非线性能量汇胞元减振效率分析

非线性能量汇(nonlinear energy sink, NES)具有减振频带宽、减振效果好等诸多优点.但是NES没有线性刚度的特征导致其难以驱动大重量的NES振子,从而难以应用于对大型工程结构的减振.因此,将NES以高效和便捷的方式应用于工程减振,仍然是有待研究的问题.将NES以胞元的形式装配于振动的主结构中,通过多个NES胞元的共同作用,是一种有前景的减振策略.文章在偏心转子激励下,探究了多个NES胞元对远大于单个NES自身重量的振动结构的减振效果,分析了多个NES胞元耦合主结构组成的系统的整体响应特征.建立了NES胞元减振系统的运动微分方程,采用复化平均法(complexification-averaging,CxA)导出系统的慢不变流形及稳态响应满足的近似解析表达式,通过慢变流形的扰动运动微分方程对稳态解进行稳定性分析,再利用伪弧长法获得系统响应的近似解,分析了NES胞元的减振规律及系统响应规律,最后利用龙格-库塔(Runge-Kutta, R-K)法进行数值验证.结果表明,通过多个NES胞元共同作用,能够有效控制较大重量的主系统振动,而且减振效率随NES胞元个数和重量的增加...     

含非线性能量汇的简支输液管非线性振动控制研究

论文建立了一个含有非线性能量汇(NES)装置并输运脉动内流的简支输液管道理论模型, 研究了NES装置对管道的非线性动力学特性与振动控制的影响. 利用Galerkin和龙格库塔法, 得到了在含NES和不含NES装置时管道动力学响应的数值结果. 研究表明, NES装置能有效地抑制管道振动. 通过对比可知, NES对管道系统的稳定性和非线性振动控制有着明显的影响. 此外, 本文还详细讨论了NES装置相关参数对系统的动力学影响. 结果表明, 增大NES的弹簧刚度、阻尼和质量比有利于管道减振, 且最佳安装位置在管道中点. 此外, 增大阻尼?能缩小失稳激励频率区域, 而其他参数的变化对失稳激励频率区域影响较小.     

含有混和阻尼的非线性能量阱吸振器动力学分析

非线性能量阱(NES)是一种具有优良减振性能的非线性吸振器,主要由线性阻尼、非线性刚度和一个小质量块组成。本文在立方刚度NES基础上引入了两种不同类型的阻尼(库仑阻尼、立方阻尼),提出了一种具有混合阻尼的NES吸振器,研究了不同类型阻尼混合对系统动力学性能的影响。利用谐波平衡和伪弧长延拓法近似解析了系统的非线性运动方程,通过与数值解进行对比验证了解析解的准确性。基于振动传递率和能量耗散对比分析了混合阻尼NES系统的动力学特性。通过传递率评估和优化了混合阻尼NES吸振器(质量、刚度、阻尼)参数对系统减振性能的影响。结果表明:含有混合阻尼的NES吸振器相比于常规的NES吸振器在振动抑制方面具有显著的优势;在系统受到外部激励后,含有混合阻尼的NES吸振器比常规的NES吸振器具有更高的能量吸收耗散比例;不同类型阻尼的混合在系统减振性和能量耗散方面的优势也显示了其在其他工程领域应用的可能性和潜力。     

电动力学中衰减机械系统的非线性振荡方法

衰减机械系统的非线性振荡可用来研究长约瑟夫逊结的电动力学方程式，而这方程式等同于弱衰减机械系统的非线性振荡。本文应用的方法是将控制方程线性化及结合谐波平衡法（线性谐波平衡法）而产生色散关系，再把平均法应用在弱非线性的耗散系统中得到非常准确的瞬变反应。在此提出的方法不仅考虑能量耗散，而且利用简单的线性代数等式关系来代替冗长及复杂的分析近似解。     

双稳态电磁式振动能量捕获器超谐波响应研究

超谐波响应是非线性振动系统在较大激励下表现的特性,在某种条件下双稳态振动能量捕获系统的超谐波响应可使系统产生优越的输出功率。本文将质量-非线性弹簧-阻尼系统与双稳态振动能量捕获器相结合,提出了附加非线性振子的双稳态电磁式振动能量捕获器,建立系统的力学模型及控制方程。采用两项式谐波平衡法,获得了双稳态系统在简谐激励下产生大幅运动的基谐波和超谐波响应的解析解,借助数值仿真分析了质量比和调频比对双稳态振动能量捕获器产生大幅运动的影响规律,获得了双稳态系统的结构参数的最佳配置范围,且当外部激励频率处于低频段时,系统发电主要表现为超谐波发电,随着激励频率的增大,振动发电系统主要呈现基谐波发电。上述研究,为双稳态能量捕获装置的理论研究提供了参考。     

具有组合非线性阻尼的非线性能量阱振动抑制响应分析

非线性能量阱是一种振动能量吸收装置,其在结构振动抑制中具有十分重要的作用.文章对具有组合非线性阻尼非线性能量阱的系统进行振动抑制相关的分析.首先对具有组合非线性阻尼非线性能量阱的系统进行理论模型的描述,对系统模型的运动方程利用复变量平均法进行推导,得到系统的慢变方程.其次对系统的慢变方程运用多尺度法进行强调制响应的分析,通过对系统进行慢不变流形和相轨迹的研究,描述系统强调制响应发生的条件基础.此外,还利用一维映射对系统进行分析,揭示外激励幅值对强调制响应存在时频率失谐系数取值区间的影响规律.最后利用能量谱、时间响应和庞加莱映射对耦合组合非线性阻尼非线性能量阱系统进行了振动抑制的相关研究,揭示组合非线性阻尼的非线性能量阱不同阻尼比、阻尼和刚度对其振动抑制效果的影响规律,得出组合非线性阻尼非线性能量阱和主结构响应存在一致性的现象,并验证所提出的组合非线性阻尼非线性能量阱模型具有较好的振动抑制能力.     

可积反对称Duhem迟滞系统在非白噪声激励下的随机响应分析

运用随机平衡法，研究可积反对称Duhem迟滞系统在非白噪声激励下的随机响应根据能量等价性，将Duhem迟滞系统转化成非迟滞的非线性系统；再运用随机平均法，导出关于系统能量It^O随机微分方程与相应的FPK方程；求解该方程得到平稳概率密度，从而可计算响应统计量。通过例子分析表明，本文方法的结果与数字模拟非常吻合。     

简谐激励下黏弹性非线性能量阱的研究

黏弹性材料作为一种良好的减振材料,广泛应用于机械、航空和土木等领域.本文用黏弹性Maxwell器件代替传统非线性能量阱中的阻尼元件,提出一种新型的黏弹性非线性能量阱,并对该模型在简谐激励下的减振性能进行分析.首先,根据牛顿第二定律建立系统的动力学方程,采用谐波平衡法求解系统的幅频响应曲线,并利用MATLAB中的Runge-Kutta数值方法验证解析解的正确性,结果吻合良好.然后,分析黏弹性非线性能量阱的减振性能和参数的影响.最后,分析了不同质量比下非线性刚度比和阻尼比同时变化时减振效果的变化趋势,并讨论了黏弹性非线性能量阱的最佳取值范围.研究结果表明:主系统的最大振幅随着非线性刚度的增加先减小后增大;当参数选取恰当时,黏弹性非线性能量阱比传统非线性能量阱的减振效果更优;另外,随着质量比的增加,主系统最大振幅的最小值出现先减小后趋于不变的现象,且非线性刚度比和阻尼比的最佳取值范围有所增大.以上结论对黏弹性非线性能量阱的实际应用提供了一定的理论依据.     

强迫Van der Pol振子的动力学特性

采用增量谐波平衡方法导出强迫Van der Pol振子稳态周期响应的IHB计算格式．以外激励频率为参数进行跟踪延续获得了系统主共振时的幅频响应特性，并作出了特定系统参数下的周期响应极限环．其结果与Runge—Kutta方法进行了对比，结果表明该算法精度可以灵活控制，且收敛速度快，结果可靠，是非线性电路系统等工程应用中强非线性问题动力学特性分析的有效方法．     

等效线性化——Prohl传递矩阵迭代法

本文提出了通过逐次将非线性力等效线性化,然后用具有许多优点的 Prohl 法计算等效系统响应的迭代法,用以求非线性转子系统的稳态不平衡响应.实例计算了装有中介轴挤压油膜阻尼器的双转子发动机的稳态不平衡响应.     

Integration of a nonlinear energy sink and a piezoelectric energy harvester

A mechanical-piezoelectric system is explored to reduce vibration and to harvest energy. The system consists of a piezoelectric device and a nonlinear energy sink(NES), which is a nonlinear oscillator without linear stiffness. The NES-piezoelectric system is attached to a 2-degree-of-freedom primary system subjected to a shock load. This mechanical-piezoelectric system is investigated based on the concepts of the percentages of energy transition and energy transition measure. The strong target energy transfer occurs for some certain transient excitation amplitude and NES nonlinear stiffness. The plots of wavelet transforms are used to indicate that the nonlinear beats initiate energy transitions between the NES-piezoelectric system and the primary system in the transient vibration, and a 1:1 transient resonance capture occurs between two subsystems.The investigation demonstrates that the integrated NES-piezoelectric mechanism can reduce vibration and harvest some vibration energy.     

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.     

非线性振动能量俘获技术的若干进展

随着工程中低功耗电子设备和自供能无线传感网络的迅速发展, 使得振动能量俘获在航空航天工程、机械工程、生物医学工程和可持续能源工程等领域得到了广泛地应用. 振动能量俘获不仅可以将振动能转化为可用的电能为微电子设备供电, 还能减少有害振动保护仪器设备. 根据振动能量不同转换机制, 可以将振动能量俘获系统分为静电式、电磁式、压电式、磁致伸缩式、摩擦起电式以及它们的混合式. 其中压电和电磁振动能量转化机制由于结构简单、容易组装、能量转换性能高等优点, 已被广泛应用于各种工程领域中. 受极端环境干扰, 工程中容易出现宽带、低频等振动, 迫使振动能量俘获技术向非线性方向迅猛发展, 进一步吸引了诸多学者对振动能量俘获系统的结构和电路进行优化设计研究. 本文首先综述了非线性振动能量俘获技术近十年来的研究进展, 主要包括设计技术基础、非线性结构设计、动力学分析等方面的研究现状. 其次, 重点阐述了振动能量俘获与振动抑制一体化的主要研究成果, 包括非线性准零刚度和非线性能量汇在振动能量俘获领域的应用. 最后, 总结了振动能量俘获外接电路和主动控制策略的优化设计, 分析了进一步提升非线性振动能量俘获效能的有效方法.      

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 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...     

一类二自由度非线性能量阱系统的减振性能分析

研究了包含一类新型二自由度非线性能量阱的机械振动系统.建立非线性系统的运动微分方程,用泰勒级数展开近似表达二级振子所受到的非线性力.运用数值方法对该非线性能量阱的减振性能进行分析.从其结构参数以及初始能量的角度出发,研究其发生靶向能量传递的条件.结果表明:该非线性能量阱可以有效降低主结构的能量,其振动抑制效果明显优于单...     

Forced response of quadratic nonlinear oscillator: comparison of various approaches

The primary resonances of a quadratic nonlinear system under weak and strong external excitations are investigated with the emphasis on the comparison of different analytical approximate approaches. The forced vibration of snap-through mechanism is treated as a quadratic nonlinear oscillator. The Lindstedt-Poincaré method, the multiple-scale method, the averaging method, and the harmonic balance method are used to determine the amplitude-frequency response relationships of the steady-state responses. It is demonstrated that the zeroth-order harmonic components should be accounted in the application of the harmonic balance method. The analytical approximations are compared with the numerical integrations in terms of the frequency response curves and the phase portraits. Supported by the numerical results, the harmonic balance method predicts that the quadratic nonlinearity bends the frequency response curves to the left. If the excitation amplitude is a second-order small quantity of the bookkeeping parameter, the steady-state responses predicted by the second-order approximation of the LindstedtPoincaré method and the multiple-scale method agree qualitatively with the numerical results. It is demonstrated that the quadratic nonlinear system implies softening type nonlinearity for any quadratic nonlinear coefficients.     

Aeroelastic suppression of an airfoil with control surface using nonlinear energy sink

Aeroelasticity exists in airfoil with control surface freeplay, which may induce instability in an incompressible flow. In this paper, a nonlinear energy sink (NES) is used to suppress the aeroelasticity of an airfoil with a control surface. The freeplay and cubic nonlinearity in pitch are taken into account. The harmonic balance method is used to analytically determine the limit cycle oscillations (LCOs) amplitudes of the airfoil–NES system. Linear and nonlinear flutter speeds are detected from the airfoil with control surface freeplay. When NES is attached, both the linear flutter speed of airfoil without freeplay and the nonlinear flutter speed of airfoil with a freeplay are increased. Moreover, the LCO amplitude of airfoil is decreased due to NES. Then, the influences of NES parameters on the increase in flutter boundary of airfoil are carefully studied.     

Limit cycle oscillation suppression of 2-DOF airfoil using nonlinear energy sink

This paper presents a novel mechanical attachment, i.e., nonlinear energy sink （NES）, for suppressing the limit cycle oscillation （LCO） of an airfoil. The dynamic responses of a two-degree-of-freedom （2-DOF） airfoil coupled with an NES are studied with the harmonic balance method. Different structure parameters of the NES, i.e., mass ratio between the NES and airfoil, NES offset, NES damping, and nonlinear stiffness in the NES, are chosen for studying the effect of the LCO suppression on an aeroelastic system with a supercritical Hopf bifurcation or subcritical Hopf bifurcation, respectively. The results show that the structural parameters of the NES have different influence on the supercritical Hopf bifurcation system and the subcritical Hopf bifurcation system.     

Resonance response of fluid-conveying pipe with asymmetric elastic supports coupled to lever-type nonlinear energy sink

This paper studies the vibration absorber for a fluid-conveying pipe, where the lever-type nonlinear energy sink (LNES) and spring supports are coupled to the asymmetric ends of the system. The pseudo-arc-length method integrated with the harmonic balance method is used to investigate the steady-state responses analytically. Meanwhile, the numerical solution of the fluid-conveying pipe is calculated with the Runge-Kutta method. Moreover, a special response, called the collapsible closed detached response (CCDR), is first observed when the vibration response of mechanical structures is studied. Then, the relationship between the CCDR and the main structure primary response (PR) is obtained. In addition, the closed detached response (CDR) is also observed to research the resonance response of the fluid-conveying pipe. The appearance of either the CCDR or the CDR does affect the resonance attenuation. Furthermore, the mentioned two phenomena underline that the trend of vibration responses under external excitation goes continuous and gradual. Besides, the main advantage of the LNES is presented by contrasting the LNES with the nonlinear energy sink (NES) coupled to the same pipe system. It is found that the LNES can reduce the resonance response amplitude by 91.33%.