Vibration reduction evaluation of a linear system with a nonlinear energy sink under a harmonic and random excitation

The nonlinear behaviors and vibration reduction of a linear system with a nonlinear energy sink(NES)are investigated.The linear system is excited by a harmonic and random base excitation,consisting of a mass block,a linear spring,and a linear viscous damper.The NES is composed of a mass block,a linear viscous damper,and a spring with ideal cubic nonlinear stiffness.Based on the generalized harmonic function method,the steady-state Fokker-Planck-Kolmogorov equation is presented to reveal the response of the system.The path integral method based on the Gauss-Legendre polynomial is used to achieve the numerical solutions.The performance of vibration reduction is evaluated by the displacement and velocity transition probability densities,the transmissibility transition probability density,and the percentage of the energy absorption transition probability density of the linear oscillator.The sensitivity of the parameters is analyzed for varying the nonlinear stiffness coefficient and the damper ratio.The investigation illustrates that a linear system with NES can also realize great vibration reduction under harmonic and random base excitations and random bifurcation may appear under different parameters,which will affect the stability of the system.     

Steady State Passive Nonlinear Energy Pumping in Coupled Oscillators: Theoretical and Experimental Results

We study theoretically and experimentally the effect that anonlinear energy sink (NES) has on the steady state dynamics of a weaklycoupled system. The NES possesses essentially nonlinear(nonlinearizable) stiffness nonlinearity of the third degree. We findthat, in contrast to the classical linear vibration absorber, the NES iscapable of absorbing steady state vibration energy from the linearoscillator over a relatively broad frequency range. This results inlocalization of the steady state vibration in the NES, away from thedirectly forced subsystem. For a forward frequency sweep the localizedbranch of steady state motions is suddenly eliminated by a jump to alinearized low-amplitude motion, whereas, for a backward frequency sweepa reverse jump occurs. The difference in the frequencies of the twojumps introduces a nonlinear hysteresis loop. This work extends to thesteady state case of earlier transient passive energy pumping results.The notion of passively transferring vibration energy to an a prioridetermined NES, weakly attached to a main structure, is novel. The useof nonlinear energy sinks for passively absorbing energy from a linearmain structure can form the basis of relatively simple and modularvibration and shock isolation designs of mechanical systems.     

Dynamic design of a nonlinear energy sink with NiTiNOL-steel wire ropes based on nonlinear output frequency response functions

A novel vibration isolation device called the nonlinear energy sink(NES)with Ni Ti NOL-steel wire ropes(Ni Ti-ST) is applied to a whole-spacecraft system. The Ni Ti-ST is used to describe the damping of the NES, which is coupled with the modified Bouc-Wen model of hysteresis. The NES with Ni Ti-ST vibration reduction principle uses the irreversibility of targeted energy transfer(TET) to concentrate the energy locally on the nonlinear oscillator, and then dissipates it through damping in the NES with Ni Ti-ST.The generalized vibration transmissibility, obtained by the root mean square treatment of the harmonic response of the nonlinear output frequency response functions(NOFRFs),is first used as the evaluation index to analyze the whole-spacecraft system in the future.An optimization analysis of the impact of system responses is performed using different parameters of NES with Ni Ti-ST based on the transmissibility of NOFRFs. Finally, the effects of vibration suppression by varying the parameters of Ni Ti-ST are analyzed from the perspective of energy absorption. The results indicate that NES with Ni Ti-ST can reduce excessive vibration of the whole-spacecraft system, without changing its natural frequency. Moreover, the NES with Ni Ti-ST can be directly used in practical engineering applications.     

Vibration suppression and higher branch responses of beam with parallel nonlinear energy sinks

The effects of nonlinear energy sink (NES) on vibration suppression of a simply supported beam are investigated in this work. The slow flow equations of the system are derived by using complexification–averaging method, and the validity of the derivation is verified. By comparing the vibration absorption of single and parallel NESs of equal mass, it is found that the latter exhibits superior vibration absorption performance. In addition, the parallel NES can eliminate higher branch responses of the system under the harmonic load. Furthermore, it is found that parallel NES can eliminate the higher branches of the system more effectively by tuning nonlinear stiffness and damping. Moreover, the thermal effect on natural frequencies of the simply supported beam is considered, and the influences of the parallel NES’s parameters on the energy dissipation rate under shock load are investigated. The nonlinear responses of the simply supported beam with parallel NES under harmonic load and with the increase of temperature are described.     

Vibration absorption of parallel-coupled nonlinear energy sink under shock and harmonic excitations

Nonlinear energy sink(NES) can passively absorb broadband energy from primary oscillators. Proper multiple NESs connected in parallel exhibit superior performance to single-degree-of-freedom(SDOF) NESs. In this work, a linear coupling spring is installed between two parallel NESs so as to expand the application scope of such vibration absorbers. The vibration absorption of the parallel and parallel-coupled NESs and the system response induced by the coupling spring are studied. The results show that the responses of the system exhibit a significant difference when the heavier cubic oscillators in the NESs have lower stiffness and the lighter cubic oscillators have higher stiffness. Moreover, the efficiency of the parallel-coupled NES is higher for medium shocks but lower for small and large shocks than that of the parallel NESs. The parallel-coupled NES also shows superior performance for medium harmonic excitations until higher response branches are induced. The performance of the parallel-coupled NES and the SDOF NES is compared. It is found that, regardless of the chosen SDOF NES parameters, the performance of the parallel-coupled NES is similar or superior to that of the SDOF NES in the entire force range.     

Numerical and experimental investigations of a rotating nonlinear energy sink

In this work, passive nonlinear targeted energy transfer (TET) is addressed by numerically and experimentally investigating a lightweight rotating nonlinear energy sink (NES) which is coupled to a primary two-degree-of-freedom linear oscillator through an essentially nonlinear (i.e., non-linearizable) inertial nonlinearity. It is found that the rotating NES passively absorbs and rapidly dissipates a considerable portion of impulse energy initially induced in the primary oscillator. The parameters of the rotating NES are optimized numerically for optimal performance under intermediate and strong loads. The fundamental mechanism for effective TET to the NES is the excitation of its rotational nonlinear mode, since its oscillatory mode dissipates far less energy. This involves a highly energetic and intense resonance capture of the transient nonlinear dynamics at the lowest modal frequency of the primary system; this is studied in detail by constructing an appropriate frequency–energy plot. A series of experimental tests is then performed to validate the theoretical predictions. Based on the obtained numerical and experimental results, the performance of the rotating NES is found to be comparable to other current translational NES designs; however, the proposed rotating device is less complicated and more compact than current types of NESs.     

Targeted energy transfer of a parallel nonlinear energy sink

A parallel nonlinear energy sink(NES) is proposed and analyzed. The parallel NES is composed of a vibro-impact(VI) NES and a cubic NES. The dynamical equation is given, and the essential analytical investigation is carried out to deal with the cubic nonlinearity and impact nonlinearity. Multiple time-scale expansion is introduced, and the zeroth order is derived to give a rough outline of the system. The underlying Hamilton dynamic equation is given, and then the optimal stiffness is expressed. The clearance is regarded as a critical factor for the VI. Based on the periodical impact treatment by analytical investigation, the relationships of the cubic stiffness, the clearance, and the zeroth-order attenuation amplitude of the linear primary oscillator(LPO) are obtained.A cubic NES under the optimal condition is compared with the parallel NES. Harmonic signals, harmonic signals with noises, and the excitation generated by a second-order?lter are considered as the potential excitation forces on the system. The targeted energy transfer(TET) in the designed parallel NES is shown to be more e?cient.     

Attractors of harmonically forced linear oscillator with attached nonlinear energy sink. II: Optimization of a nonlinear vibration absorber

This paper is the second one in the series of two papers devoted to detailed investigation of the response regimes of a linear oscillator with attached nonlinear energy sink (NES) under harmonic external forcing and assessment of possible application of the NES for vibration absorption and mitigation. In this paper, we study the performance of a strongly nonlinear, damped vibration absorber with relatively small mass attached to a periodically excited linear oscillator. We present a nonlinear absorber tuning procedure in the vicinity of (1:1) resonance which provides the best total system energy suppression, using analytical and numerical tools. A linear absorber is also tuned according to the same criterion of total system energy suppression as the nonlinear one. Both optimally tuned absorbers are compared under common parameters of damping, external forcing but different absorber stiffness characteristics; certain cases for which nonlinear absorber is preferable over the linear one are revealed and confirmed numerically.     

NES cell

A broadband adaptive vibration control strategy with high reliability and flexible versatility is proposed. The high vibration damping performance of nonlinear energy sink (NES) has attracted attention. However, targeted energy transfer may cause severe vibration of NES. Besides, it is difficult to realize pure nonlinear stiffness without the linear part. As a result, the reliability of NES is not high. The low reliability of NES has hindered its application in engineering. In addition, the performance of NES depends on its mass ratio of the primary system, and NES lacks versatility for different vibration systems. Therefore, this paper proposes the concept of NES cell. The advantages of the adaptive vibration control of NES are applied to cellular NES. By applying a large number of NES cells in parallel, the reliability of NES and its versatility to complex vibration structures are improved. An elastic beam is used as the primary vibration structure, and a limited NES is used as the cell. The relationship between the vibration suppression effect of NES cells and the number of NES cell is studied. In addition, the effect of the distribution of NES cells on the multi-mode resonance suppression of the beam is also studied. In summary, the mode of the primary structure can be efficiently controlled by a large number of lightweight NES cell. Therefore, the lightweight NES cell is flexible for vibration control of complex structures. In addition, it improves the reliability of NES applications. Therefore, the distributed application of NES cells proposed in this paper is a valuable vibration suppression strategy.     

谐波平衡法与复平均法计算强非线性系统稳态响应的区别

近些年,很多学者致力于利用非线性增强振动响应减少的效果或者能量采集器的效率。因而非线性系统的响应值需要从理论计算方面更准确地预测。另外,根据学者已取得的研究成就,非线性能量汇(NES)中存在的立方刚度非线性可以将结构中宽频域的振动能量传递至非线性振子部分。文章将一种由NES和压电能量采集器组成的NES-piezo装置与两自由度主结构耦合连接,系统受谐和激励作用。文章采用谐波平衡法和复平均法分别推导了系统稳态响应,参照数值结果,对比两种近似解析方法在求解强非线性系统稳态响应时的异同。计算结果表明,系统体现较弱非线性时,二者计算结果差异很小;当系统体现强非线性时,复平均法不能准确地呈现系统高阶响应,提高阶数的谐波平衡法能更准确地表示系统响应值。基于谐波平衡法和数值算法,讨论NES-piezo装置对于系统宽频域减振的影响。与仅加入非线性能量汇情况对比,结果表明NES-piezo装置不会恶化宽频域减振效果,并且在第一阶共振频率附近,可以稍微提高结构减振效率。另外,计算结果也表明,采用恰当的NES-piezo装置可实现宽频域范围的结构减振和压电能量采集一体化。此项研究工作为研究不同情形强非线性系统的响应提供了理论方法的指导。另外,研究结果也为宽频域范围的结构减振和压电能量采集一体化提供了理论依据。