• Proceedings of the Computational Structural Engineering Institute Conference
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• 2010.04a
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• pp.449-453
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• 2010

본 논문에서는 점성 및 감쇠가 있는 단자유도 구조물의 등가감쇠비를 효율적으로 구하는 방법을 제시하였다. 건물에 설치된 마찰감쇠기는 외력의 크기에 따라 정지와 운동의 상태를 반복하여 외부 입력에너지를 소산시키기 때문에 외력과 응답관계가 비선형이다. 마찰감쇠기가 설치된 단자유도 건물은 마찰감쇠기외에 점성감쇠가 동시에 존재하므로 해석적인 정해를 구하기가 어렵다. 등가감쇠비를 산정하기 위해서 첫째, 점성과 마찰감쇠가 있는 단자유도계 건물의 자유진동 정해를 통하여 변위응답과 가속도 응답특성을 분석하였다. 둘째, 자유진동의 경우 응답이 멈출 때까지 소산에너지식을 이용하여 등가점성감쇠비를 구하였다. 셋째, 조화가진 일 때는 수치해석을 통하여 마찰력비 $F_r$에 따른 응답 특성을 알아보았다. 넷째, 조화가진의 경우 에너지 균형식을 바탕으로 등가점성감쇠비를 유도하였다. 등가점성감쇠비는 변위응답비의 영향을 받으므로 응답을 알아야만 구할 수 있다. 건물 응답의 진동수 특성은 협소영역(narrow band)이므로 고유진동수에 의해 지배된다고 가정하여 등가점성감쇠비를 구하였다. 마지막으로, 유도한 자유진동과 조화가진의 등 가점성감쇠비를 이용한 등가선형운동방정식의 해를 비선형 수치해석 한 결과와 비교하여 검증하였다.

• Journal of the Earthquake Engineering Society of Korea
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• v.12 no.2
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• pp.1-8
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• 2008

Friction pendulum system is developed to prevent the damage of transformer, which is the most important among the electric power facilities, due to the earthquake and its seismic capacity is verified through the shaking table test. The applicability of friction pendulum system is confirmed as test results of compressive capacity test and friction test. Especially, as a result of shaking table test with a large scale transformer model, friction pendulum system gives to the reduction of maximum response acceleration by 30% at anchorage of transformer and 59% at the top of porcelain bushing comparing with the existing anchorage type. In addition to the reduction of maximum response acceleration, natural frequency of transformer is shifted to long period due to the friction pendulum system. In case that friction pendulum system is applied to the transformer, the damage of transformer can be prevented effectively under the earthquake.

• Journal of the Korean Society of Propulsion Engineers
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• v.14 no.5
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• pp.15-23
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• 2010

To reduce the vibration levels, additional dissipation elements such as dry friction dampers are sometimes integrated into bladed disk assembly. In this study, forced response analysis systems for a tuned bladed disk with friction dampers were developed and verified. For the efficient nonlinear vibration analysis, multi-harmonic balanced method and cyclic boundary condition were used. Also, mode shapes obtained using fictitious mass method were used to describe the motion of the structures with the concentrated structural nonlinearity, friction damper. The relative convergence of fictitious mass and traditional unconstrained modes were compared.

• The Journal of the Acoustical Society of Korea
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• v.15 no.2
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• pp.33-39
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• 1996

A theoretical study of the forced vibration response of a cantilevered beam with non-linear dry friction damping is analyzed by various slip displacements and force levels for the position coordinates of spring-mass-damper and external exciting force. A component mode analysis is carried out based on the constraint conditions and Lagrange multipliers to treat physical systems with non-linear damping. The analysis has shown that the basic phenomena observed for a simply supported beam with a dry friction damper attached are also observed for cantilevered beam.

• Journal of KSNVE
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• v.16 no.1 s.79
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• pp.40-47
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• 2006

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2009.10a
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• pp.850-854
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• 2009

Approximate analysis for a building installed with a friction damper is revisited to get insight of its dynamic behavior. Energy balance equation is used to have a closed analytical form solution of dynamic magnification factor (DMF) for the building with combined viscous and friction damping. It is found out that DMF is dependent on friction force ratio and resonance frequency. Linear transfer function from input external force to output building displacement is obtained by simplifying DMF equation. Root mean square of building displacement is derived under earthquake-like random excitation. Finally, design of friction damper is proposed by processing target control ratio, damping ratio factor, and friction force in sequence.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.6
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• pp.491-498
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• 2011

The structural vibration due to earthquake or outside impact causes serious problem for building safety. A dynamic model of a friction damper which can be constructed and installed easily is needed to reduce the vibration of the building. In this paper, the experimental equation of a circular friction damper is derived and designed for reduction of a earthquake vibration of a building. The developed experimental equation is defined to simply design the capacity on design of the circular friction damper based on the results of the performance test. Finally this experimental equation can be used for the design of a circular friction damper.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.23 no.2
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• pp.199-208
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• 2010

A friction damper installed at a building shows nonlinear behavior since its stick and slip states are occurred repeatedly depending on the amplitude of external loadings to dissipate input energy. Friction damping is existed for the building with a friction damper. In additionally viscous one is inherently included. Therefore, the building installed in such combined damping is quite involved to find the analytical solution. In this study, first, displacement and acceleration characteristics are identified based on the exact solution for a single-degree-freedom building with a friction damper having both friction and viscous damping. Second, in free vibration, the equivalent viscous damping ratio is obtained by the energy dissipation. Third, numerical analysis is carried out to find response configuration with various friction force ratios. Fourth, corresponding equivalent viscous damping ratio is derived with the finding that the response reaches into steady-state for both friction and viscous damped structure. It is deduced using balance of input external energy and output dissipation energy for steady-state response. Finally, the equivalent viscous damping ratios of free or harmonic vibration are verified through nonlinear analysis.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1990.10a
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• pp.157-162
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• 1990

기계의 정밀도 향상을 위하여는 기계에 대한 보다 정확한 해석을 요구한다. 그러나 실제 기계 시스템은 마찰, Backlash, Saturation등과 같은 비서형 특 성을 가지고 있어 시스템의 해석 및 제어가 어렵게 된다. 특히, 축, 링크, 기 어, 풀리, 베어링등의 기계요소에서는 마찰로 인해 정밀도가 크게 덜어지고 있어, 마찰에 의한 동특성 및 제어는 많은 연구자들에 의해 관심의 대상이 되어 왔다. 마찰력을 고려한 기계시스템의 운동은 정지상태 근처에서 마찰력 의 변화가 심한 비선형 동특성을 보이고 있어 그 해석에 어려움을 겪고 있 다. 실제 마찰이 저속에서 고급 비선형임에도 불구하고 가장 널리 사용되는 형태의 모델로서 쿨통 마찰을 고려한 운동방정식 조차 비선형성으로 인하여 해석에 어려움이 따르고 있다. 마찰은 오랜동안 연구되어 오면서 Fig.1, Fig2 와 같이 등가선형점성 감쇠, 쿨통마찰, 정적마찰로 모델화되거나 이들의 조 합으로 나타내었다[1-5]. 마찰력은 시간영역에서도 연구되어 Walrath[7]는 Fig.3-a의 속도가 역전되는 지점에서 마찰토오크가 .+-.Tf를 공유하는 문제 를 고려하기 위해, Fig.3-b와 같이 동적마찰모델을 사용하였다. 최근의 연구 로서 Armstrong[7]은 마찰의 위치의존성을 고려한 정확한 마찰모델을 설정 하여 개루프제어에 적용, 좋은 제어특성을 확인하였고, Canudas[8]는 저속영 역에서 overcompensation시 limit cycle과 gain의 관계를 해석하였다.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.33 no.1
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• pp.9-16
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• 2020

The objective of this study is to propose closed-form solutions to the free vibration response of single-degree-of-freedom (SDOF) systems, as part of fundamental research on dynamic systems with Coulomb friction. The motion of a dynamic system with Coulomb friction is described by a nonlinear differential equation, and, due to the variation in the sign of friction force term with the direction of motion, it is difficult to obtain the closed-form solution. To solve this problem, the nonlinear differential equation is directly computed by numerical integration, or an approximated solution is indirectly obtained using a linear differential equation wherein the damping effect due to Coulomb friction is replaced by an equivalent viscous damping term. However, these conventional methods do not provide a closed-form solution from a mathematical point of view. In this regard, closed-form solutions to the free vibration response of SDOF systems with Coulomb friction are derived herein by considering that the sign of the friction force term is reversed in each half-cycle of motion and by expanding it to the entire time history using the power series function. In addition, for a given initial condition, both the number of free vibration half-cycles and the response at the instant when free vibration motion stops are predicted under the condition that the motion of free vibration is stopped when the amplitude of the friction force is higher than that of the restoring force due to stiffness.