Attractors of harmonically forced linear oscillator with attached nonlinear energy sink. II: Optimization of a nonlinear vibration absorber

2007 ◽  
Vol 51 (1-2) ◽  
pp. 47-57 ◽  
Author(s):  
Y. Starosvetsky ◽  
O. V. Gendelman
2018 ◽  
Vol 86 (2) ◽  
Author(s):  
Xiao-Ye Mao ◽  
Hu Ding ◽  
Li-Qun Chen

A new kind of nonlinear energy sink (NES) is proposed to control the vibration of a flexible structure with simply supported boundaries in the present work. The new kind of absorber is assembled at the end of structures and absorbs energy through the rotation angle at the end of the structure. It is easy to design and attached to the support of flexible structures. The structure and the absorber are coupled just with a nonlinear restoring moment and the damper in the absorber acts on the structure indirectly. In this way, all the linear characters of the flexible structure will not be changed. The system is investigated by a special perturbation method and verified by simulation. Parameters of the absorber are fully discussed to optimize the efficiency of it. For the resonance, the maximum motion is restrained up to 90% by the optimized absorber. For the impulse, the vibration of the structure could attenuate rapidly. In addition to the high efficiency, energy transmits to the absorber uniaxially. For the high efficiency, convenience of installation and the immutability of linear characters, the new kind of rotating absorber provides a very good strategy for the vibration control.


2011 ◽  
Vol 42 (10) ◽  
pp. 62-67
Author(s):  
Song Li ◽  
Bo Fang ◽  
Tianzhi Yang ◽  
Wenhu Huang

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.


Author(s):  
Etienne Gourc ◽  
Guilhem Michon ◽  
Sébastien Seguy ◽  
Alain Berlioz

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.


2006 ◽  
Vol 74 (2) ◽  
pp. 325-331 ◽  
Author(s):  
O. V. Gendelman ◽  
Yu. Starosvetsky

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.


2017 ◽  
Vol 91 (4) ◽  
pp. 2319-2330 ◽  
Author(s):  
Tao Li ◽  
Claude-Henri Lamarque ◽  
Sébastien Seguy ◽  
Alain Berlioz

Author(s):  
Anubhab Sinha ◽  
Saurabh Kumar Bharti ◽  
Arun Kumar Samantaray ◽  
Ranjan Bhattacharyya

Two eccentric rotors are mounted rigidly on a common vibrating base structure. Each of these rotors are separately driven by two motors, which are by nature non-ideal. Although power input for both rotors are different, the two rotors acquire the same speed via communication through the energized vibrating base. The phenomena is known as ‘self-synchronization’. Additionally, the presence of two non-ideal drives within the vibrating system also lead to the onset of the nonlinear jump phenomena (formally known as the Sommerfeld effect). Numerical simulations are carried out on a model developed on MSC Adams. From the generated responses, an overview of ‘self-synchronization’ as well as the various modes of synchronization are studied adjacent to the nature of Sommerfeld effect inherent within this system. The aim is to reduce the structural vibrations, mainly by virtue of self-synchronization. Henceforth, the behavior of the synchronized system is also examined in the presence of two secondary vibration reducing devices — a tuned Dynamic Vibration Absorber (DVA) and a Nonlinear Energy Sink (NES). Both are designed to passively absorb the excess vibrating energy from the synchronized system, at the onset of resonance.


2021 ◽  
Author(s):  
Yunfa Zhang ◽  
Xianren Kong ◽  
Chengfei Yue ◽  
Huai Xiong

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.


2018 ◽  
Vol 95 (2) ◽  
pp. 1435-1456 ◽  
Author(s):  
K. Zhou ◽  
F. R. Xiong ◽  
N. B. Jiang ◽  
H. L. Dai ◽  
H. Yan ◽  
...  

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