Optimal Performance Comparison of Nonlinear Energy Sinks and Linear Tuned Mass Dampers

2021 ◽  
Author(s):  
Ivan Yegorov (Egorov) ◽  
Austin Uden ◽  
Daniil Yurchenko
Keyword(s):  
Nonlinear Energy Sink ◽  
Free Vibrations ◽  
Performance Comparison ◽  
Optimal Performance ◽  
Primary System ◽  
Secondary System ◽  
Impulsive Excitation ◽  
Secondary Systems ◽  
Energy Sink ◽  
Nonlinear Energy

Abstract This paper studies a targeted energy transfer (TET) mechanism for a two-degree-of-freedom (TDOF) model in free vibration. The model comprises a primary linear system and a secondary system in the form of an energy sink which can be nonlinear. The free vibrations are considered subject to an impulsive excitation exerted on the primary system, leading to a nonzero initial velocity. The goal is to obtain the spring parameters in the nonlinear energy sink (NES) so as to maximize an energy dissipation measure (EDM) representing the percentage of impulsive energy that is absorbed and dissipated in the NES. A global optimization algorithm is used for this purpose. The optimal performance is assessed for the purely linear, linear-cubic, and purely cubic configurations of the spring connecting the primary and secondary systems. The corresponding results are compared with each other. The optimization process is performed for the EDM averaged over given ranges of the initial impulse and natural frequency in the primary system. It is shown that the type of the optimal configuration can vary depending on these ranges.

Reliability analysis of the hysteretic nonlinear energy sink in shock mitigation considering uncertainties

2020 ◽  
Vol 26 (23-24) ◽  
pp. 2261-2273 ◽  
Author(s):  
George C Tsiatas ◽  
Dimitra A Karatzia
Keyword(s):  
Reliability Analysis ◽  
Nonlinear Energy Sink ◽  
System Response ◽  
Primary System ◽  
Dissipation Energy ◽  
Linear Elastic ◽  
Shock Mitigation ◽  
Energy Sink ◽  
Elastic Spring ◽  
Nonlinear Energy

The reliability of the hysteretic nonlinear energy sink in shock mitigation is investigated herein. The hysteretic nonlinear energy sink is a passive vibration control device which is coupled to a primary linear oscillator. Apart from its small mass and a nonlinear elastic spring of the Duffing oscillator, it also comprises a purely hysteretic and a linear elastic spring of potentially negative stiffness. The Bouc–Wen model is used to describe the force produced by both the purely hysteretic and linear elastic springs. The hysteretic nonlinear energy sink protects the primary system through the energy pumping mechanism which transfers energy from the primary system and dissipates it in the hysteretic nonlinear energy sink. Three nonlinear equations of motion describe the resulting two-degree-of-freedom system response. The parameters of the system to be considered as uncertain are the natural frequency of the primary system and the hysteretic nonlinear energy sink linear elastic spring, which follow a normal distribution. A reliability analysis is then performed to evaluate the robustness of the coupled system in the presence of uncertainty. Specifically, the reliability index is calculated based on first passage probabilities of distinct dissipation energy level crossings using the Monte Carlo method. Several examples are examined considering various levels of initial input energy, and useful conclusions are drawn concerning the influence of uncertainty in the system robustness.

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.

Design and performance analysis of a nonlinear energy sink attached to a beam with different support conditions

2015 ◽  
Vol 230 (4) ◽  
pp. 527-542 ◽  
Author(s):  
Majid Kani ◽  
Siamak E Khadem ◽  
Mohammad H Pashaei ◽  
Morteza Dardel
Keyword(s):  
Particle Swarm Optimization ◽  
Performance Analysis ◽  
Nonlinear Energy Sink ◽  
Optimization Method ◽  
Primary System ◽  
Swarm Optimization ◽  
Energy Sink ◽  
Support Conditions ◽  
And Performance ◽  
Nonlinear Energy

In this work, design and performance analysis of a nonlinear energy sink, attached to a beam (the primary system) with different support conditions, will be investigated. Here, the effects of both beam properties and external shock excitation are studied. For this purpose, equations of motion are derived by the Lagrange method. Then, parameters of the nonlinear energy sink are optimized by both sensitivity analysis and particle swarm optimization method. The results show that, increasing the first natural frequency of the primary system, on which an external impulse is imposed, will postpone the nonlinear energy sink activation. Also, increasing the amplitude of the shock excitation will tend to decrease the optimum value of the nonlinear energy sink stiffness. Using the particle swarm optimization method to obtain the optimized parameters of the nonlinear energy sink and its interaction with the primary system, which is a continuous one, is a new research area presented in this work.

An Eccentric Rotator as a Novel Design of a Nonlinear Energy Sink

2011 ◽  
Author(s):  
Oleg V. Gendelman ◽  
Grigori Sigalov ◽  
Mercedes Mane ◽  
Lawrence A. Bergman ◽  
Alexander F. Vakakis ◽  
...  
Keyword(s):  
Numerical Study ◽  
Nonlinear Energy Sink ◽  
Primary System ◽  
Targeted Energy Transfer ◽  
Impulsive Loads ◽  
Chaotic Modes ◽  
Energy Sink ◽  
Novel Design ◽  
Nonlinear Energy ◽  
Good Agreement

We introduce a novel type of the nonlinear energy sink (NES) designed as an eccentric mass rotating within a horizontal plane. The gravity is not a factor here, therefore such a rotator has no eigenfrequency and can inertially couple and resonate with any mode of the primary system. The dynamics of the system consisting of a primary linear oscillator and the eccentric rotator is rich beyond expectations and features multiple resonances and chaotic modes. A numerical study shows that the system, when subject to high impulsive loads, inevitably enters a 1:1 resonance that enables highly efficient targeted energy transfer from the primary mass to the NES. The results of an experimental investigation are in good agreement with the analytical and numerical estimates.

scholarly journals Tuned Nonlinear Energy Sink With Conical Spring: Design Theory and Sensitivity Analysis

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Donghai Qiu ◽  
Sébastien Seguy ◽  
Manuel Paredes
Keyword(s):  
Sensitivity Analysis ◽  
Design Theory ◽  
Linear Part ◽  
Nonlinear Energy Sink ◽  
Design Criterion ◽  
Primary System ◽  
System Specification ◽  
Energy Sink ◽  
Negative Stiffness Mechanism ◽  
Nonlinear Energy

This paper is devoted to the study of a nonlinear energy sink (NES) intended to attenuate vibration induced in a harmonically forced linear oscillator (LO) and working under the principle of targeted energy transfer (TET). The purpose motivated by practical considerations is to establish a design criterion that first ensures that the NES absorber is activated and second provides the optimally tuned nonlinear stiffness for efficient TET under a given primary system specification. Then a novel NES design yielding cubic stiffness without a linear part is exploited. To this end, two conical springs are specially sized to provide the nonlinearity. To eliminate the linear stiffness, the concept of a negative stiffness mechanism is implemented by two cylindrical compression springs. A small-sized NES system is then developed. To validate the concept, a sensitivity analysis is performed with respect to the adjustment differences of the springs and an experiment on the whole system embedded on an electrodynamic shaker is studied. The results show that this type of NES can not only output the expected nonlinear characteristics, but can also be tuned to work robustly over a range of excitation, thus making it practical for the application of passive vibration control.

scholarly journals Integration of Geometrical and Material Nonlinear Energy Sink with Piezoelectric Material Energy Harvester

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Ye-Wei Zhang ◽  
Chuang Wang ◽  
Bin Yuan ◽  
Bo Fang
Keyword(s):  
Vibration Control ◽  
Energy Harvester ◽  
Mechanical Energy ◽  
Piezoelectric Element ◽  
Nonlinear Energy Sink ◽  
Primary System ◽  
Hysteresis Behavior ◽  
Energy Sink ◽  
Material Nonlinear ◽  
Nonlinear Energy

This paper presents a novel design by integrating geometrical and material nonlinear energy sink (NES) with a piezoelectric-based vibration energy harvester under shock excitation, which can realize vibration control and energy harvesting. The nonlinear spring and hysteresis behavior of the NES could reflect geometrical and material nonlinearity, respectively. Two configurations of the piezoelectric device, including the piezoelectric element embedded between the NES mass and the single-degree-of-freedom system or ground, are utilised to examine the energy dissipated by damper and hysteresis behavior of NES and the energy harvested by the piezoelectric element. Similar numerical research methods of Runge-Kutta algorithm are used to investigate the two configurations. The energy transaction measure (ETM) is adopted to examine the instantaneous energy transaction between the primary and the NES-piezoelectricity system. And it demonstrates that the dissipated and harvested energy transaction is transferred from the primary system to the NES-piezoelectricity system and the instantaneous transaction of mechanical energy occupies a major part of the energy of transaction. Both figurations could realize vibration control efficiently.

Design and Application of a Nonlinear Energy Sink to Mitigate Vibrations of an Air Spring Supported Slab

2005 ◽  
Author(s):  
Sanjay Goyal ◽  
Timothy M. Whalen
Keyword(s):  
Vibrational Energy ◽  
Low Frequency ◽  
Nonlinear Energy Sink ◽  
Design Parameters ◽  
Primary System ◽  
Air Spring ◽  
Low Frequency Vibration ◽  
Energy Sink ◽  
Isolation Device ◽  
Nonlinear Energy

In this paper we consider the application of a nonlinear energy sink (NES), a passive isolation device, to damp out energy from the low frequency modes of an air-spring supported slab to be installed at Purdue University’s Birck Nanotechnology Center. Analytical expressions to obtain energy sink design parameters, given some primary system specifications, have been derived. These expressions are then used to design the NES for the Birck air-spring supported slab. The designed NES is then analyzed via finite elements to study its efficacy in absorbing low frequency vibration from the slab. The study reveals that NES can serve as a good aid in dissipating vibrational energy induced by small disturbances in the slab.

scholarly journals Variable pitch spring for nonlinear energy sink: Application to passive vibration control

2018 ◽  
Vol 233 (2) ◽  
pp. 611-622 ◽  
Author(s):  
Donghai Qiu ◽  
Manuel Paredes ◽  
Sébastien Seguy
Keyword(s):  
Vibration Control ◽  
Nonlinear Energy Sink ◽  
Displacement Function ◽  
Generic Model ◽  
Primary System ◽  
Passive Vibration Control ◽  
Variable Pitch ◽  
Energy Sink ◽  
Force Displacement ◽  
Nonlinear Energy

This paper aims to propose a generalized methodology for designing a novel nonlinear energy sink with variable pitch springs. To this end, a generic model of the nonlinear energy sink system providing the nonlinearity of pure cubic stiffness is introduced. Key features of the model include: (i) specifically sizing two variable pitch springs to provide the force polynomial components with only linear and cubic terms; (ii) pre-compressing two springs at the transition point to produce smooth nonlinear force characteristics; (iii) adding a negative stiffness mechanism to counterbalance the linear term. To generate the variable pitch spring, design parametrization is implemented. The type of shape and the pitch distribution adopted for the spring are shown to fit the objective force–displacement function well. To validate the concept, a special sized nonlinear energy sink system is developed. Identification of the force–displacement relation and experiments for the whole system embedded on an electrodynamic shaker are studied. The results show that this nonlinear energy sink can not only output the anticipated nonlinearity, but can also produce energy pumping to protect the primary system in a large band of frequencies, thus making it practical for the application of passive vibration control.

Evaluation of Energy and Power Flow in a Nonlinear Energy Sink Attached to a Linear Primary Oscillator

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Christian E. Silva ◽  
Amin Maghareh ◽  
Hongcheng Tao ◽  
Shirley J. Dyke ◽  
James Gibert
Keyword(s):  
Power Flow ◽  
Degrees Of Freedom ◽  
Nonlinear Energy Sink ◽  
Primary System ◽  
Combined System ◽  
Analytical Treatment ◽  
Different Types ◽  
Energy Sink ◽  
And Performance ◽  
Nonlinear Energy

Abstract The objective of this study is to develop a novel methodology to assess the energy flow between a nonlinear energy sink (NES) and the primary system it is attached to in terms of energy orientation, which is directly related to the sign of the power present on the primary system. To extend the work done in previous studies, which have focused primarily on the analytical treatment, characterization, and performance evaluation of NES as passive nonlinear dampers for structures under different types of excitations, this study incorporates a methodology for determining whether energy is entering or leaving a primary oscillator when interacting with an NES, by means of considering the power flow of the primary oscillator. Several current measures for evaluating the effectiveness of the NES at extracting and dissipating energy irreversibly are considered through numerical simulations of systems with different damping cases of the NES. Each case provides a different dissipation scenario in the combined system, which is subjected to different types of base excitation signals such as impulse and seismic records. The methodology is further validated experimentally using a two degrees-of-freedom system with an NES attached to the second mass. Comparisons of the modeled responses versus the measured responses are provided for several physical damping realization scenarios in the NES.

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