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.

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.

Bifurcation of nonlinear normal modes of a cantilever beam under harmonic excitation

2020 ◽  
Vol 90 (6) ◽  
pp. 1247-1266 ◽  
Author(s):  
Lokanna Hoskoti ◽  
Ajay Misra ◽  
Mahesh M. Sucheendran
Keyword(s):  
Cantilever Beam ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Harmonic Excitation ◽  
Nonlinear Normal

scholarly journals Targeted Energy Transfer Under Harmonic Forcing With a Vibro-Impact Nonlinear Energy Sink: Analytical and Experimental Developments

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Etienne Gourc ◽  
Guilhem Michon ◽  
Sébastien Seguy ◽  
Alain Berlioz
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Nonlinear Energy Sink ◽  
Small Mass ◽  
Harmonic Excitation ◽  
Mass Ratio ◽  
Electrodynamic Shaker ◽  
Energy Sink ◽  
Nonlinear Energy ◽  
Good Agreement

Recently, it has been demonstrated that a vibro-impact type nonlinear energy sink (VI-NES) can be used efficiently to mitigate vibration of a linear oscillator (LO) under transient loading. The objective of this paper is to investigate theoretically and experimentally the potential of a VI-NES to mitigate vibrations of an LO subjected to a harmonic excitation (nevertheless, the presentation of an optimal VI-NES is beyond the scope of this paper). Due to the small mass ratio between the LO and the flying mass of the NES, the obtained equations of motion are analyzed using the method of multiple scales in the case of 1:1 resonance. It is shown that in addition to periodic response, system with VI-NES can exhibit strongly modulated response (SMR). Experimentally, the whole system is embedded on an electrodynamic shaker. The VI-NES is realized with a ball which is free to move in a cavity with a predesigned gap. The mass of the ball is less than 1% of the mass of the LO. The experiment confirms the existence of periodic and SMR regimes. A good agreement between theoretical and experimental results is observed.

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.

Dynamics and evaluation of a nonlinear energy sink integrated by a piezoelectric energy harvester under a harmonic excitation

2018 ◽  
Vol 25 (4) ◽  
pp. 851-867 ◽  
Author(s):  
Xiang Li ◽  
Ye-Wei Zhang ◽  
Hu Ding ◽  
Li-Qun Chen
Keyword(s):  
Energy Harvesting ◽  
Vibration Suppression ◽  
Average Energy ◽  
Nonlinear Energy Sink ◽  
Harmonic Excitation ◽  
Response Curves ◽  
Piezoelectric Energy ◽  
Energy Sink ◽  
Piezoelectric Harvester ◽  
Nonlinear Energy

The harmonically excited structure coupled with the nonlinear energy sink (NES) and a piezoelectric harvester is investigated. The complexification-averaging method is developed to analyze ordinary differential equations which also include one first order differential equation. Effects of varying parameters for the piezoelectric harvester on the saddle-node bifurcation and the Hopf bifurcation are explored. Analytical results of the amplitude–frequency response curves are verified by the numerical evidence. Global bifurcations for NES parameters are presented. Comparisons of periodic results for bifurcation diagrams are performed both numerically and analytically as well as their stable ranges. The integration of nonlinear vibration suppression and energy harvesting is discussed. The output voltage, power, displacement transmissibility, and average energy are calculated to explore the integration. Quasi-periodic responses near the resonance frequency contribute to effectively reducing the resonant amplitude and improving the bandwidth of energy harvesting, as well as targeted energy transfer. Results confirm that the integration of vibration suppression and piezoelectric energy harvesting can be enhanced by adjusting cubic nonlinearity.

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.

scholarly journals Comparison of Galerkin, POD and Nonlinear-Normal-Modes Models for Nonlinear Vibrations of Circular Cylindrical Shells

2006 ◽  
Author(s):  
M. Amabili ◽  
C. Touze´ ◽  
O. Thomas
Keyword(s):  
Nonlinear Vibrations ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Harmonic Excitation ◽  
Nonlinear Responses ◽  
Nonlinear Normal ◽  
The Galerkin Method ◽  
Proper Orthogonal

The aim of the present paper is to compare two different methods available to reduce the complicated dynamics exhibited by large amplitude, geometrically nonlinear vibrations of a thin shell. The two methods are: the proper orthogonal decomposition (POD) and an asymptotic approximation of the Nonlinear Normal Modes (NNMs) of the system. The structure used to perform comparisons is a water-filled, simply supported circular cylindrical shell subjected to harmonic excitation in the spectral neighbourhood of the fundamental natural frequency. A reference solution is obtained by discretizing the Partial Differential Equations (PDEs) of motion with a Galerkin expansion containing 16 eigenmodes. The POD model is built by using responses computed with the Galerkin model; the NNM model is built by using the discretized equations of motion obtained with the Galerkin method, and taking into account also the transformation of damping terms. Both the POD and NNMs allow to reduce significantly the dimension of the original Galerkin model. The computed nonlinear responses are compared in order to verify the accuracy and the limits of these two methods. For vibration amplitudes equal to 1.5 times the shell thickness, the two methods give very close results to the original Galerkin model. By increasing the excitation and vibration amplitude, significant differences are observed and discussed.

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