• Structural Engineering and Mechanics
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• v.9 no.4
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• pp.397-416
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• 2000

The present study deals with the nonlinear dynamics and stability of autonomous dissipative either imperfect potential (limit point) systems or perfect (bifurcational) non-potential ones. Through a fully nonlinear dynamic analysis, performed on two simple 2-DOF models corresponding to the classes of systems mentioned above, and with the aid of basic definitions of the theory of nonlinear dynamical systems, new important phenomena are revealed. For the first class of systems a third possibility of postbuckling dynamic response is offered, associated with a point attractor on the prebuckling primary path, while for the second one the new findings are chaos-like (most likely chaotic) motions, consecutive regions of point and periodic attractors, series of global bifurcations and point attractor response of always existing complementary equilibrium configurations, regardless of the value of the nonconservativeness parameter.

• Structural Engineering and Mechanics
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• v.28 no.1
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• pp.107-127
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• 2008

Wind turbine blades are increasing in magnitude without a proportional increase of stiffness for which reason geometrical and inertial nonlinearities become increasingly important. Often these effects are analysed using a nonlinear truncated expansion in undamped fixed base mode shapes of a blade, modelling geometrical and inertial nonlinear couplings in the fundamental flap and edge direction. The purpose of this article is to examine the applicability of such a reduced-degree-of-freedom model in predicting the nonlinear response and stability of a blade by comparison to a full model based on a nonlinear co-rotating FE formulation. By use of the reduced-degree-of-freedom model it is shown that under strong resonance excitation of the fundamental flap or edge modes, significant energy is transferred to higher modes due to parametric or nonlinear coupling terms, which influence the response and stability conditions. It is demonstrated that the response predicted by such models in some cases becomes instable or chaotic. However, as a consequence of the energy flow the stability is increased and the tendency of chaotic vibrations is reduced as the number of modes are increased. The FE model representing the case of infinitely many included modes, is shown to predict stable and ordered response for all considered parameters. Further, the analysis shows that the reduced-degree-of-freedom model of relatively low order overestimates the response near resonance peaks, which is a consequence of the small number of included modes. The qualitative erratic response and stability prediction of the reduced order models take place at frequencies slightly above normal operation. However, for normal operation of the wind turbine without resonance excitation 4 modes in the reduced-degree-of-freedom model perform acceptable.

• Journal of applied mathematics & informatics
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• v.8 no.2
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• pp.613-625
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• 2001

In this paper, we investigate a simplified model of a particle suspended elastically from two towers by two nonlinear elastic springs, with a restoring force similar to Hooke’s law under extension and with no resistance to compression. Numerical results are presented, showing the solutions can be either of the same period oscillation the forcing term, can be a subharmonic response of multiple period, or can be noisy periodic which is apparently chaotic. Multiplicity of periodic solutions for certain physical parameters are demonstrated.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.19 no.7
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• pp.16-23
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• 2018

Chaos is one of the most significant topics in nonlinear science, and has been intensively studied since the Lorenz system was introduced. One characteristic of a chaotic system is that the signals produced by it do not synchronize with any other system. It therefore seems impossible for two chaotic systems to synchronize with each other, but if the two systems exchange information in just the right way, they can synchronize. This paper addresses the problem of synchronization in a modified Lorenz chaotic system based on active control, sliding mode control, and the Lyapunov stability theory. The considered synchronization scheme consists of identical drive and response generalized systems coupled with linear state error variables. For this, a brief overview of the modified Lorenz chaotic system is given. Then, control rules are derived for chaos synchronization via active control and slide mode control theory, with a strategy for solving the chattering problem. The asymptotic stability of the overall feedback system is established using the Lyapunov stability theory. A set of computer simulation works is presented graphically to confirm the validity of the proposed method.

• Structural Engineering and Mechanics
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• v.61 no.3
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• pp.347-357
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• 2017

The applications of active control is being more popular nowadays. Several control algorithms have been developed to determine optimum control force. In this paper, a Chaotic Particle Swarm Optimization (CPSO) technique, based on Logistic map, is used to compute the optimum control force of active tendon system. A chaotic exploration is used to search the solution space for optimum control force. The response control of Multi-Degree of Freedom (MDOF) shear buildings, equipped with active tendons, is introduced as an optimization problem, based on Instantaneous Optimal Active Control algorithm. Three MDOFs are simulated in this paper. Two examples out of three, which have been previously controlled using Lattice type Probabilistic Neural Network (LPNN) and Block Pulse Functions (BPFs), are taken from prior works in order to compare the efficiency of the current method. In the present study, a maximum allowable value of control force is added to the original problem. Later, a twenty-story shear building, as the third and more realistic example, is considered and controlled. Besides, the required Central Processing Unit (CPU) time of CPSO control algorithm is investigated. Although the CPU time of LPNN and BPFs methods of prior works is not available, the results show that a full state measurement is necessary, especially when there are more than three control devices. The results show that CPSO algorithm has a good performance, especially in the presence of the cut-off limit of tendon force; therefore, can widely be used in the field of optimum active control of actual buildings.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 1999.05a
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• pp.313-318
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• 1999

A number of recent paper have investigated the feasibility of synchronizing chaotic system. In this paper we proposed the chaotic synchronization of the canonical Chua's circuit with RLCG transmission line by drive-response system. We expected that to be available to apply this secure communication with RLCG transmission line.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.05a
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• pp.578-582
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• 2000

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 the separation plate, including some experimental works. In the paper, both numerical analyses and experiments are conducted to study the chaotic vibration characteristics and the dynamic response of a fixed-free beam which has restrained motion at the free end by the separation plates. Results are presented for various magnetic forces and gaps between stops.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.20 no.9
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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.

• Journal of Electrical Engineering and Technology
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• v.1 no.4
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• pp.546-549
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• 2006

In this paper the neuron operation based on Brillouin-active fiber in optical fiber is described. The inherent optical feedback by the backscattered stokes wave in optical fiber leads to instabilities in the form of optical chaos. Controlling of chaos induced transient instability in Brillouin-active fiber is implemented with Kerr nonlinearity having a non-instantaneous response in network systems. The controlling chaotic instabilities can lead to multistable periodic states; create optical logic 'on' or high level '1' or 'off', or low level '0'. It is theoretically possible to apply the multi-stability regimes as an optical memory device for encoding and decoding series and complex data transmission in optical systems.

• Fisheries and Aquatic Sciences
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• v.8 no.3
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• pp.177-181
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• 2005

Fishing selectivity is determined by the level of voluntary escaping behavior in accordance with decision-making based on the relationship between fish size and mesh size. This study examined movement during the swimming behavior of black porgy in a trawl's towing cod-end and analyzed the movement components such as swimming speed, angular velocity of turning, and distance to the net over time. Most of the observed fish exhibited an optomotor response, maintaining position and swimming speed without changing direction. Others exhibited erratic or 'panic' behavior with sudden changes in swimming speed and direction. The latter behavior involved very irregular and aperiodic variations in swimming speed and angular velocity, termed 'chaotic behavior.' Thus, the results of this study can be applied to a chaotic behavior model as a time series of swimming movements in the towing cod-end for the fishing selectivity.