5,688 research outputs found

    The Response Spectrum Map, a Frequency Domain Equivalent to the Bifurcation Diagram

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    The Response Spectrum Map (RSM) is introduced as a frequency domain equivalent to the Bifurcation Diagram. The RSM is a map of the energy distribution of a system in the frequency domain, where subharmonics, superharmonics and chaos generation can be revealed. The RSM is used in this paper to qualitatively analyse and detect various dynamical states exhibited by a nonlinear system

    Subharmonic oscillation modeling and MISO Volterra series

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    Subharmonic generation is a complex nonlinear phenomenon which can arise from nonlinear oscillations, bifurcation and chaos. It is well known that single-input–single-output Volterra series cannot currently be applied to model systems which exhibit subharmonics. A new modeling alternative is introduced in this paper which overcomes these restrictions by using local multiple input single output Volterra models. The generalized frequency-response functions can then be applied to interpret systems with subharmonics in the frequency domain

    Analysis of nonlinear oscillators in the frequency domain using volterra series Part II : identifying and modelling jump Phenomenon

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    In this the second part of the paper, a common and severe nonlinear phenomenon called jump, a behaviour associated with the Duffing oscillator and the multi-valued properties of the response solution, is investigated. The new frequency domain criterion of establishing the upper limits of the nonlinear oscillators, developed in Part I of this paper, is applied to predict the onset point of the jump, and the Volterra time and frequency domain analysis of this phenomenon are carried out based on graphical and numerical techniques

    Analysis of a duffing oscillator that exhibits hysteresis with varying excitation frequency and amplitude

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    Hysteresis, or jump phenomenon, are a common and severe nonlinear behaviour associated with the Duffing oscillator and the multi-valued properties of the response solution. Jump phenomenon can be induced by either varying the amplitude or the frequency of excitation. In this paper a new time and frequency domain analysis is applied to this class of system based on the response curve and the response spectrum map

    A unified model for the dynamics of driven ribbon with strain and magnetic order parameters

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    We develop a unified model to explain the dynamics of driven one dimensional ribbon for materials with strain and magnetic order parameters. We show that the model equations in their most general form explain several results on driven magnetostrictive metallic glass ribbons such as the period doubling route to chaos as a function of a dc magnetic field in the presence of a sinusoidal field, the quasiperiodic route to chaos as a function of the sinusoidal field for a fixed dc field, and induced and suppressed chaos in the presence of an additional low amplitude near resonant sinusoidal field. We also investigate the influence of a low amplitude near resonant field on the period doubling route. The model equations also exhibit symmetry restoring crisis with an exponent close to unity. The model can be adopted to explain certain results on magnetoelastic beam and martensitic ribbon under sinusoidal driving conditions. In the latter case, we find interesting dynamics of a periodic one orbit switching between two equivalent wells as a function of an ac magnetic field that eventually makes a direct transition to chaos under resonant driving condition. The model is also applicable to magnetomartensites and materials with two order parameters.Comment: 11 pages, 18 figure

    Analysis of nonlinear oscillators using volterra series in the frequency domain Part I : convergence limits

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    The Volterra series representation is a direct generalisation of the linear convolution integral and has been widely applied in the analysis and design of nonlinear systems, both in the time and the frequency domain. The Volterra series is associated with the so-called weakly nonlinear systems, but even within the framework of weak nonlinearity there is a convergence limit for the existence of a valid Volterra series representation for a given nonlinear differential equation. Barrett(1965) proposed a time domain criterion to prove that the Volterra series converges with a given region for a class of nonlinear systems with cubic stiffness nonlinearity. In this paper this time-domain criterion is extended to the frequency domain to accommodate the analysis of nonlinear oscillators subject to harmonic excitation

    Piecewise Volterra modelling of the Duffing oscillator in the frequency domain

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    When analysing the nonlinear Duffing oscillator, the weak nonlinearity is basically dependent on the amplitude range of the input excitation. The nonlinear differential equation models of such nonlinear oscillators, which can be transformed into the frequency domain, can generally only provide Volterra modelling and analysis in the frequency-domain over a fraction of the entire framework of weak nonlinearity. This paper discusses the problem of using a new non-parametric routine to extend the capability of Volterra analysis, in the frequency domain, to weakly nonlinear Duffing systems at a wider range of excitation amplitude range which the current underlying nonlinear differential equation models fail to address

    Bifurcations and synchronization using an integrated programmable chaotic circuit

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    This paper presents a CMOS chip which can act as an autonomous stand-alone unit to generate different real-time chaotic behaviors by changing a few external bias currents. In particular, by changing one of these bias currents, the chip provides different examples of a period-doubling route to chaos. We present experimental orbits and attractors, time waveforms and power spectra measured from the chip. By using two chip units, experiments on synchronization can be carried out as well in real-time. Measurements are presented for the following synchronization schemes: linear coupling, drive-response and inverse system. Experimental statistical characterizations associated to these schemes are also presented. We also outline the possible use of the chip for chaotic encryption of audio signals. Finally, for completeness, the paper includes also a brief description of the chip design procedure and its internal circuitry

    A new frequency domain representation and analysis for subharmonic oscillation

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    For a weakly nonlinear oscillator, the frequency domain Volterra kernels, often called the generalised frequency response functions, can provide accurate analysis of the response in terms of amplitudes and frequencies, in a transparent algebraic way. However a Volterra series representation based analysis will become void for nonlinear oscillators that exhibit subharmonics, and the problem of finding a solution in this situation has been mainly treated by the traditional analytical approximation methods. In this paper a novel method is developed, by extending the frequency domain Volterra representation to the subharmonic situation, to allow the advantages and the benefits associated with the traditional generalised frequency response functions to be applied to severely nonlinear systems that exhibit subharmonic behaviour
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