Response regimes of a linear oscillator with a nonlinear energy sink involving an active damper with delay

2019 ◽  
Vol 97 (2) ◽  
pp. 1667-1684 ◽  
Author(s):  
Sergio Bellizzi ◽  
Kwok-Wai Chung ◽  
Rubens Sampaio
Keyword(s):  
Nonlinear Energy Sink ◽  
Linear Oscillator ◽  
Energy Sink ◽  
Active Damper ◽  
Nonlinear Energy

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.

scholarly journals Design Optimisation of a Nonlinear Energy Sink Embedded on a Harmonically Forced Linear Oscillator: Theoretical and Experimental Developments

2012 ◽  
Author(s):  
Etienne Gourc ◽  
Guilhem Michon ◽  
Sébastien Seguy ◽  
Alain Berlioz
Keyword(s):  
Invariant Manifolds ◽  
Relaxation Oscillation ◽  
Design Procedure ◽  
Nonlinear Energy Sink ◽  
Experimental Results ◽  
Linear Oscillator ◽  
Mapping Procedure ◽  
Modulation Equations ◽  
Energy Sink ◽  
Nonlinear Energy

In this paper, the dynamic response of a harmonically forced Linear Oscillator (LO) strongly coupled to a Nonlinear Energy Sink (NES) is investigated theoretically and experimentally. The system studied comprises a linear oscillator subject to an imposed displacement with an embedded, purely cubic, NES. The behavior of the system is analyzed in the vicinity of 1:1 resonance. The complexification averaging technique is used to obtain modulation equations and the associated fixed points. These modulation equations are analyzed using asymptotic expansion to study the regimes related as relaxation oscillation of the slow flow called Strongly Modulated Response (SMR). The zones where SMR occur are computed using a mapping procedure. The Slow Invariant Manifolds (SIM) is used to derive a proper optimization procedure. It is shown that there exist an optimal zone in the parameter plane forcing amplitude–nonlinear stiffness, where SMR occurs without having a high amplitude detached resonance tongue. An experimental setup exhibits a strong mass asymmetry (mass ratio ≈ 1%). The cubic stiffness is realized geometrically with two linear spring that extend axially and are free to rotate. Using the previous optimized stiffness of the NES, different frequency response curves and associated zones of SMR are obtained for various forcing amplitude. Good agreement between theoretical and experimental results is observed. The reported experimental results confirm the design procedure, and the possible application of NES for vibration mitigation under periodic forcing.

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.

scholarly journals Chaotic characteristic of a linear oscillator coupled with vibro-impact nonlinear energy sink

2017 ◽  
Vol 91 (4) ◽  
pp. 2319-2330 ◽  
Author(s):  
Tao Li ◽  
Claude-Henri Lamarque ◽  
Sébastien Seguy ◽  
Alain Berlioz
Keyword(s):  
Nonlinear Energy Sink ◽  
Linear Oscillator ◽  
Chaotic Characteristic ◽  
Energy Sink ◽  
Nonlinear Energy

Dynamic Analysis of 1-Dof and 2-Dof Nonlinear Energy Sink With Geometrically Nonlinear Damping and Combined Stiffness

2021 ◽  
Author(s):  
Yunfa Zhang ◽  
Xianren Kong ◽  
Chengfei Yue ◽  
Huai Xiong
Keyword(s):  
Bifurcation Analysis ◽  
Vibration Suppression ◽  
Harmonic Balance Method ◽  
Nonlinear Energy Sink ◽  
Nonlinear Damping ◽  
Linear Oscillator ◽  
Frequency Detuning ◽  
Incremental Harmonic Balance Method ◽  
Energy Sink ◽  
Nonlinear Energy

Abstract Nonlinear energy sink (NES) refers to a typical passive vibration device connected to linear or weakly nonlinear structures for vibration absorption and mitigation. This study investigates the dynamics of 1-dof and 2-dof NES with nonlinear damping and combined stiffness connected to a linear oscillator. For the system of 1-dof NES, a truncation damping and failure frequency are revealed through bifurcation analysis using the complex variable averaging method. The frequency detuning interval for the existence of the strongly modulated response (SMR) is also reported . For the system of 2-dof NES, it is reported in a similar bifurcation analysis that the mass distribution between NES affects the maximum value of saddle-node bifurcation. To obtain the periodic solution of the 2-dof NES system with the consideration of frequency detuning, the incremental harmonic balance method (IHB) and Floquet theory are employed. The corresponding response regime is obtained by Poincare mapping, it shows that the responses of the linear oscillator and 2-dof NES are not always consistent, and 2-dof NES can generate extra SMR than 1-dof NES. Finally, the vibration suppression effect of the proposed NES with nonlinear damping and combined stiffness is analyzed and verified by the energy spectrum, and it also shows that the 2-dof NES system demonstrates better performance.

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