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.

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.

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 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.

Targeted Energy Transfer Between a Swept Wing and Winglet-Housed Nonlinear Energy Sink

AIAA Journal ◽  
2014 ◽  
Vol 52 (12) ◽  
pp. 2633-2651 ◽  
Author(s):  
Sean A. Hubbard ◽  
D. Michael McFarland ◽  
Lawrence A. Bergman ◽  
Alexander F. Vakakis ◽  
Gerald Andersen
Keyword(s):  
Energy Transfer ◽  
Nonlinear Energy Sink ◽  
Targeted Energy Transfer ◽  
Swept Wing ◽  
Energy Sink ◽  
Nonlinear Energy

Frequency-Energy Dependence of the Bistable Nonlinear Energy Sink

2017 ◽  
Author(s):  
Mohammad A. AL-Shudeifat ◽  
Adnan S. Saeed
Keyword(s):  
Stable Equilibrium ◽  
Initial Conditions ◽  
Energy Levels ◽  
Nonlinear Energy Sink ◽  
Nonlinear Stiffness ◽  
Targeted Energy Transfer ◽  
Simulation Techniques ◽  
Coupling Force ◽  
Energy Sink ◽  
Nonlinear Energy

Recently, the bistable attachment has been employed as a nonlinear energy sink (NES) for passive targeted energy transfer (TET) from linear structures. The bistable NES (BNES) has been coupled with a linear oscillator (LO) where the resulting LO-BNES system has been studied for passive TET. The nonlinear coupling force between the BNES and the associated LO comprises both negative and nonnegative linear and nonlinear stiffness components. Here, the dynamic behavior of the LO-BNES system on the frequency-energy plot is analyzed. The related FEP plot is obtained via numerical simulation techniques where the wavelet transform is imposed into the FEP for variety of initial conditions and damping content. It is found that the FEP has backbone branches at low energy levels associated with the oscillation of the bistable attachments about one of its stable equilibrium positions where passage through the unstable equilibrium position does not occur.

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.

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