Optimization mechanism of targeted energy transfer with vibro-impact energy sink under periodic and transient excitation

Targeted energy transfer (TET) refers to the spatial transfer of energy between a primary structure of interest and isolated oscillators called the energy sink (ES). In this work, the primary structure of interest is a slender beam modeled by the Euler-Bernoulli theory, and the ES is a single-degree-of-freedom oscillator with either linear or cubic nonlinear stiffness property. The objective of this study is to characterize the TET and the effectiveness of ES under impact and periodic excitations. By using the scientific computation package, MATLAB, numerical simulations are carried out based on excitations of various strength and locations. Both time and frequency domain characterizations are used. For the impact excitation, the ES with the cubic nonlinear stiffness property is more superior to the linear oscillator in that larger percentage of the impact energy can be dissipated there. The main energy transfer was found to be due to a 3- to-1 frequency coupling between the first bending mode and the ES. For the periodic excitation, however, both linear and nonlinear ES exhibit generally poorer performance than the case with the impact excitation. Future works should focus on the frequency-energy relationship of the periodic solution of the underlying Hamiltonian, as well as using finite element model to verify the simulation results.

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Targeted Energy Transfer to a Rotary Nonlinear Energy Sink

Volume 5: 22nd International Conference on Design Theory and Methodology; Special Conference on Mechanical Vibration and Noise ◽

10.1115/detc2010-28840 ◽

2010 ◽

Cited By ~ 1

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.

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

Acta Mechanica ◽

10.1007/s00707-011-0492-0 ◽

2011 ◽

Vol 221 (1-2) ◽

pp. 175-200 ◽

Cited By ~ 71

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

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Experimental Targeted Energy Transfer to a Rotary Nonlinear Energy Sink

51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference<BR> 18th AIAA/ASME/AHS Adaptive Structures Conference<BR> 12th ◽

10.2514/6.2010-3045 ◽

2010 ◽

Cited By ~ 4

Author(s):

Sean Hubbard ◽

D. McFarland ◽

Lawrence Bergman ◽

Alexander Vakakis

Keyword(s):

Energy Transfer ◽

Nonlinear Energy Sink ◽

Targeted Energy Transfer ◽

Energy Sink ◽

Nonlinear Energy

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Targeted energy transfer in stochastically excited system with nonlinear energy sink

European Journal of Applied Mathematics ◽

10.1017/s0956792518000505 ◽

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.

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Dynamics of an Eccentric Rotational Nonlinear Energy Sink

Journal of Applied Mechanics ◽

10.1115/1.4005402 ◽

2011 ◽

Vol 79 (1) ◽

Cited By ~ 57

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.

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Mechanism of Optimal Targeted Energy Transfer

Journal of Applied Mechanics ◽

10.1115/1.4034929 ◽

2016 ◽

Vol 84 (1) ◽

Cited By ~ 7

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.

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

Volume 8: 22nd Reliability, Stress Analysis, and Failure Prevention Conference; 25th Conference on Mechanical Vibration and Noise ◽

10.1115/detc2013-13510 ◽

2013 ◽

Cited By ~ 1

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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