Effects of bi-stable grounded nonlinear energy sink on energy dissipation of the system

2021 ◽  
pp. 146441932110460
Author(s):  
Arash Khalatbari ◽  
Amir Jalali ◽  
Habib Ahmadi ◽  
Kamran Foroutan
Keyword(s):  
Energy Dissipation ◽  
Total Energy ◽  
Invariant Manifolds ◽  
Equations Of Motion ◽  
Nonlinear Energy Sink ◽  
Multiple Scale ◽  
Excitation Amplitude ◽  
Energy Pumping ◽  
Energy Sink ◽  
Nonlinear Energy

In this paper, one of the most efficient passive absorbers, called nonlinear energy sink (NES), is analytically studied. A two-degree-of-freedom system is considered which consists of a linear oscillator (LO) with a base excitation and an NES, called grounded NES (GNES), which is connected to the ground with a nonlinear spring. In this study, we proposed a new arrangement of potential elements in GNES and studied invariant manifolds of the system, as well as the energy absorption performance of the NES. The system is considered in the vicinity of 1:1 resonance to investigate the strongly modulated response (SMR). To this end, after obtaining the equations of motion, the Manevitch complex variable and multiple scale method are applied to solve the equations, analytically. Then, the slow invariant manifold (SIM) is obtained. Also, the energy dissipation ratio of the NES and the percentage of the instantaneous total energy stored in the NES are calculated via the time-amplitude diagram. The results show that when the nonlinear effect decreases, the occurrence of energy pumping is less probable. Also, when the excitation amplitude decreases, the percentage of the instantaneous total energy stored in the NES increases as well as the amount of energy dissipation.

Piezoelectric Actuated Nonlinear Energy Sink With Tunable Attenuation Efficiency

2019 ◽  
Vol 87 (2) ◽  
Author(s):  
Jian Zhao ◽  
Ming Lyu ◽  
Hongxi Wang ◽  
Najib Kacem ◽  
Yu Huang ◽  
...  
Keyword(s):  
Nonlinear Energy Sink ◽  
Mathematic Model ◽  
Threshold Value ◽  
Excitation Amplitude ◽  
Wide Frequency Range ◽  
Application Range ◽  
High Attenuation ◽  
Energy Pumping ◽  
Energy Sink ◽  
Nonlinear Energy

Abstract Comparing to linear vibration absorbers, nonlinear energy sinks (NESs) have attracted worldwide attention for their intrinsic characteristics of targeted energy transfer or energy pumping in a relatively wide frequency range. Unfortunately, they are highly dependent on the vibration amplitude to be attenuated and will play its role only if the external load exceeds a specific threshold value. Different from the passive bistable NES, a novel piezoelectric nonlinear energy sink (PNES) is designed by introducing in-phase actuation to compensate or enhance the external vibration loads, thus triggering the NES operating in high attenuation efficiency. The nonlinear mathematic model of the PNES is established for investigating the dynamic response and determining the threshold compensation strategy. And the results show that the maximum attenuation efficiency can be improved by 58.16% compared to the traditional passive NES. Also, the amplitude-dependent coefficient (ADC) can be significantly reduced to 0.33 from 1.0, which means that the PNES can effectively mitigate vibrations even when the excitation amplitude is 67% smaller than the original threshold value. Finally, the feasibility of the in-phase compensation method is experimentally validated, which can further expand the application range of NES.

The effects of nonlinear energy sink and piezoelectric energy harvester on aeroelastic instability of an airfoil

2021 ◽  
pp. 107754632199358
Author(s):  
Ali Fasihi ◽  
Majid Shahgholi ◽  
Saeed Ghahremani
Keyword(s):  
Energy Harvester ◽  
Equations Of Motion ◽  
Continuation Method ◽  
Dynamical Behavior ◽  
Harmonic Balance Method ◽  
Nonlinear Energy Sink ◽  
Piezoelectric Energy ◽  
Energy Sink ◽  
Two Degree Of Freedom ◽  
Nonlinear Energy

The potential of absorbing and harvesting energy from a two-degree-of-freedom airfoil using an attachment of a nonlinear energy sink and a piezoelectric energy harvester is investigated. The equations of motion of the airfoil coupled with the attachment are solved using the harmonic balance method. Solutions obtained by this method are compared to the numerical ones of the pseudo-arclength continuation method. The effects of parameters of the integrated nonlinear energy sink-piezoelectric attachment, namely, the attachment location, nonlinear energy sink mass, nonlinear energy sink damping, and nonlinear energy sink stiffness on the dynamical behavior of the airfoil system are studied for both subcritical and supercritical Hopf bifurcation cases. Analyses demonstrate that absorbing vibration and harvesting energy are profoundly affected by the nonlinear energy sink parameters and the location of the attachment.

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.

scholarly journals Design Optimisation of a Nonlinear Energy Sink Embedded on a Harmonically Forced Linear Oscillator: Theoretical and Experimental Developments

2012 ◽  
Author(s):  
Etienne Gourc ◽  
Guilhem Michon ◽  
Sébastien Seguy ◽  
Alain Berlioz
Keyword(s):  
Invariant Manifolds ◽  
Relaxation Oscillation ◽  
Design Procedure ◽  
Nonlinear Energy Sink ◽  
Experimental Results ◽  
Linear Oscillator ◽  
Mapping Procedure ◽  
Modulation Equations ◽  
Energy Sink ◽  
Nonlinear Energy

In this paper, the dynamic response of a harmonically forced Linear Oscillator (LO) strongly coupled to a Nonlinear Energy Sink (NES) is investigated theoretically and experimentally. The system studied comprises a linear oscillator subject to an imposed displacement with an embedded, purely cubic, NES. The behavior of the system is analyzed in the vicinity of 1:1 resonance. The complexification averaging technique is used to obtain modulation equations and the associated fixed points. These modulation equations are analyzed using asymptotic expansion to study the regimes related as relaxation oscillation of the slow flow called Strongly Modulated Response (SMR). The zones where SMR occur are computed using a mapping procedure. The Slow Invariant Manifolds (SIM) is used to derive a proper optimization procedure. It is shown that there exist an optimal zone in the parameter plane forcing amplitude–nonlinear stiffness, where SMR occurs without having a high amplitude detached resonance tongue. An experimental setup exhibits a strong mass asymmetry (mass ratio ≈ 1%). The cubic stiffness is realized geometrically with two linear spring that extend axially and are free to rotate. Using the previous optimized stiffness of the NES, different frequency response curves and associated zones of SMR are obtained for various forcing amplitude. Good agreement between theoretical and experimental results is observed. The reported experimental results confirm the design procedure, and the possible application of NES for vibration mitigation under periodic forcing.

scholarly journals Chatter Control in Turning Process with a Nonlinear Energy Sink

2013 ◽  
Vol 698 ◽  
pp. 89-98 ◽  
Author(s):  
Etienne Gourc ◽  
Sébastien Seguy ◽  
Guilhem Michon ◽  
Alain Berlioz
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Nonlinear Energy Sink ◽  
Turning Process ◽  
Strongly Coupled ◽  
Different Types ◽  
Chatter Control ◽  
Energy Sink ◽  
Nonlinear Energy ◽  
Cubic Stiffness

This paper presents the interest of an original absorber of vibration in order to reduce chatter vibration in turning process. The device is composed of a linear oscillator corresponding to a flexible cutting tool subject to chatter strongly coupled to a Nonlinear Energy Sink (NES), with purely cubic stiffness. The novelty of this work is the use of a nonlinear cutting law, more accurate for modeling the cutting process. The delayed equations of motion are analyzed using a combination of the method of multiple scales and harmonic balance. Different types of responses regimes are revealed such as periodic response and also Strongly Modulated Response (SMR). Analytic results are then compared with numerical simulations. Finally, the potential of the NES is demonstrated to control chatter in turning process.

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.

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.

scholarly journals Free Response of a Rotational Nonlinear Energy Sink: Complete Dissipation of Initial Energy for Small Initial Rectilinear Displacements

2020 ◽  
Vol 88 (1) ◽  
Author(s):  
Ke Ding ◽  
Arne J. Pearlstein
Keyword(s):  
Coupling Parameter ◽  
Equations Of Motion ◽  
Nonlinear Energy Sink ◽  
Initial Energy ◽  
Rectilinear Motion ◽  
Initial Condition ◽  
Free Response ◽  
Primary Mass ◽  
Energy Sink ◽  
Nonlinear Energy

Abstract For two combinations of a dimensionless rotational damping parameter and a dimensionless inertial coupling parameter, we consider free response of a rectilinearly vibrating linearly sprung primary mass inertially coupled to damped rotation of a second mass, for which Gendelman et al. (2012, “Dynamics of an Eccentric Rotational Nonlinear Energy Sink,” ASME J. Appl. Mech. 79(1), 011012) developed equations of motion in the context of a rotational nonlinear energy sink (NES) with no direct damping of the rectilinear motion. For dimensionless initial rectilinear displacements comparable with those considered by Gendelman et al., we identify a region in the motionless projection of the initial condition space (i.e., for zero values of the initial rectilinear and rotational velocities) in which every initial condition leads to a previously unrecognized zero-energy solution, with all initial energy dissipated by rotation. We also show that the long-time nonrotating, rectilinear solutions of the type found by Gendelman et al. are (orbitally) stable only in limited ranges of amplitude. Finally, we show how direct viscous damping of rectilinear motion of the primary mass affects dissipation, and that results with no direct rectilinear dissipation provide excellent guidance for performance when direct rectilinear dissipation occurs. Some applications are discussed.

scholarly journals Global Dynamics and Optimal Design of a New Highly Efficient Nonlinear Energy Sink Based on Magnetic-Elastic Impacts with Negative Stiffness

2021 ◽  
Author(s):  
Shuangbao Li ◽  
Tingting Wang ◽  
Jianen Chen
Keyword(s):  
Energy Dissipation ◽  
Optimal Design ◽  
Nonlinear Energy Sink ◽  
Negative Stiffness ◽  
Global Dynamics ◽  
Elastic Impact ◽  
Highly Efficient ◽  
Dissipation Rates ◽  
Energy Sink ◽  
Nonlinear Energy

Abstract A new highly efficient elastic-impact bistable nonlinear energy sink (EI-BNES) based on magnetic-elastic impacts with negative stiffness and bistability is proposed and optimized through global dynamical analysis. The EI-BNES has better robustness and higher energy dissipation rates with nearly more than 96.5\% for broadband impulsive excitations than the traditional cubic NESs and single bistable NESs. The structure of negative stiffness impacts is realized by reasonable layout of permanent ring magnets and springs. A two-degree-of-freedom (two-DOF) elastic-impact system is established to describe the coupled nonlinear interaction between the main structure and the attached EI-BNES. A global Melnikov reduction analysis (GMRA) is proposed to study global dynamics and homoclinic bifurcations of the reduced two-dimensional subsystem, which is used to explain the mechanism of nonlinear targeted energy transfer (TET) and detect the threshold of impulsive amplitudes of EI-BNES for in-well and compound motions between in-well and cross-well resonance responses. A special type of saddle-center equilibrium points is also found in the non-smooth system of the EI-BNES and can be used to effectively increase the energy dissipation rates. The optimal design criterion of the tuned EI-BNES for better dissipation performance is also first discussed based on the GMRA and numerical techniques for calculating the Melnikov function of the non-smooth systems. The effectiveness of the analytical GMRA is also verified by numerical simulations.

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.

Sign in / Sign up

Export Citation Format

Share Document