Periodic Motion and Frequency Energy Plots of Dynamical Systems Coupled with Piecewise Nonlinear Energy Sink

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.4053509 ◽

2022 ◽

Author(s):

Mohammad Al-Shudeifat ◽

Adnan Saeed

Keyword(s):

Dynamical Systems ◽

Normal Modes ◽

Nonlinear Energy Sink ◽

Dynamical Behaviour ◽

Subharmonic Resonance ◽

Numerical Continuation ◽

Continuation Methods ◽

Linear Dynamical Systems ◽

Energy Sink ◽

Nonlinear Energy

Abstract The frequency-energy plots (FEPs) of two-degree-of-freedom linear structures attached to a piecewise nonlinear energy sink (PNES) are generated here and thoroughly investigated. This study provides the FEP analysis of such systems for further understanding to nonlinear targeted energy transfer (TET) by the PNES. The attached PNES to the considered linear dynamical systems incorporates a symmetrical clearance zone of zero stiffness content where the boundaries of the zone are coupled with the linear structure by linear stiffness elements. In addition, linear viscous damping is selected to be continuous during the 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 in multiple resonance captures where it is dominated by the nonlinear action of the PNES.

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

10.21203/rs.3.rs-252523/v1 ◽

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.

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.325-326.214 ◽

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.

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Nonlinear Energy Sink With Uncertain Parameters

Journal of Computational and Nonlinear Dynamics ◽

10.1115/1.2198213 ◽

2006 ◽

Vol 1 (3) ◽

pp. 187-195 ◽

Cited By ~ 24

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.

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Nonlinear normal modes and optimization of a square root nonlinear energy sink

Nonlinear Dynamics ◽

10.1007/s11071-021-06334-1 ◽

2021 ◽

Author(s):

Guo-Xu Wang ◽

Hu Ding ◽

Li-Qun Chen

Keyword(s):

Normal Modes ◽

Nonlinear Energy Sink ◽

Nonlinear Normal Modes ◽

Square Root ◽

Energy Sink ◽

Nonlinear Normal ◽

Nonlinear Energy

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Frequency-Energy Plots of Bistable Nonlinear Energy Sink

10.21203/rs.3.rs-197669/v1 ◽

2021 ◽

Author(s):

Mohammed Ameen Al Shudeifat ◽

Adnan Salem Saeed

Keyword(s):

Large Scale ◽

Initial Conditions ◽

Energy Levels ◽

Dynamical Behavior ◽

Nonlinear Energy Sink ◽

Low Energy ◽

Unstable Equilibrium ◽

Numerical Continuation ◽

Energy Sink ◽

Nonlinear Energy

Abstract The nonlinear energy sink (NES), which is proven to perform rapid and passive targeted energy transfer (TET), has been has been employed for vibration mitigation in many primary small- and large-scale structures. Recently, the feature of bistability, in which two nontrivial stable equilibria and one trivial unstable equilibrium exist, is utilized for passive TET in what is known as Bistable NES (BNES). The BNES generates a nonlinear force that incorporates negative linear and multiple positive or negative nonlinear stiffness components. In this paper, the BNES is coupled to a linear oscillator (LO) where the dynamic behavior of the resulting LO-BNES system is studied through frequency-energy plots (FEPs), which are generated by analytical approximation using the complexification-averaging method and by numerical continuation techniques. The effect of the length and stiffness of the transverse coupling springs is found to affect the stability and topology of the branches and indicates the importance of the exact physical realization of the system. The rich nonlinear dynamical behavior of the LO-BNES system is also highlighted through the appearance of multiple symmetrical and unsymmetrical in- and out of- phase backbone branches, especially at low energy levels. The wavelet transform is imposed into the FEP for variety of initial conditions and damping content and it is found that the FEP has backbone branches at low energy levels associated with the oscillation of the bistable attachments about one of its stable equilibrium positions where passage through the unstable equilibrium position does not occur.

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Suppression of Limit Cycle Oscillations in a Van der Pol Oscillator by Means of a Passive Nonlinear Energy Sink

Volume 1: 20th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C ◽

10.1115/detc2005-84691 ◽

2005 ◽

Author(s):

Young S. Lee ◽

Alexander F. Vakakis ◽

Lawrence A. Bergman ◽

D. Michael McFarland

Keyword(s):

Vibration Control ◽

Limit Cycle ◽

Nonlinear Energy Sink ◽

Van Der Pol Oscillator ◽

Numerical Continuation ◽

Parameter Study ◽

Limit Cycle Oscillations ◽

Van Der Pol ◽

Energy Sink ◽

Nonlinear Energy

We present a study of passive but efficient vibration control, wherein a so-called nonlinear energy sink (NES) completely eliminates the limit cycle oscillations (LCOs) of a van der Pol oscillator. We first perform a parameter study in order to get overall understanding of responses with respect to parameters. Then, we establish a slow flow dynamics model to perform analytical study of the suppression mechanism which corresponds to classical nonlinear energy pumping, i.e., passive, broadband, and targeted energy transfer through 1:1 resonance capture. Utilizing the method of numerical continuation of equilibrium, we also study the bifurcation of the steady state solutions. It turns out that the system may have either subcritical or supercritical LCOs, and that for some parameter domain the LCOs are completely eliminated. This suggests applicability of the NES to vibration control in self-excited systems.

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