Journal ArticleDOI
Non-linear dynamics of a system of coupled oscillators with essential stiffness non-linearities
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TLDR
In this article, the resonant dynamics of a two-degree-of-freedom system composed of a linear oscillator weakly coupled to a strongly non-linear one, with an essential (non-linearizable) cubic stiffness nonlinearity, were studied.Abstract:
We study the resonant dynamics of a two-degree-of-freedom system composed of a linear oscillator weakly coupled to a strongly non-linear one, with an essential (non-linearizable) cubic stiffness non-linearity. For the undamped system this leads to a series of internal resonances, depending on the level of (conserved) total energy of oscillation. We study in detail the 1:1 internal resonance, and show that the undamped system possesses stable and unstable synchronous periodic motions (non-linear normal modes—NNMs), as well as, asynchronous periodic motions (elliptic orbits—EOs). Furthermore, we show that when damping is introduced certain NNMs produce resonance capture phenomena, where a trajectory of the damped dynamics gets ‘captured’ in the neighborhood of a damped NNM before ‘escaping’ and becoming an oscillation with exponentially decaying amplitude. In turn, these resonance captures may lead to passive non-linear energy pumping phenomena from the linear to the non-linear oscillator. Thus, sustained resonance capture appears to provide a dynamical mechanism for passively transferring energy from one part of the system to another, in a one-way, irreversible fashion. Numerical integrations confirm the analytical predictions.read more
Citations
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Journal ArticleDOI
Designs, analysis, and applications of nonlinear energy sinks
Hu Ding,Li-Qun Chen +1 more
TL;DR: A comprehensive review of state-of-the-art researches on NESs, highlighting possible complex dynamics resulting in a NES coupled to a structure and suggesting further promising directions, such as NESs for multidirectional vibration reduction, NESs with nonlinearities beyond the cubic, and potential deterioration caused by a NES.
Journal ArticleDOI
Vibration control of a nonlinear beam with a nonlinear energy sink
TL;DR: In this paper, a nonlinear beam with simply supported ends is attached to a non-linear energy sink and the parameters of the NES are optimized by both sensitivity analysis and particle swarm optimization (PSO) method.
Journal ArticleDOI
Passive non-linear targeted energy transfer and its applications to vibration absorption: A review
Young S. Lee,Alexander F. Vakakis,Lawrence A. Bergman,D. M. McFarland,Gaëtan Kerschen,Francesco Nucera,Stylianos Tsakirtzis,Panayotis Panagopoulos +7 more
TL;DR: The concept of TET may be regarded as contrary to current common engineering practice, which generally views nonlinearities in engineering systems as either unwanted or, at most, small perturbations of linear behaviour as discussed by the authors.
Journal ArticleDOI
Experimental study of targeted energy transfer from an acoustic system to a nonlinear membrane absorber
TL;DR: In this paper, an experimental set-up has been developed using the air inside a tube as the acoustic linear system, a thin circular visco-elastic membrane as an essentially cubic oscillator and the air outside a box as a weak coupling between those two elements.
Journal ArticleDOI
Nonlinear energy sink with inerter
TL;DR: In this paper, a novel archetype of nonlinear energy sink (NES) enhanced by an inerter is proposed for vibration reduction of vibrating systems, which suppressed vibration more effectively than a convenient NES measured by both energy dissipation and amplitude frequency responses.
References
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Journal ArticleDOI
A universal instability of many-dimensional oscillator systems
TL;DR: In this article, the authors demonstrate the mechanism for a universal instability, the Arnold diffusion, which occurs in the oscillating systems having more than two degrees of freedom, which results in an irregular, or stochastic, motion of the system as if the latter were influenced by a random perturbation even though, in fact, the motion is governed by purely dynamical equations.
Book
Handbook of Elliptic Integrals for Engineers and Physicists
Paul F. Byrd,Morris D. Friedman +1 more
Journal ArticleDOI
Energy Pumping in Nonlinear Mechanical Oscillators: Part II—Resonance Capture
TL;DR: 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.
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
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.