Isolated Resonance Captures and Resonance Capture Cascades Leading to Single- or Multi-Mode Passive Energy Pumping in Damped Coupled Oscillators

2004 ◽  
Vol 126 (2) ◽  
pp. 235-244 ◽  
Author(s):  
Alexander F. Vakakis ◽  
D. Michael McFarland ◽  
Lawrence Bergman ◽  
Leonid I. Manevitch ◽  
Oleg Gendelman
Keyword(s):  
Numerical Simulations ◽  
Coupled Oscillators ◽  
Normal Modes ◽  
Nonlinear Energy Sink ◽  
Nonlinear Normal Modes ◽  
Resonance Capture ◽  
New Paradigm ◽  
Energy Pumping ◽  
Multi Mode ◽  
Nonlinear Energy

We examine passive energy pumping in a system of damped coupled oscillators. This is a one-way, passive and irreversible energy flow from a linear main system to a nonlinear attachment that acts, in essence, as a nonlinear energy sink (NES). Energy pumping is caused by 1:1 resonance captures on resonant manifolds of the damped systems. We show that the NES is capable of absorbing significant portions of the energies generated by transient, broadband external excitations. By performing a series of numerical simulations we confirm that the energy dependence of the nonlinear normal modes (NNMs) of the underlying undamped, unforced system determines, in essence, the resonance capture and energy pumping dynamics in the corresponding damped system. We present numerical simulations of single- and multi-mode energy pumping, that involve isolated resonance captures or resonance capture cascades, respectively. In addition, we discuss methodologies for enhancing the nonlinear energy pumping phenomenon by properly selecting the system parameters. The described technique of passively localizing and locally eliminating externally induced energy provides a new paradigm for vibration and shock isolation of mechanical oscillators.

Nonlinear Energy Sink With Uncertain Parameters

2006 ◽  
Vol 1 (3) ◽  
pp. 187-195 ◽  
Author(s):  
E. Gourdon ◽  
C. H. Lamarque
Keyword(s):  
Normal Modes ◽  
Nonlinear Energy Sink ◽  
Nonlinear Normal Modes ◽  
Supplementary Information ◽  
Uncertain Parameters ◽  
Energy Pumping ◽  
Energy Sink ◽  
Nonlinear Normal ◽  
Polynomial Chaos Expansions ◽  
Nonlinear Energy

The effects of a nonlinear energy sink during the instationary regime are analyzed by introducing uncertain parameters to verify the robustness of the transient spatial energy transfer when parameters are not well known. It was shown that it is possible to passively absorb energy from a linear nonconservative system (damped) structure to a nonlinear attachment weakly coupled to the linear one. This rapid and irreversible transfer of energy, named energy pumping, is studied by taking into account uncertainties on parameters, especially damping (since damping plays a great role and there is a lack of knowledge about it). In essence, the nonlinear subsystem acts as a passive nonlinear energy sink for impulsively applied external vibrational disturbances. The aim is to be able to apply energy pumping in practice where the nonlinear attachment realization will never perfectly reflect the design. Since strong nonlinearities are involved, polynomial chaos expansions are used to obtain information about random displacements. Not only are numerical investigations done, but nonlinear normal modes and the role of damping are also analytically studied, which confirms the numerical studies and shows the supplementary information obtained compared to a parametrical study.

Passive Vibration Control Through Nonlinear Energy Pumping

2003 ◽  
Author(s):  
Alexander F. Vakakis ◽  
D. Michael McFarland ◽  
Lawrence Bergman ◽  
Leonid Manevitch ◽  
Oleg Gendelman
Keyword(s):  
Vibration Control ◽  
Nonlinear Energy Sink ◽  
New Paradigm ◽  
Energy Pumping ◽  
Nonlinear Energy Pumping ◽  
Mechanical Oscillators ◽  
Damped Systems ◽  
Mode Energy ◽  
Multi Mode ◽  
Nonlinear Energy

We examine vibration control through passive energy pumping in a system of damped coupled oscillators. This is a one-way, passive and irreversible energy flow from a linear main system to a nonlinear attachment that acts, in essence, as a nonlinear energy sink (NES). Energy pumping is caused by 1:1 resonance captures on resonant manifolds of the damped systems. We show that the NES is capable of absorbing significant portions of the energies generated by transient, broadband external excitations. We present numerical simulations of single- and multi-mode energy pumping, that involve isolated resonance captures or resonance capture cascades, respectively. In addition, we discuss methodologies for enhancing the nonlinear energy pumping phenomenon by properly selecting the system parameters. The described technique of passively localizing and locally eliminating externally induced energy provides a new paradigm for vibration and shock isolation of mechanical oscillators.

Nonlinear Energy Pumping With Strongly Nonlinear Coupling: Identification of Resonance Captures in Numerical and Experimental Results

2005 ◽  
Author(s):  
E. Gourdon ◽  
S. Coutel ◽  
C. H. Lamarque ◽  
S. Pernot
Keyword(s):  
Normal Modes ◽  
Coupled System ◽  
Nonlinear Energy Sink ◽  
Nonlinear Normal Modes ◽  
Small Mass ◽  
Abrupt Decrease ◽  
Building Model ◽  
Energy Pumping ◽  
Nonlinear Normal ◽  
Nonlinear Energy

The present work aims to study the effect of a nonlinear energy sink (NES) with relatively small mass on the dynamics of a coupled system under impulsion with free oscillations. The process of energy transfer is governed by structure of damped nonlinear normal modes of the system. In particular the energy pumping occurs if the nonlinear normal mode is quickly broken down with rather abrupt decrease of both amplitudes, i.e. a bifurcation (brutal change of frequency) is associated with the breakdown of the resonant regime of vibrations. The theoretical effects are experimentally verified with a mechanical experiment which confirms the above results by using a small building model. To identify those frequency migrations, a new wavelet-based methodology, namely quasi-continuous wavelet method, is used.

Nonlinear Normal Modes of a Continuous Cantilever Beam with Nonlinear Energy Sink Absorber

2013 ◽  
Vol 325-326 ◽  
pp. 214-217
Author(s):  
Yong Chen ◽  
Yi Xu
Keyword(s):  
Cantilever Beam ◽  
Vibration Suppression ◽  
Normal Modes ◽  
Nonlinear Energy Sink ◽  
Nonlinear Normal Modes ◽  
Harmonic Excitation ◽  
Energy Sink ◽  
Nonlinear Normal ◽  
Nonlinear Energy ◽  
Good Agreement

Using nonlinear energy sink absorber (NESA) is a good countermeasure for vibration suppression in wide board frequency region. The nonlinear normal modes (NNMs) are helpful in dynamics analysis for a NESA-attached system. Being a primary structure, a cantilever beam whose modal functions contain hyperbolic functions is surveyed, in case of being attached with NESA and subjected to a harmonic excitation. With the help of Galerkins method and Raushers method, the NNMs are obtained analytically. The comparison of analytical and numerical results indicates a good agreement, which confirms the existence of the nonlinear normal modes.

scholarly journals Frequency Energy Plots of Dynamical Systems Attached to Piecewise Nonlinear Energy Sink

2021 ◽  
Author(s):  
Mohammed Ameen Ameen Al Shudeifat ◽  
Adnan Salem Saeed
Keyword(s):  
Normal Modes ◽  
Linear Structure ◽  
Nonlinear Energy Sink ◽  
Nonlinear Normal Modes ◽  
Dynamical Behaviour ◽  
Subharmonic Resonance ◽  
Numerical Continuation ◽  
Continuation Methods ◽  
Energy Sink ◽  
Nonlinear Energy

Abstract The frequency-energy plots (FEPs) of two-degree-of-freedom linear structures attached to piecewise nonlinear energy sink (PNES) are generated here and thoroughly investigated. This study provides the FEP analysis of such systems for further understanding of nonlinear targeted energy transfer (TET) by the PNES. The attached PNES incorporates a symmetrical clearance zone of zero stiffness content about its equilibrium position where the boundaries of the zone are coupled with linear structure by linear stiffness elements. In addition, linear viscous damping is selected to be continuous during PNES mass oscillation. The underlying nonlinear dynamical behaviour of the considered structure-PNES systems is investigated by generating the fundamental backbone curves of the FEP and the bifurcated subharmonic resonance branches using numerical continuation methods. Accordingly, interesting dynamical behaviour of the nonlinear normal modes (NNMs) of the structure-PNES system on different backbones and subharmonic resonance branches has been observed. In addition, the imposed wavelet transform frequency spectrums on the FEPs have revealed that the TET takes place where it is dominated by the nonlinear action of the PNES.

Nonlinear Dynamics of a System of Coupled Oscillators With Essential Stiffness Nonlinearities

2003 ◽  
Author(s):  
Alexander F. Vakakis ◽  
Richard H. Rand
Keyword(s):  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Resonance Capture ◽  
Periodic Motions ◽  
Internal Resonances ◽  
Dynamical Mechanism ◽  
Elliptic Orbits ◽  
Weakly Coupled ◽  
Resonant Dynamics ◽  
Nonlinear Normal

We study the resonant dynamics of a two-degree-of-freedom system composed a linear oscillator weakly coupled to a strongly nonlinear one, with an essential (nonlinearizable) cubic stiffness nonlinearity. 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 (nonlinear 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 nonlinear energy pumping phenomena from the linear to the nonlinear 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.

Bifurcation of Nonlinear Normal Modes by Means of Synge’s Stability

2011 ◽  
Author(s):  
Young S. Lee ◽  
Heng Chen
Keyword(s):  
Harmonic Balance ◽  
Coupled Oscillators ◽  
Normal Modes ◽  
Harmonic Balance Method ◽  
Orbital Stability ◽  
Nonlinear Normal Modes ◽  
Energy Transfers ◽  
Wide Range ◽  
Energy Domain ◽  
Nonlinear Normal

We study bifurcation of fundamental nonlinear normal modes (FNNMs) in 2-degree-of-freedom coupled oscillators by utilizing geometric mechanics approach based on Synges concept, which dictates orbital stability rather than Lyapunovs classical asymptotic stability. Use of harmonic balance method provides reasonably accurate approximation for NNMs over wide range of energy; and Floquet theory incorporated into Synges stability analysis predicts the respective bifurcation points as well as their types. Constructing NNMs in the frequency-energy domain, we seek applications to study of efficient targeted energy transfers.

Targeted Energy Transfer With Several NES in Parallel: Theory and Experiments

2009 ◽  
Author(s):  
Alireza Ture Savadkoohi ◽  
Stephane Pernot ◽  
Claude Henri Lamarque
Keyword(s):  
Nonlinear Energy Sink ◽  
Single Degree Of Freedom ◽  
Strongly Nonlinear ◽  
Seismic Engineering ◽  
Energy Pumping ◽  
In Series ◽  
Energy Sink ◽  
Energy Activation ◽  
Nonlinear Energy ◽  
Theory And Experiments

The crucial point in the field of seismic engineering is to diminish the induced vibration energy as much as possible in a fast and almost irreversible manner. Recently the concept of Nonlinear Energy Sink (NES) has been developed such that the imposed energy to a linear single Degree of Freedom (DoF) substructure is transferred to one or series of strongly nonlinear light attachments; the mechanism is based on a 1:1 resonance capture. Nonlinear attachments can be designed to passively vibrate with any frequency; hence the system is efficient for both of transient and periodic excitations. Some drawbacks of these systems are as follows: they cannot kill the first peak of oscillation in the free time response that is linked to the energy activation of NES; moreover, the transformation of energy vanishes in time due to decrease of the strength of energy pumping. Using NES in series even cannot accelerate the phenomenon of energy pumping and some strange behavior due to the delay in the cooperation of NES in series is noticed. In this study, the transient dynamic behavior of multiple DoF systems with trees of parallel NES at each DoF is investigated, then experimental and numerical results of a four DoF structure with two parallel NES at the top floor are demonstrated and commented upon.

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