scholarly journals Understanding targeted energy transfer from a symmetry breaking perspective

2021 ◽  
Vol 477 (2251) ◽  
pp. 20210045
Author(s):  
Dongxiao Hong ◽  
Thomas L. Hill ◽  
Simon A. Neild
Keyword(s):  
Energy Transfer ◽  
Symmetry Breaking ◽  
Original System ◽  
Nonlinear Energy Sink ◽  
Initial Energy ◽  
Primary System ◽  
Targeted Energy Transfer ◽  
Backbone Curve ◽  
Breaking Effect ◽  
Energy Sink

Targeted energy transfer (TET) represents the phenomenon where energy in a primary system is irreversibly transferred to a nonlinear energy sink (NES). This only occurs when the initial energy in the primary system is above a critical level. There is a natural asymmetry in the system due to the desire for the NES to be much smaller than the primary structure it is protecting. This asymmetry is also essential from an energy transfer perspective. To explore how the essential asymmetry is related to TET, this work interprets the realization of TET from a symmetry breaking perspective. This is achieved by introducing a symmetrized model with respect to the generically asymmetric original system. Firstly a classic example, which consists of a linear primary system and a nonlinearizable NES, is studied. The backbone curve topology that is necessary to realize TET is explored and it is demonstrated how this topology evolves from the symmetric case. This example is then extended to a more general case, accounting for nonlinearity in the primary system and linear stiffness in the NES. Exploring the symmetry-breaking effect on the backbone curve topologies, enables the regions in the NES parameter space that lead to TET to be identified.

Dynamics of an Eccentric Rotational Nonlinear Energy Sink

2011 ◽  
Vol 79 (1) ◽  
Author(s):  
O. V. Gendelman ◽  
G. Sigalov ◽  
L. I. Manevitch ◽  
M. Mane ◽  
A. F. Vakakis ◽  
...  
Keyword(s):  
Energy Transfer ◽  
Nonlinear Energy Sink ◽  
Experimental Investigations ◽  
Primary System ◽  
Targeted Energy Transfer ◽  
Energy Sink ◽  
Nonlinear Energy

The paper introduces a novel type of nonlinear energy sink, designed as a simple rotating eccentric mass, which can rotate with any frequency and; therefore, inertially couple and resonate with any mode of the primary system. We report on theoretical and experimental investigations of targeted energy transfer in this system.

Targeted Energy Transfer to a Rotary Nonlinear Energy Sink

2010 ◽  
Author(s):  
Sean A. Hubbard ◽  
D. Michael McFarland ◽  
Alexander F. Vakakis ◽  
Lawrence A. Bergman
Keyword(s):  
Finite Element ◽  
Energy Transfer ◽  
Finite Element Model ◽  
Nonlinear Energy Sink ◽  
Element Model ◽  
Targeted Energy Transfer ◽  
Discrete Equations ◽  
Resonant Interactions ◽  
Energy Sink ◽  
Nonlinear Energy

We study computationally the passive, nonlinear targeted energy transfers induced by resonant interactions between a single-degree-of-freedom nonlinear energy sink and a uniform-plate model of a flexible, swept aircraft wing. We show that the nonlinear energy sink can be designed to quickly and efficiently absorb energy from one or more wing modes in a completely passive manner. Results indicate that it is feasible to use such a device to suppress or prevent aeroelastic instabilities like limit-cycle oscillations. The design of a compact nonlinear energy sink is introduced and the parameters of the device are examined. Simulations performed using a finite-element model of the wing coupled to discrete equations governing the energy sink indicate that targeted energy transfer is achievable, resulting, for example, in a rapid and significant reduction in the second bending mode response of the wing. Finally, the finite element model is used to simulate the effects of increased nonlinear energy sink stiffness, and to show the conditions under which the nonlinear energy sink will resonantly interact with higher-frequency wing modes.

Targeted energy transfer in mechanical systems by means of non-smooth nonlinear energy sink

2011 ◽  
Vol 221 (1-2) ◽  
pp. 175-200 ◽  
Author(s):  
Claude-Henri Lamarque ◽  
Oleg V. Gendelman ◽  
Alireza Ture Savadkoohi ◽  
Emilie Etcheverria
Keyword(s):  
Energy Transfer ◽  
Mechanical Systems ◽  
Nonlinear Energy Sink ◽  
Targeted Energy Transfer ◽  
Energy Sink ◽  
Nonlinear Energy

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.

Numerical Investigation of Rotating Nonlinear Energy Sink for Shock Mitigation

2013 ◽  
Author(s):  
Mohammad A. Al-Shudeifat ◽  
Lawrence A. Bergman ◽  
Alexander F. Vakakis
Keyword(s):  
Energy Transfer ◽  
Linear Structure ◽  
Nonlinear Energy Sink ◽  
Initial Energy ◽  
Shock Mitigation ◽  
Nonlinear Targeted Energy Transfer ◽  
Primary Test ◽  
Energy Sink ◽  
Two Degree Of Freedom ◽  
Nonlinear Energy

Passive nonlinear targeted energy transfer (TET) is addressed here by investigating a lightweight rotating nonlinear energy sink (NES). The rotating sink mass has an essentially nonlinear inertial coupling with the two degree-of-freedom linear system (the primary test structure). The proposed rotating NES is numerically investigated where it is found to passively absorb and rapidly dissipate a considerable portion of the initial energy induced by impulse to the linear structure. The parameters of the rotating NES are optimized for the best performance in the vicinity of intermediate and high loads. The fundamental mechanism for significant energy transfer to the NES is its rotational mode; the oscillatory mode of the NES dissipates far less energy. The frequency-energy dependences are investigated through the frequency-energy plot (FEP). Early and strong resonance capture at the lowest modal frequency is observed between the rotator and the structure, at which a significant portion of the induced energy is transferred and dissipated by the rotator. The performance of this device is found to be comparable to existing, stiffness-based NES designs. However, this device is less complicated and more compact.

Mechanism of Optimal Targeted Energy Transfer

2016 ◽  
Vol 84 (1) ◽  
Author(s):  
Y. M. Wei ◽  
Z. K. Peng ◽  
X. J. Dong ◽  
W. M. Zhang ◽  
G. Meng
Keyword(s):  
Energy Transfer ◽  
Passive Control ◽  
Initial Conditions ◽  
Physical Phenomenon ◽  
Active Vibration Control ◽  
Design Procedure ◽  
Nonlinear Energy Sink ◽  
Targeted Energy Transfer ◽  
Active Vibration ◽  
Energy Sink

A novel nonlinear vibration reduction mechanism based on targeted energy transfer (TET) is proposed. Targeted energy transfer is a physical phenomenon that describes a one-way irreversible energy flow from a linear oscillator (LO) to a nonlinearizable (essentially) nonlinear auxiliary substructure, noted as nonlinear energy sink (NES). The optimal targeted energy transfer where NES is set on the optimal state is investigated in this study. Complexification-averaging methodology is used to derive the optimal TET of the undamped system for different initial conditions. It is revealed that the optimal TET is dependent on the energy, indicating that passive control of NES cannot be optimally set for arbitrary initial conditions. In addition, it is found that for the undamped system, the optimal phrase difference between the linear primary oscillator and the nonlinear attachment is π/2. From the perspective of active control, the NES can be taken as an actuator to keep the system vibrating on the optimal TET. An available modification form of the optimal equations is proposed for the impulse excitation with relatively small damping. The comparisons of the effectiveness of the optimal TET is validated by using numerical simulations with the excitations including impulse, harmonic, to input with sufficient bandwidth, and random signal. The design procedure would pave the way for practical implications of TET in active vibration control.

An Eccentric Rotator as a Novel Design of a Nonlinear Energy Sink

2011 ◽  
Author(s):  
Oleg V. Gendelman ◽  
Grigori Sigalov ◽  
Mercedes Mane ◽  
Lawrence A. Bergman ◽  
Alexander F. Vakakis ◽  
...  
Keyword(s):  
Numerical Study ◽  
Nonlinear Energy Sink ◽  
Primary System ◽  
Targeted Energy Transfer ◽  
Impulsive Loads ◽  
Chaotic Modes ◽  
Energy Sink ◽  
Novel Design ◽  
Nonlinear Energy ◽  
Good Agreement

We introduce a novel type of the nonlinear energy sink (NES) designed as an eccentric mass rotating within a horizontal plane. The gravity is not a factor here, therefore such a rotator has no eigenfrequency and can inertially couple and resonate with any mode of the primary system. The dynamics of the system consisting of a primary linear oscillator and the eccentric rotator is rich beyond expectations and features multiple resonances and chaotic modes. A numerical study shows that the system, when subject to high impulsive loads, inevitably enters a 1:1 resonance that enables highly efficient targeted energy transfer from the primary mass to the NES. The results of an experimental investigation are in good agreement with the analytical and numerical estimates.

Targeted Energy Transfer for Suppressing Regenerative Instabilities in a 2-DOF Machine Tool Model

2013 ◽  
Author(s):  
Amir Nankali ◽  
Young S. Lee ◽  
Tamas Kalmar-Nagy
Keyword(s):  
Energy Transfer ◽  
Machine Tool ◽  
Nonlinear Energy Sink ◽  
Dominant Mode ◽  
Numerical Continuation ◽  
Complete Suppression ◽  
Targeted Energy Transfer ◽  
Subcritical Hopf Bifurcation ◽  
Energy Exchanges ◽  
Energy Sink

We study targeted energy transfer (TET) mechanisms by applying a nonlinear energy sink (NES) to suppress regenerative instabilities in a 2-DOF planar machine tool model. With the help of a numerical continuation tool, DDEBIFTOOL, we show that the tool instability is generated through a subcritical Hopf bifurcation in this simplified tool model. Studying modal energy exchanges reveals that only one of the DOFs is predominant, which may lead to the standard single-DOF machine tool model. Then, we apply an ungrounded NES to the 2-DOF tool model such that the NES interacts only with the dominant mode, which turns out to be more efficient than applying the NES to the other insignificant mode. Simple numerical simulations and bifurcation analysis demonstrate that the three typical TET mechanisms can be identified — That is, recurrent burstouts and suppression, and partial and complete suppression of tool instability.

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