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 Frequency-Energy Plots of Bistable Nonlinear Energy Sink

2021 ◽  
Author(s):  
Mohammed Ameen Al Shudeifat ◽  
Adnan Salem Saeed
Keyword(s):  
Large Scale ◽  
Initial Conditions ◽  
Energy Levels ◽  
Dynamical Behavior ◽  
Nonlinear Energy Sink ◽  
Low Energy ◽  
Unstable Equilibrium ◽  
Numerical Continuation ◽  
Energy Sink ◽  
Nonlinear Energy

Abstract The nonlinear energy sink (NES), which is proven to perform rapid and passive targeted energy transfer (TET), has been has been employed for vibration mitigation in many primary small- and large-scale structures. Recently, the feature of bistability, in which two nontrivial stable equilibria and one trivial unstable equilibrium exist, is utilized for passive TET in what is known as Bistable NES (BNES). The BNES generates a nonlinear force that incorporates negative linear and multiple positive or negative nonlinear stiffness components. In this paper, the BNES is coupled to a linear oscillator (LO) where the dynamic behavior of the resulting LO-BNES system is studied through frequency-energy plots (FEPs), which are generated by analytical approximation using the complexification-averaging method and by numerical continuation techniques. The effect of the length and stiffness of the transverse coupling springs is found to affect the stability and topology of the branches and indicates the importance of the exact physical realization of the system. The rich nonlinear dynamical behavior of the LO-BNES system is also highlighted through the appearance of multiple symmetrical and unsymmetrical in- and out of- phase backbone branches, especially at low energy levels. The wavelet transform is imposed into the FEP for variety of initial conditions and damping content and 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.

Tuned pendulum as nonlinear energy sink for broad energy range

2016 ◽  
Vol 23 (3) ◽  
pp. 373-388 ◽  
Author(s):  
Maor Farid ◽  
Oleg V Gendelman
Keyword(s):  
Initial Conditions ◽  
Nonlinear Energy Sink ◽  
Primary System ◽  
Targeted Energy Transfer ◽  
Broad Energy Range ◽  
Wide Range ◽  
Mass Damper ◽  
Energy Sink ◽  
Nonlinear Energy ◽  
Broad Energy

Nonlinear energy sinks (NES) are widely studied as a possible engineering solution for mitigation of steady-state, impulsive and transient broadband excitations. Current work is devoted to the applicability of common pendulum as the NES for mitigation of impulsive excitations. It turns out that the pendulum NES can overcome one of the main shortcomings of more traditional NES designs, since it is able to mitigate excitation of a primary system in a relatively wide range of initial energies. This is because the pendulum can be captured into a resonance with primary oscillator both for rotational and oscillatory responses. If parameters are chosen properly, for small energies the pendulum responds almost as a common tuned mass damper. However, at higher energies, the pendulum acts as rotational NES. Thus, relatively broad diapason of initial energies can be covered. This paper presents numeric evidence for the efficiency of this design of the NES and discusses its optimal tuning. Another important finding is that the NES’s efficiency exhibits rather broad deviations for different realizations of the initial conditions with the same energy. We present a theoretical analysis of the damped targeted energy transfer into the pendulum NES from the primary mass with an account of corrections caused by the effect of gravity.

Piecewise Nonlinear Energy Sink

2015 ◽  
Author(s):  
Mohammad A. Al-Shudeifat
Keyword(s):  
Dead Zone ◽  
Linear Structure ◽  
Nonlinear Energy Sink ◽  
Viscous Damping ◽  
Nonlinear Stiffness ◽  
Flexible Design ◽  
Energy Inputs ◽  
Energy Sink ◽  
The Dead ◽  
Nonlinear Energy

Symmetric piecewise nonlinearities are employed here to design highly efficient nonlinear energy sink (NES). These symmetric piecewise nonlinearities are usually called in the literature as dead-zone nonlinearities. The proposed dead-zone NES includes symmetric clearance about its equilibrium position in which zero stiffness and linear viscous damping are incorporated. At the boundaries of the symmetric clearance, the NES is coupled to the linear structure by either linear or nonlinear stiffness components in addition to similar viscous damping to that in the clearance zone. By this flexible design of the dead-zone NES, we obtain a considerable enhancement in the NES efficiency at moderate and severe energy inputs. Moreover, the dead-zone NES is also found here through numerical simulations to be more robust for damping and stiffness variations than the linear absorber and some other types of NESs.

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.

scholarly journals Analytical Analysis for Parameter Design of Attached Nonlinear Energy Sink

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Tianjiao Zhang ◽  
Luyu Li ◽  
Yilin Zheng
Keyword(s):  
Initial Conditions ◽  
Nonlinear Energy Sink ◽  
Excitation Amplitude ◽  
Harmonic Excitation ◽  
Dynamic Responses ◽  
Parameter Design ◽  
Target Energy ◽  
Energy Sink ◽  
Optimal Stiffness ◽  
Nonlinear Energy

The dynamic responses of a linear primary structure coupled with a nonlinear energy sink (NES) are investigated under harmonic excitation in the 1 : 1 resonance regime. In civil engineering, initial conditions are usually zero or approximately zero. Therefore, in this study, only these conditions are considered. The strongly modulated response (SMR), whose occurrence is conditional, is the precondition for effective target energy transfer (TET) in this system. Therefore, this study aims to determine the parameter range in which the SMR can occur. The platform phenomenon and other related phenomena are observed while analyzing slow-varying equations. An excitation amplitude interval during which the SMR can occur is obtained, and an approximate analytical solution of the optimal nonlinear stiffness is found. The numerical results show that the NES based on the optimal stiffness performs better in terms of control performance.

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