Passive Nonlinear Energy Pumping in Coupled Oscillators: Steady State Results

2003 ◽  
Author(s):  
Xiaoai Jiang ◽  
D. Michael McFarland ◽  
Lawrence A. Bergman ◽  
Alexander F. Vakakis
Keyword(s):  
Steady State ◽  
A Priori ◽  
Coupled System ◽  
Nonlinear Energy Sink ◽  
Vibration Energy ◽  
Frequency Sweep ◽  
Main Structure ◽  
Energy Pumping ◽  
Weakly Coupled System ◽  
Nonlinear Energy

We study theoretically and numerically the effect that a nonlinear energy sink (NES) has on the steady state dynamics of a weakly coupled system. The NES possesses essentially nonlinear (nonlinearizable) stiffness nonlinearity of the third degree. We find that, in contrast to the classical linear vibration absorber, the NES is capable of absorbing steady state vibration energy from the linear oscillator over a relatively broad frequency range. This results in localization of the steady state vibration in the NES, away from the directly forced subsystem. For a forward frequency sweep the localized branch of steady state motions is suddenly eliminated by a jump to a linearized low-amplitude motion, whereas, for a backward frequency sweep a reverse jump occurs. The difference in the frequencies of the two jumps introduces a nonlinear hysteresis loop. This work extends to the steady state case of earlier transient passive energy pumping results. The notion of passively transferring vibration energy to an a priori determined NES, weakly attached to a main structure, is novel. The use of essentially nonlinear energy sinks for passively absorbing energy from a linear main structure can form the basis of relatively simple and modular vibration and shock isolation designs of mechanical systems.

Nonlinear Energy Pumping With Strongly Nonlinear Coupling: Identification of Resonance Captures in Numerical and Experimental Results

2005 ◽  
Author(s):  
E. Gourdon ◽  
S. Coutel ◽  
C. H. Lamarque ◽  
S. Pernot
Keyword(s):  
Normal Modes ◽  
Coupled System ◽  
Nonlinear Energy Sink ◽  
Nonlinear Normal Modes ◽  
Small Mass ◽  
Abrupt Decrease ◽  
Building Model ◽  
Energy Pumping ◽  
Nonlinear Normal ◽  
Nonlinear Energy

The present work aims to study the effect of a nonlinear energy sink (NES) with relatively small mass on the dynamics of a coupled system under impulsion with free oscillations. The process of energy transfer is governed by structure of damped nonlinear normal modes of the system. In particular the energy pumping occurs if the nonlinear normal mode is quickly broken down with rather abrupt decrease of both amplitudes, i.e. a bifurcation (brutal change of frequency) is associated with the breakdown of the resonant regime of vibrations. The theoretical effects are experimentally verified with a mechanical experiment which confirms the above results by using a small building model. To identify those frequency migrations, a new wavelet-based methodology, namely quasi-continuous wavelet method, is used.

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.

Nonlinear Energy Sink With Uncertain Parameters

2006 ◽  
Vol 1 (3) ◽  
pp. 187-195 ◽  
Author(s):  
E. Gourdon ◽  
C. H. Lamarque
Keyword(s):  
Normal Modes ◽  
Nonlinear Energy Sink ◽  
Nonlinear Normal Modes ◽  
Supplementary Information ◽  
Uncertain Parameters ◽  
Energy Pumping ◽  
Energy Sink ◽  
Nonlinear Normal ◽  
Polynomial Chaos Expansions ◽  
Nonlinear Energy

The effects of a nonlinear energy sink during the instationary regime are analyzed by introducing uncertain parameters to verify the robustness of the transient spatial energy transfer when parameters are not well known. It was shown that it is possible to passively absorb energy from a linear nonconservative system (damped) structure to a nonlinear attachment weakly coupled to the linear one. This rapid and irreversible transfer of energy, named energy pumping, is studied by taking into account uncertainties on parameters, especially damping (since damping plays a great role and there is a lack of knowledge about it). In essence, the nonlinear subsystem acts as a passive nonlinear energy sink for impulsively applied external vibrational disturbances. The aim is to be able to apply energy pumping in practice where the nonlinear attachment realization will never perfectly reflect the design. Since strong nonlinearities are involved, polynomial chaos expansions are used to obtain information about random displacements. Not only are numerical investigations done, but nonlinear normal modes and the role of damping are also analytically studied, which confirms the numerical studies and shows the supplementary information obtained compared to a parametrical study.

Vortex-Induced Vibration of a Sprung Rigid Circular Cylinder Augmented With a Nonlinear Energy Sink

2012 ◽  
Author(s):  
Ravi Kumar R. Tumkur ◽  
Ramon Calderer ◽  
Arif Masud ◽  
Lawrence A. Bergman ◽  
Alexander F. Vakakis ◽  
...  
Keyword(s):  
Circular Cylinder ◽  
Stokes Equations ◽  
Computational Study ◽  
Coupled System ◽  
Nonlinear Energy Sink ◽  
Small Mass ◽  
Limit Cycle Oscillation ◽  
Vortex Induced Vibration ◽  
Energy Sink ◽  
Nonlinear Energy

We study the nonlinear fluid-structure interaction of an elastically supported rigid circular cylinder in a laminar flow. Periodic shedding of counter-rotating vortices from either side of the cylinder results in vortex-induced vibration of the cylinder. We demonstrate the passive suppression of the limit cycle oscillation (LCO) of the cylinder with the use of an essentially nonlinear element, the nonlinear energy sink (NES). The computational study is performed at a Reynolds number (Re) of 100; Re is defined based on the cylinder diameter and inlet velocity. The variational multiscale residual-based stabilized finite-element method is used to compute approximate solutions of the incompressible Navier-Stokes equations. The NES is comprised of a small mass, an essentially nonlinear spring, and a linear damper. With appropriate values for the NES parameters, the coupled system of flow-cylinder-NES exhibits resonant interactions, resulting in targeted energy transfer (TET) from the flow via the cylinder to the NES, where the energy is dissipated by the linear damper. The NES interacts with the fluid via the cylinder by altering the phase relation between the lift force and the cylinder displacement; this brings about significant reduction in the LCO amplitude of the cylinder for several set of values of the NES parameters.

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.

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