Inducing Passive Nonlinear Energy Sinks in Vibrating Systems

2001 ◽  
Vol 123 (3) ◽  
pp. 324-332 ◽  
Author(s):  
A. F. Vakakis
Keyword(s):  
Vibrational Energy ◽  
Linear Chain ◽  
Strongly Coupled ◽  
Strongly Nonlinear ◽  
Energy Pumping ◽  
Nonlinear Energy Pumping ◽  
Practical Engineering ◽  
Nonlinear Energy ◽  
Vibrating Systems ◽  
Envelope Modulation

We study the inducement of passive nonlinear sinks in linear vibrating systems. These are substructures that absorb vibrational energy in a one-way, irreversible fashion. The systems considered are composed of strongly coupled, grounded damped linear oscillators with a strongly nonlinear attachment at the end. Applying a complex averaging technique we derive a set of modulation equations that is directly amenable to physical interpretation, and provides insight into the energy pumping phenomenon. For the case of a two DOF system we show that nonlinear energy pumping occurs when a certain frequency of envelope modulation crosses through zero; then the dynamics of the envelope modulation of the motion resemble the dynamics of a forced rigid body. For the case of an impulsively loaded multi-DOF chain with a nonlinear attachment at the end, we show that after some initial transients the response of the nonlinear attachment sets to a motion dominated by a “fast” frequency identical to the lower bound of the propagation zone of the linear chain. This feature reduces the study of energy pumping in the chain to a two DOF equivalent problem. The applications of the energy pumping phenomenon to practical engineering problems are discussed.

Study on Nonlinear Energy Pumping of the Vibration System with Cubic Damping Absorber

2010 ◽  
Vol 34-35 ◽  
pp. 1243-1247 ◽  
Author(s):  
Si Mi Tang ◽  
Shi Jian Zhu ◽  
Jing Jun Lou
Keyword(s):  
Vibration System ◽  
Optimal Parameters ◽  
Time Frequency ◽  
Energy Pumping ◽  
Pumping Efficiency ◽  
Nonlinear Energy Pumping ◽  
Two Degree Of Freedom ◽  
Nonlinear Energy ◽  
Cubic Stiffness ◽  
Main Oscillator

The nonlinear energy pumping in a two-degree-of-freedom system comprising a damped linear oscillator coupled to cubic damping absorber is studied. It is verified that the nonlinear pumping energy can be performed by cubic damping absorber besides cubic stiffness absorber. The resonance capture is verified by time-frequency analysis (Hilbert Transform). The energy pumping efficiency is put forward for quantitative analysis, and the optimal parameters of system are obtained. The amplitude of main oscillator can be attenuated in a very short duration. The result may be significative for engineering implementation.

Optimal Vibration Control and Energy Scavenging Using Collocated Nonlinear Energy Sinks and Piezoelectric Elements

2018 ◽  
Author(s):  
Zahra Nili Ahmadabadi ◽  
Siamak Esmaeilzadeh Khadem
Keyword(s):  
Piezoelectric Element ◽  
Dissipated Energy ◽  
Vibration Energy ◽  
Energy Scavenging ◽  
Optimization Approach ◽  
Energy Harvesters ◽  
Energy Pumping ◽  
Nonlinear Energy Pumping ◽  
Energy Dissipated ◽  
Nonlinear Energy

This paper presents an optimal design for a system comprising multiple nonlinear energy sinks (NESs) and piezoelectric-based vibration energy harvesters attached to a free–free beam under shock excitation. The energy harvesters are used for scavenging vibration energy dissipated by the NESs. Grounded and ungrounded configurations are examined, and the systems parameters are optimized globally to maximize the dissipated energy by the NESs. The performance of the system was optimized using a dynamic optimization approach. Compared to the system with only one NES, using multiple NESs resulted in a more effective realization of nonlinear energy pumping particularly in the ungrounded configuration. Having multiple piezoelectic elements also increased the harvested energy in the grounded configuration relative to the system with only one piezoelectric element.

SHOCK ISOLATION THROUGH PASSIVE ENERGY PUMPING CAUSED BY NONSMOOTH NONLINEARITIES

2005 ◽  
Vol 15 (06) ◽  
pp. 1989-2001 ◽  
Author(s):  
F. GEORGIADIS ◽  
A. F. VAKAKIS ◽  
D. M. MCFARLAND ◽  
L. BERGMAN
Keyword(s):  
Vibration Absorber ◽  
Primary System ◽  
Linear Vibration ◽  
Practical Applications ◽  
Energy Pumping ◽  
Weakly Coupled ◽  
Nonlinear Energy Pumping ◽  
Shock Isolation ◽  
Isolation Performance ◽  
Nonlinear Energy

We investigate shock isolation designs based on nonlinear energy pumping caused by nonsmooth stiffness elements. In particular, we numerically study the shock isolation properties of a primary linear system of two coupled nonconservative oscillators with weakly coupled attachments possessing clearance nonlinearities. Under shock excitation the nonlinear attachments (termed nonlinear energy sinks — NESs) can be designed to absorb a significant portion of the input energy, thus enhancing the shock isolation performance of the primary system. In contrast to the classical linear vibration absorber whose operation is restricted to narrowband frequency ranges, the NESs are capable of efficiently absorbing energies caused by transient broadband disturbances, a feature that facilitates their implementation in practical applications. Moreover, the nonsmooth nonlinearities considered in this work are easily implementable since they are realized by means of linear stiffness elements.

Motion Confinement in a Linear Chain of Coupled Oscillators With a Strongly Nonlinear End Attachment

2003 ◽  
Author(s):  
Leonid Manevitch ◽  
Oleg Gendelman ◽  
Andrey I. Musienko ◽  
Alexander F. Vakakis ◽  
Lawrence Bergman
Keyword(s):  
Coupled Oscillators ◽  
Nonlinear Oscillator ◽  
Linear Chain ◽  
Standing Waves ◽  
Strongly Nonlinear ◽  
Resonant Interactions ◽  
Energy Pumping ◽  
Weakly Coupled ◽  
Strongly Nonlinear Oscillator ◽  
Infinite Linear

We study the dynamics of a semi-infinite linear chain of particles that is weakly coupled to a strongly nonlinear oscillator at its free end. We analyze families of localized standing waves situated inside the lower or upper attenuation zones of the linear chain, corresponding to energy predominantly confined in the nonlinear oscillator. These families of standing waves are generated due to resonant interactions between the chain and the nonlinear attachment. A scenario for the realization of energy pumping phenomena in the system under consideration is discussed, and is confirmed by direct numerical simulations of the chain-attachment dynamic interaction.

Steady-State Dynamics of Smooth and Non-Smooth Systems With Strong Nonlinearities

2003 ◽  
Author(s):  
Xiaoai Jiang ◽  
Alexander F. Vakakis
Keyword(s):  
Steady State ◽  
Vibration Isolation ◽  
High Order ◽  
State Behavior ◽  
Energy Pumping ◽  
Nonlinear Energy Pumping ◽  
Clearance Nonlinearity ◽  
High Order Nonlinearity ◽  
Odd Nonlinearity ◽  
Nonlinear Energy

The nonlinear energy sinks (NESs) with strong essential stiffness nonlinearities have been shown to result in vibration isolation in the studied system. In comparison, we also studied the steady-state dynamic response of a system with its smooth high-order odd nonlinearity replaced with the best fitted nonsmooth “clearance nonlinearity”. The analysis was based on the complexification technique and the separation of the dynamic terms into the “slow-varying” and the “fast-varying” components. We found that the steady-state behavior of a system with the non-smooth NES resembles that of the system with the smooth high-order nonlinearity, preserving the nonlinear energy-pumping feature. This finding paves the way for constructing practical NESs and applying them to practical vibration-isolation problems.

Shock Isolation Through Passive Energy Pumping in a System With Piecewise Linear Stiffnesses

2003 ◽  
Author(s):  
Fotios Georgiadis ◽  
Alexander F. Vakakis ◽  
D. Michael McFarland ◽  
Lawrence Bergman
Keyword(s):  
Piecewise Linear ◽  
Primary System ◽  
Linear Vibration ◽  
Practical Applications ◽  
Energy Pumping ◽  
Weakly Coupled ◽  
Nonlinear Energy Pumping ◽  
Shock Isolation ◽  
Isolation Performance ◽  
Nonlinear Energy

We investigate shock isolation designs based on nonlinear energy pumping caused by piecewise stiffness elements. In particular, we numerically study the shock isolation properties of a primary linear system of two coupled non-conservative oscillators with weakly coupled attachments possessing clearance nonlinearities. Under shock excitation the nonlinear attachments (termed nonlinear energy sinks – NESs) can be designed to absorb a significant portion of the input energy, thus enhancing the shock isolation performance of the primary system. In contrast to the classical linear vibration absorber whose operation is restricted to narrowband frequency ranges, the NESs are capable of efficiently absorbing energies caused by transient broadband disturbances, a feature that facilitates their implementation in practical applications. Moreover, the non-smooth nonlinearities considered in this work are easily implementable since they are realized by means of linear stiffness elements.

Targeted Energy Transfer With Several NES in Parallel: Theory and Experiments

2009 ◽  
Author(s):  
Alireza Ture Savadkoohi ◽  
Stephane Pernot ◽  
Claude Henri Lamarque
Keyword(s):  
Nonlinear Energy Sink ◽  
Single Degree Of Freedom ◽  
Strongly Nonlinear ◽  
Seismic Engineering ◽  
Energy Pumping ◽  
In Series ◽  
Energy Sink ◽  
Energy Activation ◽  
Nonlinear Energy ◽  
Theory And Experiments

The crucial point in the field of seismic engineering is to diminish the induced vibration energy as much as possible in a fast and almost irreversible manner. Recently the concept of Nonlinear Energy Sink (NES) has been developed such that the imposed energy to a linear single Degree of Freedom (DoF) substructure is transferred to one or series of strongly nonlinear light attachments; the mechanism is based on a 1:1 resonance capture. Nonlinear attachments can be designed to passively vibrate with any frequency; hence the system is efficient for both of transient and periodic excitations. Some drawbacks of these systems are as follows: they cannot kill the first peak of oscillation in the free time response that is linked to the energy activation of NES; moreover, the transformation of energy vanishes in time due to decrease of the strength of energy pumping. Using NES in series even cannot accelerate the phenomenon of energy pumping and some strange behavior due to the delay in the cooperation of NES in series is noticed. In this study, the transient dynamic behavior of multiple DoF systems with trees of parallel NES at each DoF is investigated, then experimental and numerical results of a four DoF structure with two parallel NES at the top floor are demonstrated and commented upon.

Study on Dynamics of a Nonlinear Damping Absorber Coupled to the Linear System

2010 ◽  
Vol 143-144 ◽  
pp. 763-767
Author(s):  
Si Mi Tang ◽  
Shi Jian Zhu ◽  
Jing Jun Lou
Keyword(s):  
Linear System ◽  
Engineering Application ◽  
Nonlinear Energy Sink ◽  
Nonlinear Damping ◽  
Vibration Absorber ◽  
Energy Pumping ◽  
Nonlinear Energy Pumping ◽  
And Performance ◽  
Quadratic Damping ◽  
Nonlinear Energy

The dynamics of a two degree-of-freedom (DOF) system consisting of a linear system coupled with a quadratic damping vibration absorber is studied. The nonlinear energy pumping phenomenon is verified by simulation and analyzed by Hilbert Transform. Performance of the quadratic damping absorber that is able to absorb vibration over a broad range of frequency (nonlinear energy sink, NES) is studied, and the results are compared with that of the classical linear vibration absorber. The relationship between parameters and performance of the absorber is analyzed, that is significant for engineering application.

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