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Register a new userMechanical filtering in forced-oscillation of two coupled pendulums
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Added by
M. Ebrahim Fouladvand
Publication date
2010
fields
Physics
and research's language is
English
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Forced oscillation of a system composed of two pendulums coupled by a spring in the presence of damping is investigated. In the steady state and within the small angle approximation we solve the system equations of motion and obtain the amplitudes and phases of in terms of the frequency of the sinusoidal driving force. The resonance frequencies are obtained and the amplitude ratio is discussed in details. Contrary to a single oscillator, in this two-degree of freedom system four resonant frequencies, which are close to mode frequencies, appear. Within the pass-band interval the system is shown to exhibit a rich and complicated behaviour. It is shown that damping crucially affects the system properties. Under certain circumstances, the amplitude of the oscillator which is directly connected to the driving force becomes smaller than the one far from it. Particularly we show the existence of a driving frequency at which the connected oscillators amplitude goes zero.
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We consider the rotational dynamics in an ensemble of globally coupled identical pendulums. This model is essentially a generalization of the standard Kuramoto model, which takes into account the inertia and the intrinsic nonlinearity of the community elements. There exists the wide variety of in-phase and out-of-phase regimes. Many of these states appear due to broken symmetry. In the case of small dissipation our theoretical analysis allows one to find the boundaries of the instability domain of in-phase rotational mode for ensembles with arbitrary number of pendulums, describe all arising out-of-phase rotation modes and study in detail their stability. For the system of three elements parameter sets corresponding to the unstable in-phase rotations we find a number of out-of-phase regimes and investigate their stability and bifurcations both analytically and numerically. As a result, we obtain a sufficiently detailed picture of the symmetry breaking and existence of various regular and chaotic states.
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This paper used multi-scale method and KBM method to get approximate solution of coupled Van der Pol oscillators, based on which, researchers investigated the impact several parameters have on the prerequisite of synchronization and the time it takes to synchronize quantitatively. In addition, this paper has a brief introduction of the usage of Kuramoto Model in plural metronomes synchronization and the derivation of Van der Pol oscillator from the discrete model.
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