• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2009.10a
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• pp.321-321
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• 2009

This paper presents quasi-zero-stiffness (QZS) characteristic of a passive isolator using flexures under compression force. The passive isolator consists of a positive stiffness element (a vertical coil spring) and a negative stiffness element (flexures under compression force), and their proper combination of the positive and negative stiffness elements can produce both substantial static and zero dynamic stiffness, so called QZS. Firstly, a nonlinear dimensionless expression of a flexure under compression force is derived. A dynamic model of the passive isolator is developed and numerical simulations of its time and frequency response are performed. Then, undesirable nonlinear vibration is quantified using a period doubling bifurcation diagram and a Poincare's map of the isolator under forced excitation. Finally, experiments are performed to validate the QZS characteristic of the passive isolator.

• Structural Engineering and Mechanics
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• v.66 no.5
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• pp.621-629
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• 2018

By employing the nonlocal continuum field theory of Eringen and Von Karman nonlinear strains, this paper presents an analytical model for linear and nonlinear dynamics analysis of single-walled carbon nanotubes (SWNTs) conveying fluid with different boundary conditions. In the linear analysis the natural frequencies and critical flow velocities of SWNTs are computed. However, in the nonlinear analysis the effect of nonlocal parameter on nonlinear dynamics of cantilevered SWNTs conveying fluid is investigated by using bifurcation diagram, phase plane and Poincare map. Numerical results confirm existence of chaos as well as a period-doubling transition to chaos.

• The Pure and Applied Mathematics
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• v.16 no.2
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• pp.243-254
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• 2009

The main purpose of this paper is to use the methods of Lattice Dynamical System to establish a global model, which extends the Walrasian evolutionary cobweb model in an independent single local market to the global market evolution over an infinite chain of many local markets interacting each other through a diffusion of prices between them. For brevity of the model, we assume linear decreasing demands and quadratic supplies with naive predictors, and investigate the spatially homogeneous global price dynamics and show that the dynamics is topologically conjugate to that of well-known logistic map and hence undergoes a period-doubling bifurcation route to chaos as a parameter varies through a critical value.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.696-701
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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 존재 한다고 알려져 있다. 주공진 근처의 정상상태 응답곡선에서 최대한 5개의 안정한 응답이 존재하는 것으로 밝혀졌으며, 이들은 1개의 정상파와 4개의 진행파로 나타난다. 이 진행파 중 2개는 가진진동수가 변화함에 따라 Hope분기에 의해 안정성을 잃은 후 주기배가운동을 거쳐 흔돈운동에 이르게 된다. 초기조건에 의해 각각의 끌개(attractor)에 흡인되는 흡인영역의 경계를 주평면의 개념을 통하여 구하였으며, 가진진동수가 변화함에 따라 안정한 해가 혼돈운동에 이르는 과정에 대해 흡인영역의 경계가 변화되는 특성을 관찰하였으며, 흡인영역 경계에 대한 프랙털 차원(fractal dimension)을 계산하였다.

• Advances in nano research
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• v.10 no.4
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• pp.359-371
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• 2021

A tumor immune interaction is a main topic of interest in the last couple of decades because majority of human population suffered by tumor, formed by the abnormal growth of cells and is continuously interacted with the immune system. Because of its wide range of applications, many researchers have modeled this tumor immune interaction in the form of ordinary, delay and fractional order differential equations as the majority of biological models have a long range temporal memory. So in the present work, tumor immune interaction in fractional form provides an excellent tool for the description of memory and hereditary properties of inter and intra cells. So the interaction between effector-cells, tumor cells and interleukin-2 (IL-2) are modeled by using the definition of Caputo fractional order derivative that provides the system with long-time memory and gives extra degree of freedom. Moreover, in order to achieve more efficient computational results of fractional-order system, a discretization process is performed to obtain its discrete counterpart. Furthermore, existence and local stability of fixed points are investigated for discrete model. Moreover, it is proved that two types of bifurcations such as Neimark-Sacker and flip bifurcations are studied. Finally, numerical examples are presented to support our analytical results.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.34 no.9
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• pp.859-866
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• 2010

Nonlinear dynamics of pulsating instability-diffusional-thermal instability with Lewis numbers sufficiently higher than unity-in counterflow diffusion flames, is numerically investigated by imposing a Damkohler number perturbation. The flame evolution exhibits three types of nonlinear behaviors, namely, decaying pulsating behavior, diverging behavior (which leads to extinction), and stable limit-cycle behavior. The stable limit-cycle behavior is observed in counterflow diffusion flames, but not in diffusion flames with a stagnant mixing layer. The critical value of the perturbed Damkohler number, which indicates the region where the three different flame behaviors can be observed, is obtained. A stable simple limit cycle, in which two supercritical Hopf bifurcations exist, is found in a narrow range of Damkohler numbers. As the flame temperature is increased, the stable simple limit cycle disappears and an unstable limit cycle corresponding to subcritical Hopf bifurcation appears. The period-doubling bifurcation is found to occur in a certain range of Damkohler numbers and temperatures, which leads to extend the lower boundary of supercritical Hopf bifurcation.

• The Journal of Natural Sciences
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• v.6 no.1
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• pp.79-87
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• 1993

In the map of period-doubling bifurcation, stable fixed points bifurcate to $2^n$ fixed points, and in the chaotic region, the chaotic bands merge to 1/$2^n$ bands. In a typical map, the chaotic bands expand to a broad chaotic band during the merging process, so called crisis. In this paper, interior crises appearing during the merging process will be discussed by using our map and will be analyzed the characteristics of the phenomenon by obtaining the Lyapunov Exponents.

• Advances in aircraft and spacecraft science
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• v.2 no.2
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• pp.125-168
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• 2015

Dynamic aeroelastic behavior of structurally nonlinear Joined Wings is presented. Three configurations, two characterized by a different location of the joint and one presenting a direct connection between the two wings (SensorCraft-like layout) are investigated. The snap-divergence is studied from a dynamic perspective in order to assess the real response of the configuration. The investigations also focus on the flutter occurrence (critical state) and postcritical phenomena. Limit Cycle Oscillations (LCOs) are observed, possibly followed by a loss of periodicity of the solution as speed is further increased. In some cases, it is also possible to ascertain the presence of period doubling (flip-) bifurcations. Differences between flutter (Hopf's bifurcation) speed evaluated with linear and nonlinear analyses are discussed in depth in order to understand if a linear (and thus computationally less intense) representation provides an acceptable estimate of the instability properties. Both frequency- and time-domain approaches are compared. Moreover, aerodynamic solvers based on the potential flow are critically examined. In particular, it is assessed in what measure more sophisticated aerodynamic and interface models impact the aeroelastic predictions. When the use of the tools gives different results, a physical interpretation of the leading mechanism generating the mismatch is provided. In particular, for PrandtlPlane-like configurations the aeroelastic response is very sensitive to the wake's shape. As a consequence, it is suggested that a more sophisticate modeling of the wake positively impacts the reliability of aerodynamic and aeroelastic analysis. For SensorCraft-like configurations some LCOs are characterized by a non-synchronous motion of the inner and outer portion of the lower wing: the wing's tip exhibits a small oscillation during the descending or ascending phase, whereas the mid-span station describes a sinusoidal-like trajectory in the time-domain.