scholarly journals Dynamics of Nonlinear Primary Oscillator with Nonlinear Energy Sink under Harmonic Excitation: Effects of Nonlinear Stiffness

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Min Sun ◽  
Jianen Chen
Keyword(s):  
Averaging Method ◽  
Nonlinear Energy Sink ◽  
Excitation Amplitude ◽  
Harmonic Excitation ◽  
Nonlinear Stiffness ◽  
Frequency Range ◽  
Steady State Responses ◽  
Energy Sink ◽  
State Responses ◽  
Nonlinear Energy

The dynamics of a system consisting of a nonlinear primary oscillator, subjected to a harmonic external force, and a nonlinear energy sink (NES) are investigated. The analytical solutions for the steady-state responses are obtained by the complexification-averaging method and the analytical model is confirmed by numerical simulations. The results indicate that the introduction of the NES can effectively suppress the vibrations of the primary oscillator. However, as the excitation amplitude increased, the NES may lose its efficiency within certain frequency range due to the appearance of the high response branches. Following the results analysis, it is concluded that this failure can be eliminated by reducing the nonlinear stiffness of the NES properly. The effects of nonlinear stiffness of the primary oscillator on the corresponding responses are also studied. The increase in this nonlinear stiffness can reduce the response amplitude and alter the frequency band where the high branches exist.

Thermal Effect on Dynamics of Beam with Variable-Stiffness Nonlinear Energy Sink

2020 ◽  
Vol 21 (1) ◽  
pp. 1-10 ◽  
Author(s):  
J. E. Chen ◽  
W. Zhang ◽  
M. H. Yao ◽  
J. Liu ◽  
M. Sun
Keyword(s):  
Variable Stiffness ◽  
Nonlinear Energy Sink ◽  
Excitation Amplitude ◽  
Harmonic Excitation ◽  
Absorption Efficiency ◽  
Nonlinear Stiffness ◽  
Vibration Absorption ◽  
Low Stiffness ◽  
Energy Sink ◽  
Nonlinear Energy

AbstractIn this study, we investigate the targeted energy transfer (TET) from a simply supported beam that is subjected to thermal variations and external excitations to a local nonlinear energy sink (NES). We derive the governing equation of motion for the beam with an NES device and study the influences of NES parameters on the vibration-suppressing effect. We obtain the optimized parameters of the NES under constant-amplitude harmonic excitation at room temperature. The optimized NES gradually loses its vibration absorption efficiency as the excitation amplitude and temperature increase. We change the nonlinear stiffness of the NES to mitigate the influence of temperature variation and show that NES efficiency can be enhanced by reducing the nonlinear stiffness. We propose a variable-stiffness NES, and the results demonstrate this NES is best for maintaining efficiency over the whole temperature range. We also analyze the transient responses of the system under impulse loads. Results indicate that, like the performance of the system subjected to harmonic excitation, an NES with relatively low stiffness can better suppress vibration with increasing impulse amplitude and temperature.

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.

Self-excited oscillations attenuation of drill-string system using nonlinear energy sink

2012 ◽  
Vol 227 (2) ◽  
pp. 230-245 ◽  
Author(s):  
Z Nili Ahmadabadi ◽  
SE Khadem
Keyword(s):  
Steady State ◽  
Nonlinear Energy Sink ◽  
Drill String ◽  
Vibration Model ◽  
Steady State Responses ◽  
Stable Equilibria ◽  
Energy Sink ◽  
Parameter Values ◽  
State Responses ◽  
Nonlinear Energy

Application of nonlinear energy sink in annihilating self-excited oscillations of a slightly modified experimental and theoretical torsional vibration model of drill-string with real parameter values is studied in this article. Various configurations have been examined in order to procure steady-state responses in less time and expand the range of the existence of stable equilibria. Moreover, applied modification to the experimental model resulted in more realistic response. It is proven that attaching nonlinear energy sink to different components of a drill-string would help to acquire better responses and/or to improve applicability of the nonlinear energy sink.

scholarly journals Magnetic Nonlinear Energy Sink for Vibration Attenuation of Unbalanced Rotor System

2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
Hongliang Yao ◽  
Dasheng Zheng ◽  
Bangchun Wen
Keyword(s):  
Averaging Method ◽  
Nonlinear Energy Sink ◽  
Rotor System ◽  
Frequency Range ◽  
Runge Kutta Method ◽  
Unbalanced Rotor ◽  
Vibration Attenuation ◽  
Energy Sink ◽  
Vibration Attenuation Performance ◽  
Nonlinear Energy

A novel nonlinear energy sink (NES) consisting of permanent magnetic springs and coil springs is proposed, and the vibration attenuation performance of the NES for unbalanced rotor system is investigated. Firstly, the nonlinearity of the magnet spring is analyzed and the structure of the NES is introduced. Then, the dynamic model of the rotor system with the NES is built, and the responses and stabilities of the system are studied by applying Complexification-averaging method. The strongly modulated responses (SMR) behavior, which is the most important performance characteristic of the NES, is analytically studied by combining Complexification-averaging method and multiscale method and numerically verified by Runge-Kutta method. The results show that the NES is effective in attenuating the vibration of unbalanced rotor, and the SMR occurrence range can be broadened by increasing the nonlinearity of the NES. And also, the NES has better performance over a wider frequency range than the linear absorber.

Piecewise Nonlinear Energy Sink

2015 ◽  
Author(s):  
Mohammad A. Al-Shudeifat
Keyword(s):  
Dead Zone ◽  
Linear Structure ◽  
Nonlinear Energy Sink ◽  
Viscous Damping ◽  
Nonlinear Stiffness ◽  
Flexible Design ◽  
Energy Inputs ◽  
Energy Sink ◽  
The Dead ◽  
Nonlinear Energy

Symmetric piecewise nonlinearities are employed here to design highly efficient nonlinear energy sink (NES). These symmetric piecewise nonlinearities are usually called in the literature as dead-zone nonlinearities. The proposed dead-zone NES includes symmetric clearance about its equilibrium position in which zero stiffness and linear viscous damping are incorporated. At the boundaries of the symmetric clearance, the NES is coupled to the linear structure by either linear or nonlinear stiffness components in addition to similar viscous damping to that in the clearance zone. By this flexible design of the dead-zone NES, we obtain a considerable enhancement in the NES efficiency at moderate and severe energy inputs. Moreover, the dead-zone NES is also found here through numerical simulations to be more robust for damping and stiffness variations than the linear absorber and some other types of NESs.

Nonlinear Normal Modes of a Continuous Cantilever Beam with Nonlinear Energy Sink Absorber

2013 ◽  
Vol 325-326 ◽  
pp. 214-217
Author(s):  
Yong Chen ◽  
Yi Xu
Keyword(s):  
Cantilever Beam ◽  
Vibration Suppression ◽  
Normal Modes ◽  
Nonlinear Energy Sink ◽  
Nonlinear Normal Modes ◽  
Harmonic Excitation ◽  
Energy Sink ◽  
Nonlinear Normal ◽  
Nonlinear Energy ◽  
Good Agreement

Using nonlinear energy sink absorber (NESA) is a good countermeasure for vibration suppression in wide board frequency region. The nonlinear normal modes (NNMs) are helpful in dynamics analysis for a NESA-attached system. Being a primary structure, a cantilever beam whose modal functions contain hyperbolic functions is surveyed, in case of being attached with NESA and subjected to a harmonic excitation. With the help of Galerkins method and Raushers method, the NNMs are obtained analytically. The comparison of analytical and numerical results indicates a good agreement, which confirms the existence of the nonlinear normal modes.

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.

Piezoelectric Nonlinear Energy Sink for Energy Harvesting With Rectifying DC Interface Circuit

2018 ◽  
Author(s):  
Liuyang Xiong ◽  
Lihua Tang ◽  
Kefu Liu ◽  
Brian R. Mace
Keyword(s):  
Energy Harvesting ◽  
Electromechanical Coupling ◽  
Circuit Simulation ◽  
Harmonic Balance Method ◽  
Nonlinear Energy Sink ◽  
Harmonic Excitation ◽  
Interface Circuit ◽  
Dc Power ◽  
Energy Sink ◽  
Nonlinear Energy

In order to improve the performance of vibration energy harvesters over a broad frequency range, this paper proposes a use of piezoelectric nonlinear energy sink (NES) for energy harvesting from ambient vibrations. A standard rectifying direct current (DC) interface circuit is considered to generate DC power from the piezoelectric NES under harmonic excitation. Harmonic balance method is used to obtain the dynamic response and energy harvesting performance of the proposed piezoelectric NES, verified by the equivalent circuit simulation. Analytical and numerical results show that the design, by applying NES, improves the efficiency of energy harvesting without increasing the vibration of the primary structure in a broadband manner. The effects of the electromechanical coupling, excitation level and load resistance on the magnitude and bandwidth of the output DC power are investigated.

scholarly journals Targeted Energy Transfer Under Harmonic Forcing With a Vibro-Impact Nonlinear Energy Sink: Analytical and Experimental Developments

2015 ◽  
Vol 137 (3) ◽  
Author(s):  
Etienne Gourc ◽  
Guilhem Michon ◽  
Sébastien Seguy ◽  
Alain Berlioz
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Nonlinear Energy Sink ◽  
Small Mass ◽  
Harmonic Excitation ◽  
Mass Ratio ◽  
Electrodynamic Shaker ◽  
Energy Sink ◽  
Nonlinear Energy ◽  
Good Agreement

Recently, it has been demonstrated that a vibro-impact type nonlinear energy sink (VI-NES) can be used efficiently to mitigate vibration of a linear oscillator (LO) under transient loading. The objective of this paper is to investigate theoretically and experimentally the potential of a VI-NES to mitigate vibrations of an LO subjected to a harmonic excitation (nevertheless, the presentation of an optimal VI-NES is beyond the scope of this paper). Due to the small mass ratio between the LO and the flying mass of the NES, the obtained equations of motion are analyzed using the method of multiple scales in the case of 1:1 resonance. It is shown that in addition to periodic response, system with VI-NES can exhibit strongly modulated response (SMR). Experimentally, the whole system is embedded on an electrodynamic shaker. The VI-NES is realized with a ball which is free to move in a cavity with a predesigned gap. The mass of the ball is less than 1% of the mass of the LO. The experiment confirms the existence of periodic and SMR regimes. A good agreement between theoretical and experimental results is observed.

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