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 Theoretical and Experimental Study of an Harmonically Forced Vibro-Impact Nonlinear Energy Sink

2013 ◽  
Author(s):  
Etienne Gourc ◽  
Guilhem Michon ◽  
Sébastien Seguy ◽  
Alain Berlioz
Keyword(s):  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Nonlinear Energy Sink ◽  
Small Mass ◽  
Mass Ratio ◽  
Strongly Coupled ◽  
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. In this paper, the dynamic response of an harmonically forced LO, strongly coupled to a VI-NES is investigated theoretically and experimentally. Due to the small mass ratio between the LO and the flying mass of the NES, the obtained equation 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 response regimes. A good agreement between theoretical and experimental results is observed.

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 Chatter Control in Turning Process with a Nonlinear Energy Sink

2013 ◽  
Vol 698 ◽  
pp. 89-98 ◽  
Author(s):  
Etienne Gourc ◽  
Sébastien Seguy ◽  
Guilhem Michon ◽  
Alain Berlioz
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Nonlinear Energy Sink ◽  
Turning Process ◽  
Strongly Coupled ◽  
Different Types ◽  
Chatter Control ◽  
Energy Sink ◽  
Nonlinear Energy ◽  
Cubic Stiffness

This paper presents the interest of an original absorber of vibration in order to reduce chatter vibration in turning process. The device is composed of a linear oscillator corresponding to a flexible cutting tool subject to chatter strongly coupled to a Nonlinear Energy Sink (NES), with purely cubic stiffness. The novelty of this work is the use of a nonlinear cutting law, more accurate for modeling the cutting process. The delayed equations of motion are analyzed using a combination of the method of multiple scales and harmonic balance. Different types of responses regimes are revealed such as periodic response and also Strongly Modulated Response (SMR). Analytic results are then compared with numerical simulations. Finally, the potential of the NES is demonstrated to control chatter in turning process.

The effects of nonlinear energy sink and piezoelectric energy harvester on aeroelastic instability of an airfoil

2021 ◽  
pp. 107754632199358
Author(s):  
Ali Fasihi ◽  
Majid Shahgholi ◽  
Saeed Ghahremani
Keyword(s):  
Energy Harvester ◽  
Equations Of Motion ◽  
Continuation Method ◽  
Dynamical Behavior ◽  
Harmonic Balance Method ◽  
Nonlinear Energy Sink ◽  
Piezoelectric Energy ◽  
Energy Sink ◽  
Two Degree Of Freedom ◽  
Nonlinear Energy

The potential of absorbing and harvesting energy from a two-degree-of-freedom airfoil using an attachment of a nonlinear energy sink and a piezoelectric energy harvester is investigated. The equations of motion of the airfoil coupled with the attachment are solved using the harmonic balance method. Solutions obtained by this method are compared to the numerical ones of the pseudo-arclength continuation method. The effects of parameters of the integrated nonlinear energy sink-piezoelectric attachment, namely, the attachment location, nonlinear energy sink mass, nonlinear energy sink damping, and nonlinear energy sink stiffness on the dynamical behavior of the airfoil system are studied for both subcritical and supercritical Hopf bifurcation cases. Analyses demonstrate that absorbing vibration and harvesting energy are profoundly affected by the nonlinear energy sink parameters and the location of the attachment.

A Fractional Calculus for Nonlinear Energy Sink Used in Vibration Absorption System

2011 ◽  
Vol 42 (10) ◽  
pp. 62-67
Author(s):  
Song Li ◽  
Bo Fang ◽  
Tianzhi Yang ◽  
Wenhu Huang
Keyword(s):  
Fractional Calculus ◽  
Nonlinear Energy Sink ◽  
Small Mass ◽  
Degree Of Freedom ◽  
Linear Oscillator ◽  
Order System ◽  
Good Correspondence ◽  
Vibration Absorption ◽  
Energy Sink ◽  
Nonlinear Energy

The phenomenon of energy pumping, in which vibratory energy is transferred irreversibly within a nonlinear, multi-degree-of-freedom system with the goal of reducing the transient response of the primary substructure, has recently been investigated analytically and through numerical simulations. The dynamics of single degree of freedom linear subsystem with attached nonlinear energy sink is investigated. The response of a linear oscillator attached to nonlinear energy sink with relatively small mass under external forcing in a vicinity of main resonance is studied analytically and numerically. It is possible that targeted energy could transfer from linear oscillators to the nonlinear energy sink in this system. Analytical model is verified numerically and a fairly good correspondence is observed. Fractional calculus offers a powerful tool to describe the dynamic behavior of real vibration absorption. A version of the fractional derivative models is presented and investigated in this paper for analyzing vibration absorption behavior of nonlinear energy sink. It is shown that the fractional-order system is in a stronger position than the traditional nonlinear energy sink coupled to the linear oscillator.

Quasi-Periodic Response Regimes of Linear Oscillator Coupled to Nonlinear Energy Sink Under Periodic Forcing

2006 ◽  
Vol 74 (2) ◽  
pp. 325-331 ◽  
Author(s):  
O. V. Gendelman ◽  
Yu. Starosvetsky
Keyword(s):  
Nonlinear Energy Sink ◽  
Small Mass ◽  
Linear Instability ◽  
Linear Oscillator ◽  
Analytic Model ◽  
Periodic Response ◽  
State Regime ◽  
Energy Sink ◽  
Nonlinear Normal ◽  
Nonlinear Energy

Quasi-periodic response of a linear oscillator attached to nonlinear energy sink with relatively small mass under external sinusoidal forcing in a vicinity of main (1:1) resonance is studied analytically and numerically. It is shown that the quasi-periodic response is exhibited in well-defined amplitude-frequency range of the external force. Two qualitatively different regimes of the quasi-periodic response are revealed. The first appears as a result of linear instability of the steady-state regime of the oscillations. The second one occurs due to interaction of the dynamical flow with invariant manifold of damped-forced nonlinear normal mode of the system, resulting in hysteretic motion of the flow in the vicinity of this mode. Parameters of external forcing giving rise to the quasi-periodic response are predicted by means of simplified analytic model. The model also allows predicting that the stable quasi-periodic regimes appear for certain range of damping coefficient. All findings of the simplified analytic model are verified numerically and considerable agreement is observed.

Vortex-Induced Vibration of a Sprung Rigid Circular Cylinder Augmented With a Nonlinear Energy Sink

2012 ◽  
Author(s):  
Ravi Kumar R. Tumkur ◽  
Ramon Calderer ◽  
Arif Masud ◽  
Lawrence A. Bergman ◽  
Alexander F. Vakakis ◽  
...  
Keyword(s):  
Circular Cylinder ◽  
Stokes Equations ◽  
Computational Study ◽  
Coupled System ◽  
Nonlinear Energy Sink ◽  
Small Mass ◽  
Limit Cycle Oscillation ◽  
Vortex Induced Vibration ◽  
Energy Sink ◽  
Nonlinear Energy

We study the nonlinear fluid-structure interaction of an elastically supported rigid circular cylinder in a laminar flow. Periodic shedding of counter-rotating vortices from either side of the cylinder results in vortex-induced vibration of the cylinder. We demonstrate the passive suppression of the limit cycle oscillation (LCO) of the cylinder with the use of an essentially nonlinear element, the nonlinear energy sink (NES). The computational study is performed at a Reynolds number (Re) of 100; Re is defined based on the cylinder diameter and inlet velocity. The variational multiscale residual-based stabilized finite-element method is used to compute approximate solutions of the incompressible Navier-Stokes equations. The NES is comprised of a small mass, an essentially nonlinear spring, and a linear damper. With appropriate values for the NES parameters, the coupled system of flow-cylinder-NES exhibits resonant interactions, resulting in targeted energy transfer (TET) from the flow via the cylinder to the NES, where the energy is dissipated by the linear damper. The NES interacts with the fluid via the cylinder by altering the phase relation between the lift force and the cylinder displacement; this brings about significant reduction in the LCO amplitude of the cylinder for several set of values of the NES parameters.

Targeted energy transfer in stochastically excited system with nonlinear energy sink

2018 ◽  
Vol 30 (5) ◽  
pp. 869-886
Author(s):  
P. KUMAR ◽  
S. NARAYANAN ◽  
S. GUPTA
Keyword(s):  
Energy Transfer ◽  
Equations Of Motion ◽  
Nonlinear Energy Sink ◽  
Flow Dynamics ◽  
Slow Flow ◽  
Targeted Energy Transfer ◽  
Optimal Regime ◽  
Excited System ◽  
Energy Sink ◽  
Nonlinear Energy

This study investigates the phenomenon of targeted energy transfer (TET) from a linear oscillator to a nonlinear attachment behaving as a nonlinear energy sink for both transient and stochastic excitations. First, the dynamics of the underlying Hamiltonian system under deterministic transient loading is studied. Assuming that the transient dynamics can be partitioned into slow and fast components, the governing equations of motion corresponding to the slow flow dynamics are derived and the behaviour of the system is analysed. Subsequently, the effect of noise on the slow flow dynamics of the system is investigated. The Itô stochastic differential equations for the noisy system are derived and the corresponding Fokker–Planck equations are numerically solved to gain insights into the behaviour of the system on TET. The effects of the system parameters as well as noise intensity on the optimal regime of TET are studied. The analysis reveals that the interaction of nonlinearities and noise enhances the optimal TET regime as predicted in deterministic analysis.

scholarly journals Free Response of a Rotational Nonlinear Energy Sink: Complete Dissipation of Initial Energy for Small Initial Rectilinear Displacements

2020 ◽  
Vol 88 (1) ◽  
Author(s):  
Ke Ding ◽  
Arne J. Pearlstein
Keyword(s):  
Coupling Parameter ◽  
Equations Of Motion ◽  
Nonlinear Energy Sink ◽  
Initial Energy ◽  
Rectilinear Motion ◽  
Initial Condition ◽  
Free Response ◽  
Primary Mass ◽  
Energy Sink ◽  
Nonlinear Energy

Abstract For two combinations of a dimensionless rotational damping parameter and a dimensionless inertial coupling parameter, we consider free response of a rectilinearly vibrating linearly sprung primary mass inertially coupled to damped rotation of a second mass, for which Gendelman et al. (2012, “Dynamics of an Eccentric Rotational Nonlinear Energy Sink,” ASME J. Appl. Mech. 79(1), 011012) developed equations of motion in the context of a rotational nonlinear energy sink (NES) with no direct damping of the rectilinear motion. For dimensionless initial rectilinear displacements comparable with those considered by Gendelman et al., we identify a region in the motionless projection of the initial condition space (i.e., for zero values of the initial rectilinear and rotational velocities) in which every initial condition leads to a previously unrecognized zero-energy solution, with all initial energy dissipated by rotation. We also show that the long-time nonrotating, rectilinear solutions of the type found by Gendelman et al. are (orbitally) stable only in limited ranges of amplitude. Finally, we show how direct viscous damping of rectilinear motion of the primary mass affects dissipation, and that results with no direct rectilinear dissipation provide excellent guidance for performance when direct rectilinear dissipation occurs. Some applications are discussed.

scholarly journals Analytical Analysis for Parameter Design of Attached Nonlinear Energy Sink

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Tianjiao Zhang ◽  
Luyu Li ◽  
Yilin Zheng
Keyword(s):  
Initial Conditions ◽  
Nonlinear Energy Sink ◽  
Excitation Amplitude ◽  
Harmonic Excitation ◽  
Dynamic Responses ◽  
Parameter Design ◽  
Target Energy ◽  
Energy Sink ◽  
Optimal Stiffness ◽  
Nonlinear Energy

The dynamic responses of a linear primary structure coupled with a nonlinear energy sink (NES) are investigated under harmonic excitation in the 1 : 1 resonance regime. In civil engineering, initial conditions are usually zero or approximately zero. Therefore, in this study, only these conditions are considered. The strongly modulated response (SMR), whose occurrence is conditional, is the precondition for effective target energy transfer (TET) in this system. Therefore, this study aims to determine the parameter range in which the SMR can occur. The platform phenomenon and other related phenomena are observed while analyzing slow-varying equations. An excitation amplitude interval during which the SMR can occur is obtained, and an approximate analytical solution of the optimal nonlinear stiffness is found. The numerical results show that the NES based on the optimal stiffness performs better in terms of control performance.

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