work for the reinforced cracked plate under remote normal stress. Regardless of loading types, the reinforcement effect gets better as one joining spot is closer to the crack tip and the others are closer to the crack surface, and optimum number of the joining spots can be existed. For the present model, the remote loading parallel to crack surface produces the mode I stress intensity factor.

Design of MEMS Resonator Array for Minimization of Mode Localization Factor Subject to Random Fabrication Error (랜덤 제조 오차를 고려한 모드 편재계수를 최소화하는 반복 배열 마이크로 공진기의 최적설계)

  • Kim, Wook-Tae;Lee, Chong-Won
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 2005.05a
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    • pp.840-845
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    • 2005
  • This paper presents a robust optimal design method for a periodic structure type of MEMS resonator that is vulnerable to mode localization. The robust configuration of such a MEMS resonator to fabrication error is implemented by changing the regularity of periodic structure. For the mathematical convenience, the MEMS resonator is first modeled as a multi pendulum system. The index representing the measure of mode variation is then introduced using the perturbation method and the concept of modal assurance criterion. Finally, the optimal intentional mistuning, minimizing the expectation of the irregularity measure for each substructure, is determined for the normal distributed fabrication error and its robustness in the design of MEMS resonator to the fabrication error is demonstrated with numerical examples.

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Design of MEMS Resonator Array for Minimization of Mode Localization Factor Subject to Random Fabrication Error (랜덤 제조 오차를 고려한 모드 편재계수를 최소화하는 반복 배열 마이크로 공진기의 최적설계)

  • Kim, Wook-Tae;Lee, Chong-Won
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.15 no.8 s.101
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    • pp.931-938
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    • 2005
  • This paper presents a robust optimal design method for a periodic structure type of MEMS resonator that is vulnerable to mode localization. The robust configuration of such a MEMS resonator to fabrication error is implemented by changing the regularity of periodic structure For the mathematical convenience, the MEMS resonator is first modeled as a multi-pendulum system. The index representing the measure of mode variation is then introduced using the perturbation method and the concept of modal assurance criterion. Finally, the optimal intentional mistuning, minimizing the expectation of the irregularity measure for each substructure, is determined for the normal distributed fabrication error and its robustness in the design of MEMS resonator to the fabrication error is demonstrated with numerical examples.

A Study on the Effect of External Electromagnetic force in MIG Welding (MIG 용접 시 외부 전자기력이 미치는 영향에 관한 연구)

  • Kim Jae Seong;Kim Yong;Ryu Deok Hui;Lee Bo Yeong
    • Proceedings of the KWS Conference
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    • v.43
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    • pp.171-173
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    • 2004
  • Electromagnetic force is one of the most important factor that effect on metal transfer mode, short-circuit rate, spatter generation rate and mechanical properties of weld metal etc. Also, shielding gas and welding current have influence on metal transfer mode in GMAW. In this paper, different ways for external electromagnetic forces are applied by attaching cylindrically rounded conducting wire solenoid on touch tip holding. With the applied electromagnetic field, the arc transfer mode changes from normal mode to rotating mode and spatter generation decreased in electromagnetic fields(N-pole). In MIG welding, the influences of electromagnetic force on the spatter generation showed different tendency as in the $CO_2$ welding. It is possible reasons were discussed.

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The Improvements of Vehicle Vibration Characteristics Using Modal Contribution (모우드 기여도 분석을 이용한 차량의 진동특성 개선)

  • 안지훈;지상현;고병식
    • Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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    • 1998.04a
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    • pp.51-56
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    • 1998
  • This paper presents modal contribution method to reduce vehicle vibration. Normal mode analysis is performed to obtain modal vector matrix. The proposed method uses this modal vector matrix to evaluate forced response of an active mode to the applied engine forces and the rotating force due to wheel unbalance mass. Comparing the responses, of the specific active mode with one another, it can be easily done to determine most contributed mode in the interesting frequency band. Then we can find dominant bushes by the strain energy distribution of the mode. Vibration response is decrease with modification of those bushes.

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An Study for reuse of the waste lead battery using Pulse Charger with mode conversion type (모드 전환형 펄스충전기론 이용한 폐납축전지 재활용에 관한 연구)

  • Shin, Choon-Shik;An, Young-Joo;Kim, Sang-Dong;Shin, Young-Mi;Kim, Jong-Dal;Kim, Dong-Wan
    • Proceedings of the KIEE Conference
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    • 2007.11c
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    • pp.101-107
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    • 2007
  • In this paper, the pulse charger with mode consersion type is proposed that can reuse the waste lead battery. The pulse charger uses the switch mode of the forward convert method. The pulse charger maintain the constant voltage in state removing the lead battery and when it connected the pulse charger, it is converted the charge mode of the constant current immediately. It continues the rapid charge until the full state of the lead battery. After that the pulse charger is converted to the charge mode of constant voltage automatically, and then it continues the normal charge. The experiment results show that the effectiveness of pulse charger such as the good performance and the prolonged durability in lead battery according to capacity states.

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