• 한국소음진동공학회논문집
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• 제14권12호
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• pp.1314-1321
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• 2004

The non-linear responses of a slender rectangular cantilever beam subjected to lateral harmonic base-excitation are investigated by the 2-channel FFT analyzer. Both linear and nonlinear behaviors of the cantilever beam are compared with each other. Bending mode, torsional mode, and transverse mode are coupled in such a way that the energy transfer between them are observed. Especially, superharmonic, subharmonic, and chaotic motions which result from the unstable inertia terms in the transverse mode are analyzed by the FFT analyzer The aim is to give the explanations of the route to chaos, i.e., harmonic motion \longrightarrow superharmonic motion \longrightarrow subharmonic motion \longrightarrow chaos.

• 한국소음진동공학회논문집
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• 제12권12호
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• pp.921-928
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• 2002

Main sources of the nitration of a gear-pair system are backlash and transmission error, the difference between required and actual rotation during gear meshing. This paper presents the nonlinear dynamic characteristics of gear motions due to the existence of backlash and periodic variation of meshing stiffness, which is assumed as a one-term harmonic component. Gear motions are classified as three types with the consideration of backlash. Each response is calculated using the harmonic balance method and confirmed by numerical integration. The responses with the increase of the rotating speed show abrupt changes in its magnitude for the variation of the preload, exciting force, and damping coefficient. The result also shows that there is a chaotic motion with some specific design parameters and operating conditions In gear diving system. Consequently the design of gear driving system with low nitration and noise requires the study on the effects of nonlinear dynamic characteristics due to stiffness variation and backlash.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 춘계학술대회논문집
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• pp.430-435
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• 2005

조화가진력이 작용하는 고정경계를 가진 완전원판의 비선형 진동에 대한 응답특성을 연구하였다. 원판의 비대칭모드의 고유진동수 근처에 가진주파수가 작용하는 주공진에서의 응답은 정상파(standing wave)뿐만 아니라 진행파(traveling wave)가 존재한다고 알려져 있다. 주공진 근처의 정상상태 응답곡선에서 최대한 5개의 안정한 응답이 존재하는 것으로 밝혀졌으며, 이들은 1개의 정상파와 4개의 진행파로 나타난다. 이 진행파중 2개는 Hope분기에 의해 안정성을 잃은 후 주기배가운동을 거쳐 혼돈운동에 이르게 된다. Lyaponov 지수를 사용하여 혼돈운동을 정량적으로 평가하였으며, 주평면의 개념을 이용하여 이 혼돈운동의 흡인영역이 Fractal임을 확인하였다.

• 한국경영과학회:학술대회논문집
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• 대한산업공학회/한국경영과학회 1994년도 춘계공동학술대회논문집; 창원대학교; 08월 09일 Apr. 1994
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• pp.437-450
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• 1994

The problem of testing for a change in the parameter of a stochastic process is particularly important in simulation studies. In studies of the steady state characteristics of a simulation model, it is important to identify initialization bias and to evaluate efforts to control this problem. A simulation output have the characteristics of chaotic behavior because of sensitive dependence on initial conditions. For that reason, we will apply Lyapunov exponent for diagnosis of chaotic motion to simulation output analysis. This paper proposes two methods for diagnosis of steady state in simulation output. In order to evaluate the performance and effectiveness of these methods using chaos theory, M/M/I(.inf.) queueing model is used for testing point estimator, average bias.

• 한국소음진동공학회논문집
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• 제20권9호
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• pp.849-855
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• 2010

Damping may change the response characteristics of nonlinear oscillations due to the parametric excitation of a thin cantilever beam. When the natural frequencies of the first bending and torsional modes are of the same order of magnitude, we can observe the one-to-one combination resonance in the perturbation analysis depending on the characteristic parameters. The nonlinear behavior about the combination resonance reveals a chaotic motion depending on the natural frequencies and damping ratio. We can analyze the chaotic dynamics by using the eigenvalue analysis of the perturbed components. In this paper, we derived the equations for autonomous system and solved them to obtain the characteristic equation. The stability analysis was carried out by examining the eigenvalues. Numerical integration gave the physical behavior of each mode for given parameters.

• 한국소음진동공학회논문집
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• 제14권7호
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• pp.561-568
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• 2004

The nonlinear dynamic characteristic of a straight tube conveying fluid with constraints and an attached mass on the tube is examined in this study An experimental apparatus with an elastomer tube conveying water which has an attached mass and constraints is made and comparisons are made between the theoretical results from the non-linear equation of motion of piping system and the experimental results. The comparisons show that the tube is destabilized as the magnitude of the attached mass increases, and stabilized as the position of the attached mass closes to the fixed end. In case of a small end-mass, the system shows complicated and different types of solutions. For a constant end-mass. the system undergoes a series of bifurcations after the first Hopf bifurcation, as the flow velocity increases. which causes chaotic motions of the tube eventually.

• 한국전산유체공학회지
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• 제15권1호
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• pp.9-16
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• 2010

The characteristics of flow and heat transfer in a bubbling fluidized bed are investigated by means of computational fluid dynamics (CFD). To simulate two-phase flow for the gas and solid flows, Eulerian-Eulerian approach is applied. Attention is paid for a heat transfer from the wall to fluidized bed by bubbling motion of the flow. From the result, it is confirmed that heat transfer is promoted by chaotic bubbling motion of the flow by enhancement of mixing among solid particles. In particular, the vortical flow motion around gas bubble plays an important role for the mixing and consequent heat transfer. Discussion is made for the time and space averaged Nusselt number which shows peculiar characteristics corresponding to different flow regimes.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1995년도 추계학술대회논문집; 한국종합전시장, 24 Nov. 1995
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• pp.185-190
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• 1995

In recent years, many researcher have been interested in the stability of a thin beam. Among them, Pai and Nayfeh[1] had investigated the nonplanar motion of the cantilever beam under lateral base excitation and chaotic motion, but this study is associated with internal resonance, i.e. one to one resonance. Also Cusumano[2] had made an experiment on a thin beam, called Elastica, under bending loads. In this experiment, he had shown that there exists out-of-plane motion, involving the bending and the torsional mode. Pak et al.[3] verified the validity of Cusumano's experimental works theoretically and defined the existence of Non-Local Mode(NLM), which is came out due to the instability of torsional mode and the corresponding aspect of motions by using the Normal Modes. Lee[4] studied on a thin beam under bending loads and investigated the routes to chaos by using forcing amplitude as a control parameter. In this paper, we are interested in the motion of a thin beam under torsional loads. Here the form of force based on the natural forcing function is used. Consequently, it is found that small torsional loads result in instability and in case that the forcing amplitude is increasing gradually, the motion appears in the form of dynamic double potential well, finally leads to complex motion. This phenomenon is investigated through the poincare map and time response. We also check that Harmonic Balance Method(H.B.M.) is a suitable tool to calculate the bifurcated modes.

• 호남수학학술지
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• 제39권3호
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• pp.401-416
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• 2017

Fractional kinetic equations are investigated in order to describe the various phenomena governed by anomalous reaction in dynamical systems with chaotic motion. Many authors have provided solutions of various families of fractional kinetic equations involving special functions. Here, in this paper, we aim at presenting solutions of certain general families of fractional kinetic equations using Prabhakar-type operators. The idea of present paper is motivated by Tomovski et al. [21].

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2004년도 추계학술대회논문집
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• pp.140-144
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• 2004

Global bifurcations and chaos in modal interactions of an imperfect circular plate with one-to-one internal resonance are investigated. The case of primary resonance, in which an excitation frequency is near natural frequencies, is considered. The damping force is not included in the analysis. The Melnikov's method for heteroclinic orbits of the autonomous system was used to obtain the criteria for chaotic motion.