55 research outputs found

    Chaos in a Magnetic Pendulum Subjected to Tilted Excitation and Parametric Damping

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    The effect of tilted harmonic excitation and parametric damping on the chaotic dynamics in an asymmetric magnetic pendulum is investigated in this paper. The Melnikov method is used to derive a criterion for transition to nonperiodic motion in terms of the Gauss hypergeometric function. The regular and fractal shapes of the basin of attraction are used to validate the Melnikov predictions. In the absence of parametric damping, the results show that an increase of the tilt angle of the excitation causes the lower bound for chaotic domain to increase and produces a singularity at the vertical position of the excitation. It is also shown that the presence of parametric damping without a periodic fluctuation can enhance or suppress chaos while a parametric damping with a periodic fluctuation can increase the region of regular motions significantly

    Nonlinear characterization of a bistable energy harvester dynamical system

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    International audienceThis chapter explores the nonlinear dynamics of a piezo-magneto-elastic bistable energy device system regards the influence of external forcing parameters influence on system response. Time series, Poincaré maps, phase space trajectories, and bifurcation diagrams are employed in order to reveals system dynamics complexity and nonlinear effects, such as chaos incidence and hysteresis

    Bifurcation of Homoclinic Orbits in Autonomous Systems and in Chaotic Blue Sky Catastrophe

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    Frequency shift and hysteresis suppression in contact-mode AFM using contact stiffness modulation

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    In this paper the frequency response shift and hysteresis suppression of contact-mode atomic force microscopy is investigated using parametric modulation of the contact stiffness. Based on the Hertzian contact theory, a lumped single degree of freedom oscillator is considered for modeling the cantilever dynamics contact-mode atomic force microscopy. We use the technique of direct partition of motion and the method of multiple scales to obtain, respectively, the slow dynamic and the corresponding slow flow of the system. As results, this study shows that the amplitude of the contact stiffness modulation has a significant effect on the frequency response. Specifically, increasing the amplitude of the stiffness modulation suppresses hysteresis, decreases the peak amplitude and produces shifts towards higher and lower frequencies

    Frequency shift and hysteresis suppression in contact-mode AFM using contact stiffness modulation

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    In this paper the frequency response shift and hysteresis suppression of contact-mode atomic force microscopy is investigated using parametric modulation of the contact stiffness. Based on the Hertzian contact theory, a lumped single degree of freedom oscillator is considered for modeling the cantilever dynamics contact-mode atomic force microscopy. We use the technique of direct partition of motion and the method of multiple scales to obtain, respectively, the slow dynamic and the corresponding slow flow of the system. As results, this study shows that the amplitude of the contact stiffness modulation has a significant effect on the frequency response. Specifically, increasing the amplitude of the stiffness modulation suppresses hysteresis, decreases the peak amplitude and produces shifts towards higher and lower frequencies

    On the control of bistability in non-contact mode AFM using modulated time delay

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    We study the control of bistability in non-contact mode AFM using time delay with modulated feedback gain. We consider that the tip-sample interaction force is described by Lennard-Jones potential and the equation of motion is modeled by single degree of freedom system. Perturbation analysis is performed to obtain the modulation equations of the slow dynamic. The influence of the modulated time delay on the nonlinear characteristic of the frequency response is analyzed and the evolution of the bistability region in the modulated time delay parameter plan is examined. Results show that modulation of the feedback gain can be used to reduce the amplitude of the microcanteliver response and to suppress the bistability regime in large region of the modulated delay parameter space. The analytical predictions are compared to numerical simulations for validation

    Dynamic behaviour of rotary lip seal

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    We report on the dynamic behavior of a rotary lip seal by considering the interaction between lip, film and shaft roughness assumed to have a periodic form. The nonlinearities of stiffness and viscosity of the film are taken into account in a mass-spring-dumper model. Using the harmonic balance method, analytical prediction of the lip displacement is obtained, the frequency response is provided and the effect of the shaft undulation on the amplitude jumps of the lip displacement and on the film thickness fluctuations are discussed. The results have direct applications in reducing leakage that may occur between a smooth lip seal and a rough shaft
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