Nonlinear Energy Sink With a Non-Traditional Kind of Nonlinear Restoring Force

2015 ◽  
Author(s):  
Mohammad A. Al-Shudeifat
Keyword(s):  
Nonlinear Energy Sink ◽  
Initial Energy ◽  
Type I ◽  
Nonlinear Coupling ◽  
Restoring Force ◽  
Nonlinear Restoring Force ◽  
Coupling Force ◽  
Restoring Forces ◽  
Energy Sink ◽  
Nonlinear Energy

Enhanced nonlinear energy sink (NES) is addressed here by employing a non-traditional kind of a nonlinear restoring force. The usual nonlinear coupling element between the NES and the linear oscillator (LO) in the literature generates essentially nonlinear restoring force between the NES and the LO. Unlike Type I NES, here the nonlinear coupling force has varying components during the oscillation which appear in closed loops under the effect of damping terms. This NES attachment with the LO rapidly absorbs and immediately dissipates significant portion of the initial energy induced into the LO through a strong resonance capture between the NES and LO responses. The proposed design could also be promising for energy harvesting purposes. The obtained results by numerical simulation show that employing this type of nonlinear restoring force for passive targeted energy transfer (TET) is more promising than some other types of NESs in which purely cubic stiffness restoring forces have been incorporated.

Nonlinear Energy Sinks With Nontraditional Kinds of Nonlinear Restoring Forces

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
Mohammad A. AL-Shudeifat
Keyword(s):  
Energy Transfer ◽  
Nonlinear Energy Sink ◽  
Nonlinear Coupling ◽  
Closed Loops ◽  
Strong Resonance ◽  
Shock Mitigation ◽  
Restoring Forces ◽  
Initial Shock ◽  
Energy Sink ◽  
Nonlinear Energy

The nonlinear energy sink (NES) is usually coupled with a linear oscillator (LO) to rapidly transfer and immediately dissipate a significant portion of the initial shock energy induced into the LO. This passive energy transfer and dissipation are usually achieved through strong resonance captures between the NES and the LO responses. Here, a nontraditional set of nonlinear coupling restoring forces is numerically investigated to introduce enhanced versions of the NESs. In this new set of nonlinear coupling restoring forces, one has a varying nonlinear stiffness that includes both of hardening and softening stiffness components during the oscillation, which appear in closed-loops under the effect of the damping. The obtained results by the numerical simulation have shown that employing this kind of the nonlinear restoring forces for passive targeted energy transfer (TET) is promising for shock mitigation.

A Non-Traditional Variant Nonlinear Energy Sink: Transient Responses

2019 ◽  
Author(s):  
Youzuo Jin ◽  
Kefu Liu ◽  
Deli Li ◽  
Liuyang Xiong ◽  
Lihua Tang
Keyword(s):  
Energy Harvester ◽  
Vibration Suppression ◽  
System Modeling ◽  
Nonlinear Energy Sink ◽  
Initial Energy ◽  
Transient Responses ◽  
Continuous Contact ◽  
Magnet Coil ◽  
Energy Sink ◽  
Nonlinear Energy

Abstract In this paper, a non-traditional variant nonlinear energy sink (NES) is developed for simultaneous vibration suppression and energy harvesting in a broad frequency band. The non-traditional variant NES consists of a cantilever beam attached by a pair of magnets at its free end, a pair of the so-called continuous-contact blocks, and a pair of coils. The beam is placed between the continuous-contact blocks. The constraint of the continuous-contact blocks forces the beam to deflect nonlinearly. Each of the magnet-coil pairs forms an electromagnetic energy harvester. Different from a traditional way that attaches the coils to the primary mass, the developed setup has the coils fixed to the base. First, the developed apparatus is described. Subsequently, the system modeling and parameter identification are addressed. The performance of the apparatus under transient responses is examined by using computer simulation. The results show that the proposed apparatus behaves similarly as the NES with the following features: 1:1 resonance, targeted energy transfer, initial energy dependence, etc.

Numerical Investigation of Rotating Nonlinear Energy Sink for Shock Mitigation

2013 ◽  
Author(s):  
Mohammad A. Al-Shudeifat ◽  
Lawrence A. Bergman ◽  
Alexander F. Vakakis
Keyword(s):  
Energy Transfer ◽  
Linear Structure ◽  
Nonlinear Energy Sink ◽  
Initial Energy ◽  
Shock Mitigation ◽  
Nonlinear Targeted Energy Transfer ◽  
Primary Test ◽  
Energy Sink ◽  
Two Degree Of Freedom ◽  
Nonlinear Energy

Passive nonlinear targeted energy transfer (TET) is addressed here by investigating a lightweight rotating nonlinear energy sink (NES). The rotating sink mass has an essentially nonlinear inertial coupling with the two degree-of-freedom linear system (the primary test structure). The proposed rotating NES is numerically investigated where it is found to passively absorb and rapidly dissipate a considerable portion of the initial energy induced by impulse to the linear structure. The parameters of the rotating NES are optimized for the best performance in the vicinity of intermediate and high loads. The fundamental mechanism for significant energy transfer to the NES is its rotational mode; the oscillatory mode of the NES dissipates far less energy. The frequency-energy dependences are investigated through the frequency-energy plot (FEP). Early and strong resonance capture at the lowest modal frequency is observed between the rotator and the structure, at which a significant portion of the induced energy is transferred and dissipated by the rotator. The performance of this device is found to be comparable to existing, stiffness-based NES designs. However, this device is less complicated and more compact.

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.

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.

A Variant Nonlinear Energy Sink for Vibration Suppression and Energy Harvesting

2018 ◽  
Author(s):  
Xiaolin Li ◽  
Kefu Liu ◽  
Liuyang Xiong ◽  
Lihua Tang
Keyword(s):  
Energy Harvesting ◽  
Vibration Suppression ◽  
System Modeling ◽  
Nonlinear Energy Sink ◽  
Initial Energy ◽  
Piezoelectric Energy ◽  
Thin Steel ◽  
Energy Sink ◽  
Thin Steel Plate ◽  
Nonlinear Energy

In this paper a variant nonlinear energy sink (NES) is developed for the purpose of simultaneous vibration suppression and energy harvesting in a broad frequency band. The NES consists of a cantilever beam attached by a mass at its free end and a pair of so-called double-stop blocks. The beam is formed by a piezoelectric energy harvester and a thin steel plate. It is placed between the double-stop blocks. The constraint of the double-stop blocks forces the beam to deflect nonlinearly. First, the developed apparatus is described. Subsequently, system modeling and parameter identification are addressed. The performance of the apparatus under transient responses is examined through both numerical simulation and experimental study. The results show that the proposed apparatus behaves similarly as the NES with the following features: 1:1 resonance, targeted energy transfer, initial energy dependence, etc.

Numerical and Experimental Investigation of a New Nonlinear Energy Sink for Passive Shock Mitigation

2012 ◽  
Author(s):  
Mohammad A. AL-Shudeifat ◽  
Nicholas Wierschem ◽  
Alexander F. Vakakis ◽  
Lawrence A. Bergman ◽  
Billie F. Spencer
Keyword(s):  
Linear Structure ◽  
Nonlinear Energy Sink ◽  
Initial Energy ◽  
Numerical Results ◽  
New Device ◽  
Numerical Predictions ◽  
Energy Sink ◽  
Experimental Findings ◽  
High Level ◽  
Nonlinear Energy

A new device functioning as an efficient nonlinear energy sink (NES) is explored here. The device consists of a mass coupled to a two-story linear test structure through a single-sided vibro-impact (VI) nonlinearity in one direction and a weak linear spring in both directions. This design is found to be more efficient for passive targeted energy transfer (TET) than existing NESs. It absorbs and rapidly dissipates a significant amount of the impulsive energy induced in the linear structure. In addition, some of this initial energy is pumped to higher modes of the structure and efficiently dissipated there. The numerical results have verified that the proposed single-sided VI NES maintains high level of performance over a broad range of high input energies. It performs near to its optimum even for severe induced shocks. Moreover, the numerical results have been experimentally verified; good agreement between numerical predictions and experimental findings was observed.

scholarly journals Experimental Investigation and Theoretical Analysis of a Nonlinear Energy Sink Under Harmonic Forcing

2011 ◽  
Author(s):  
Etienne Gourc ◽  
Guilhem Michon ◽  
Se´bastien Seguy ◽  
Alain Berlioz
Keyword(s):  
Nonlinear Energy Sink ◽  
Linear Oscillator ◽  
Restoring Force ◽  
Modulation Equation ◽  
Nonlinear Dynamical ◽  
Strongly Coupled ◽  
Electrodynamic Shaker ◽  
Energy Sink ◽  
Force Displacement ◽  
Nonlinear Energy

In the present works, we examine experimentally and theoretically the dynamic behavior of linear oscillator strongly coupled to a nonlinear energy sink under external periodic forcing. The nonlinear oscillator has a nonlinear restoring force realized geometrically with two linear springs that extend axially and are free to rotate. Hence, the force-displacement relationship is cubic. The linear oscillator is directly excited via an electrodynamic shaker. Experiments realized on the test bench consist of measuring the displacement of the oscillators while increasing and decreasing frequencies around the fundamental resonance of the linear oscillator. Many nonlinear dynamical phenomena are observed on the experimental setup such as jumps, bifurcation, and quasiperiodic regimes. The retained nonlinear model is a two degree of freedom system. The behavior of the system is then explained analytically and numerically. The complexification averaging technique is used to derive a set of modulation equation governing the evolution of the complex amplitude at the frequency of excitation, and a stability analysis is performed.

Free Response of a Rotational Nonlinear Energy Sink Coupled to a Linear Oscillator: Fractality, Riddling, and Initial-Condition Sensitivity at Intermediate Initial Displacements

2021 ◽  
pp. 1-59
Author(s):  
Ke Ding ◽  
Arne Pearlstein
Keyword(s):  
Initial Conditions ◽  
Nonlinear Energy Sink ◽  
Initial Energy ◽  
Linear Oscillator ◽  
Rectilinear Motion ◽  
Free Response ◽  
Time Harmonic ◽  
Wide Range ◽  
Energy Sink ◽  
Nonlinear Energy

Abstract Free response of a rotational nonlinear energy sink (NES) inertially coupled to a linear oscillator is investigated for dimensionless initial rectilinear displacements ranging from just above the smallest amplitude at which nonrotating, harmonically rectilinear motion is unstable absent direct rectilinear damping, up to the next-largest amplitude at which such motion is orbitally stable. With motionless initial conditions (MICs), i.e., initial velocity of the primary mass and initial angular velocity of the NES mass both zero, predicted behavior for two previously investigated combinations of the dimensionless parameters (characterizing rotational damping, and coupling of rectilinear and rotational motions) differs strongly from that found at smaller initial displacements (2021, J. Appl. Mech. 88, 011005). For both combinations, a wide range of MICs leads to solutions displaying transient chaos and depending sensitively on initial conditions, giving rise to fractality and riddling in the relationship between initial conditions and asymptotic solutions. Absent direct rectilinear damping of the linear oscillator, for one combination of parameters there exists a wide range of MICs with trajectories leading to time-harmonic, orbitally stable “quot;special”quot; solutions with a single amplitude, but no MICs are found for which all initial energy is dissipated. For the other combination, no such special solutions are found, but there exist MICs for which all initial energy is dissipated. With direct rectilinear damping, sensitivity extends to a measure of settling time, which can be extremely sensitive to initial conditions. A statistical approach to this sensitivity is discussed, along with implications for design and implementation.

scholarly journals Piezoelectric energy harvesting with a nonlinear energy sink

2016 ◽  
Vol 28 (3) ◽  
pp. 307-322 ◽  
Author(s):  
Yu Zhang ◽  
Lihua Tang ◽  
Kefu Liu
Keyword(s):  
Energy Harvesting ◽  
Vibration Suppression ◽  
System Modeling ◽  
Nonlinear Energy Sink ◽  
Initial Energy ◽  
Piezoelectric Energy Harvesting ◽  
Piezoelectric Energy ◽  
Voltage Output ◽  
Energy Sink ◽  
Nonlinear Energy

This article presents a novel piezoelectric energy-harvesting device. Different from the existing designs in the literature, the proposed device is based on the principle of nonlinear energy sink in order to achieve simultaneous broadband energy harvesting from the nonlinear energy sink and vibration suppression for the primary structure. First, the concept of the proposed design is described. Subsequently, system modeling and parameter identification are addressed. The performance of the apparatus under transient responses is examined through both numerical simulation and experimental study. The results show that the proposed apparatus behaves similarly as the nonlinear energy sink with the following features: 1:1 resonance, targeted energy transfer, initial energy dependence, and so on. Broadband voltage output is achieved when the nonlinear energy sink is activated.

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