• Wind and Structures
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• v.36 no.3
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• pp.215-220
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• 2023

We study the progressive full-scale wind tunnel tests on a high solidity vertical axis wind turbine (VAWT) for various tip speeds and pitch angles to understand the VAWT shaft system's dynamics using 0-1 Test for chaos. We identify that while varying rotor speed (tip speed) of the turbine, the system's dynamics change from periodic to chaotic through quasiperiodic and strange non-chaotic (SNA) states. The present study is the first experimental evidence for the existence of these states in the VAWT shaft system to the best of our knowledge. Using the asymptotic growth value Kc in 0-1 test, when the turbine operates at the low tip speeds and high pitch angles for low incoming wind speeds, the system behaves periodic (Kc ≈ 0). However, when the incoming wind speed increases further the system's dynamics shift from periodic to chaotic vibrations through quasi-periodic and SNA. This phenomenon is due to the dynamic stalling of blades which induces chaotic vibration in the VAWT shaft system. Further, the singular continuous spectrum method validates the presence of SNA and differentiates the SNA from chaotic vibrations.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1995.04a
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• pp.121-128
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• 1995

The results are summarized as what follows: 1) The modeling of thin beams, which is a continuous system, into a two DOF system yields satisfactory results for the chaotic vibrations. 2) The concept of "natural forcing function" derived from the eigenfunction of the bifurcation mode is very useful for the natural responses of the system. 3) Among the perturbation techniques, HBM is a good estimate for the response when the geometry of motion is known. 4) It is known that there exist periodic solutions of coupled mode response for somewhat large damping and forcing amplitude, as well as weak damping and forcing. 5) The route-to-chaos related with lateral instability in thin beams is composed of period-doubling and quasiperiodic process and finally follows discontinuous period-doubling process. 6) The chaotic vibrations are verified by using Poincare maps, FFT's, time responses, trajectories in the configuration space, and the very powerful technique Lyapunov characteristics exponents.exponents.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.2
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• pp.495-508
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• 1995

The self-excited vibrations of airfoil is related to the classical flutter problems, and it has been studied as a system with linear stiffness and small damping. However, since the actual aircraft wing and the many mechanical elements of airfoil type have various design variables and parameters, some of these could have strong nonlinearities, and the nonlinearities could be unexpectedly strong as the parameters vary. This abrupt chaotic behavior undergoes ordered routes, and the behaviors after these routes are uncontrollable and unexpectable since it is extremely sensitive to initial conditions. In order to study the chaotic behavior of the system, three parameters are considered, i.e., free-stream velocity, elastic distance and zero-lift angle. If the chaotic parameter region can be identified from the mathematically modeled nonlinear differential equation system, the designs which avoid chaotic regions could be suggested. In this study, by using recently developed dynamically system methods, and chaotic regions on the parameter plane will be found and the safe design variables will be suggested.

• Journal of KSNVE
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• v.10 no.5
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• pp.849-858
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• 2000

In this paper the chaotic out-of-plane vibrations of the uniformly curved pipe with pulsating flow are theoretically investigated. The derived equations of motion contain the effects of nonlinear curvature and torsional coupling. The corresponding nonlinear ordinary differential equation is a type of nonhomogenous Hill's equation . this is transformed into the averaged equation by averaging theorem. Bifurcation curves of chaotic motion are obtained by Melnikov's method and plotted in several cases of frequency ratios. The theoretically obtained results are demonstrated by numerical simulation. And strange attractors are shown.

• Structural Engineering and Mechanics
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• v.51 no.5
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• pp.743-754
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• 2014

Investigations of regular and chaotic vibrations of the autoparametric pendulum absorber suspended on a nonlinear coil spring and a magnetorheological damper are presented in the paper. Application of a semi-active damper allows controlling the dangerous motion without stooping of system and additionally gives new possibilities for designers. The investigations are curried out close to the main parametric resonance. Obtained numerical and experimental results show that the semi-active suspension may reduce dangerous motion and it also allows to maintain the pendulum at a given attractor or to jump to another one. Moreover, the results show that, for some parameters, MR damping may transit to chaotic motions.

• Smart Structures and Systems
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• v.11 no.1
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• pp.87-102
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• 2013

Vibration-based damage detection methods are popular for structural health monitoring. However, they can only detect fairly large damages. Usually impact pulse, ambient vibrations and sine-wave forces are applied as the excitations. In this paper, we propose the method to use the chaotic excitation to vibrate structures. The attractors built from the output responses are used for the minor damage detection. After the damage is detected, it is further quantified using the Kalman Filter. Simulations are conducted. A 5-story building is subjected to chaotic excitation. The structural responses and related attractors are analyzed. The results show that the attractor distances increase monotonously with the increase of the damage degree. Therefore, damages, including minor damages, can be effectively detected using the proposed approach. With the Kalman Filter, damage which has the stiffness decrease of about 5% or lower can be quantified. The proposed approach will be helpful for detecting and evaluating minor damages at the early stage.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.12
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• pp.1852-1865
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• 2017

The vibration of the structures with restrained motion has long been observed in various engineering fields. When the motion of vibrating structure is restrained due to the adjacent objects, the frequencies and the mode shapes of the structure change and its vibration characteristics becomes unpredictable, in general. Although the importance of the study on this type of vibration model increases in many engineering areas, most studies conducted so far are limited to the theoretical study on dynamic responses of the structure with stops, including some experimental works. Specially, the study on the nonlinear phenomena due to the impact between the structure and the stops have been mainly performed theoretically. In the paper, both numerical analyses and experiments are conducted to study the chaotic vibration characteristics of the nonlinear motion and the dynamic response of a cantilevered beam which has restrained motion at the free end by the stops. Results are presented for various magnetic forces and gaps between the beam and stops. The conclusions are as follows : Firstly, Numerical simulation results have a good agreement with experimental ones. Secondly, the effect of higher modes of beams are increased with increasing magnitude of exciting force, and displacement and velocity curves become more complicated shapes. Thirdly, nonlinear characteristics tend to appear greatly with increasing magnitude of exciting force, and fractal dimension is increased.

• Journal of Advanced Marine Engineering and Technology
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• v.16 no.5
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• pp.67-76
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• 1992

This paper describes the vibration characteristic of second-order nonlinear systems subjected to parametric excitation. Emphasis is put on the examination of the hydrodynamic nonlinear damping effect on limiting the response amplitudes of parametric vibration. Since the parametric vibration is described by the Mathieu equation, the Mathieu stability chart is examined in this paper. In addition, the steady-state solutions of the nonlinear Mathieu equation in the first instability region are obtained by using a perturbation technique and are compared with those by a numerical integration method. It is shown that the response amplitudes of parametric vibration are limited even in unstable conditions by hydrodynamic nonlinear damping force. The largest reponse amplitude of parametric vibration occurs in the first instability region of Mathieu stability chart. The parametric excitation induces the response of a dynamic system to be subharmonic, superharmonic or chaotic according to their dynamic conditions.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1995.10a
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• pp.191-196
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• 1995

지지부에 비틀림 하중을 받는 Elstica는 비틀림 운동을 하며, 그 가진 주파수가 굽힘모드 근처일 때는 해당하는 굽힘 모드의 운동까지도 동시에 존재하게 된다. 이때 가진력의 크기가 작을때는 주기적인 운동이 된다. 가진력의 크기가 증가함에 따라 굽힘 운동은 굽힘 1차 모드와 연성된 유사주기운동이 발생하며, 이떤 범위 이상이 되면 굽힘 운동과 비틀림 운동이 결합된 진폭이 매우 크고 불규칙적인 비평면 운동(out of plane motion)이 발생하게 되며 이 때의 운동은 혼돈운동이다. Elastica가 굽힘 3차 고유진동수 근방의 주파수로 비틀림 하중을 받을 때의 정확한 이론적 해석을 위해서는 굽힘 3차모드 까지는 반영할 수 있는 식이 모델링 되어야 할 것으로 보인다. 이것은 복잡한 비평면운동을 할 때 굽힘 3차 모드까지 관찰된다는 사실에 근거한다.

• Journal of Ocean Engineering and Technology
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• v.7 no.1
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• pp.73-80
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• 1993

본 연구에서는 장주형 해양구조물의 횡방향 진동에 대한 파라메트릭 가진 효과를 고찰하였다. 먼저, 장주형 해양구조물의 횡방향 운동에 대한 4계 편미방지배방정식을 비선형 Mathieu 방정식으로 유도하였다. 비선형 mathieu 방정식의 해를 구하여 장주형 해양구조물의 동적 반응 특성을 해석하였다. 유체 비선형 감쇠력은 불안정 조건하에 있는 파라메트릭 진동의 반응크기를 제한 하는데 중요한 역활을 한다. 파라메트릭 진동의 경우 가장 큰 반응크기는 Mathieu 안정차트의 첫번째 불안정 구간에서 일어난다. 반면에, 파라메트릭 진동과 강제진동의 결합 진동인 경우, 가장 큰 반응 크기는 두번째 불안정 구간에서 발생된다. 파라메트릭 가진으로 인한 장주형 해양구조물의 횡방향 운동은 동적조건에 따라 subharmonic, superharmonic 또는 chaotic 운동이 되기도 한다.