Journal ArticleDOI
Energy Pumping in Nonlinear Mechanical Oscillators: Part II—Resonance Capture
TLDR
In this paper, the authors study energy pumping in an impulsively excited, two-degrees-of-freedom damped system with essential (nonlinearizable) nonlinearities by means of two analytical techniques.Abstract:
We study energy pumping in an impulsively excited, two-degrees-of-freedom damped system with essential (nonlinearizable) nonlinearities by means of two analytical techniques. First, we transform the equations of motion using the action-angle variables of the underlying Hamiltonian system and bring them into the form where two-frequency averaging can be applied. We then show that energy pumping is due to resonance capture in the 1:1 resonance manifold of the system, and perform a perturbation analysis in an O (√e) neighborhood of this manifold in order to study the attracting region responsible for the resonance capture. The second method is based on the assumption of 1:1 internal resonance in the fast dynamics of the system, and utilizes complexification and averaging to develop analytical approximations to the nonlinear transient responses of the system in the energy pumping regime. The results compare favorably to numerical simulations. The practical implications of the energy pumping phenomenon are discussed.read more
Citations
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Past, present and future of nonlinear system identification in structural dynamics
TL;DR: In this article, a review of the past and recent developments in system identification of nonlinear dynamical structures is presented, highlighting their assets and limitations and identifying future directions in this research area.
Journal ArticleDOI
Energy pumping in nonlinear mechanical oscillators : Part I : Dynamics of the underlying Hamiltonian systems
TL;DR: In this paper, the authors presented numerical evidence of energy pumping in coupled nonlinear mechanical oscillators, i.e., of one-way (irreversible) channeling of externally imparted energy from the linear to the nonlinear part of the system, provided that the energy is above a critical level.
Journal ArticleDOI
Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques
TL;DR: In this paper, a nonlinear normal mode (NNM) computation is shown to be possible with limited implementation effort, which paves the way to a practical method for determining the NNMs of nonlinear mechanical systems.
Journal ArticleDOI
Inducing Passive Nonlinear Energy Sinks in Vibrating Systems
TL;DR: In this paper, the authors study the inducement of passive nonlinear sinks in linear vibrating systems and derive a set of modulation equations that is directly amenable to physical interpretation.
Journal ArticleDOI
Energy Harvesting From Vibrations With a Nonlinear Oscillator
TL;DR: In this paper, a nonlinear electromagnetic energy harvesting device with a broadly resonant response was presented, which is generated by a particular arrangement of magnets in conjunction with an iron-cored stator.
References
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Journal ArticleDOI
Energy pumping in nonlinear mechanical oscillators : Part I : Dynamics of the underlying Hamiltonian systems
TL;DR: In this paper, the authors presented numerical evidence of energy pumping in coupled nonlinear mechanical oscillators, i.e., of one-way (irreversible) channeling of externally imparted energy from the linear to the nonlinear part of the system, provided that the energy is above a critical level.
Book
Introduction to Dynamics
Ian C. Percival,Derek Richards +1 more
TL;DR: In this article, first-order autonomous systems and second-order Hamiltonian systems of one degree of freedom are studied. But they do not consider the non-linear transformations of the plane.
Journal ArticleDOI
Passage through a separatrix in a resonance problem with a slowly-varying parameter
Book ChapterDOI
The dynamics of resonant capture
TL;DR: Resonant capture describes the behavior of a weakly coupled multi-degree-of-freedom (MDF) system when two or more of its uncoupled frequencies become locked in resonance.