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...     

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.     

高阻尼比低质量比圆柱涡激振动试验研究

针对圆柱的涡激振动问题,设计开发了高性能循环水槽与超声位移传感器,研究了高阻尼比、低质量比条件下,弹性支撑的刚性圆柱的涡激振动变化规律。结果表明:(1)高阻尼比条件下,振幅主要受独立参数阻尼比、质量比的影响;低质量比条件下,振动频率随流速增大而增大,"锁定区间"较高质量比范围扩大。(2)高阻尼比、低质量比条件下,阻尼的增大会导致振幅减小且"锁定区间"变窄;但振动频率在"锁定区间"内变化趋势一致。(3)高阻尼比、低质量比有利于涡激振动的能量转化,但阻尼不可过大,否则振幅与"锁定区间"均变小,影响电能转化。     

时滞非线性动力吸振器的减振机理

对一个带有时滞非线性动力吸振器的两自由度结构,采用多尺度法研究了时滞非线性动力吸振器对主系统的减振性能,得到了主系统的振幅-时滞响应曲线.研究结果表明,对时滞非线性动力吸振器,可以通过调节反馈增益系数和时滞控制主系统的振动. 研究还发现,对确定的反馈增益系数,可以存在时滞的一些调节区域,时滞非线性动力吸振器可以减小主系统的振动. 并且在时滞的这些可调区域里,存在一个``最大减振点'对应这一反馈增益系数下主系统振幅的最小值.对不同的反馈增益系数,``最大减振点'对应的主系统的振幅也不同.因此能够找到一组反馈增益系数和时滞量的最佳值,最大程度地减小主系统的振动.研究结果表明,当反馈增益系数和时滞量调到最佳值时,主系统的振动较无时滞非线性动力吸振器可以减少90{\%}左右, 数值模拟也证实了解析结果的正确性.      

一种含惯容和接地刚度的动力吸振器参数优化

大多数机械振动属于有害振动, 不仅会产生噪声还会降低设备的使用寿命和工作性能. 接地刚度和惯容这两种器件均能改变系统的固有频率, 在振动控制领域中有着良好的效果. 但目前的大部分研究仅着眼于单一元件对系统产生的影响, 而此类吸振器逐渐难以满足设备对振动控制需求的增长. 在Voigt型动力吸振器模型的基础上, 提出了一种含有惯容和接地刚度的新型动力吸振器模型, 详细研究了该模型的最优设计参数, 推导出最优设计公式的解析解. 首先通过牛顿第二定律建立起二自由度系统的运动微分方程, 计算出系统解析解, 发现系统存在3个与阻尼比无关的固定点, 利用固定点理论得到了动力吸振器的最优频率比. 为保证系统稳定性, 筛选最优接地刚度比时, 发现不恰当的惯容系数会导致系统产生失稳现象, 进而推导出惯容最佳工作范围, 最终得到了最优接地刚度比和近似最优阻尼比. 分析了惯容系数取值在最佳范围以外时系统的工作情况, 并给出了实际应用中的建议. 通过数值仿真验证了推导得到解析解的正确性. 与多种已有的动力吸振器在简谐激励和随机激励的工况下进行对比, 说明了该模型能够大幅降低主系统振幅, 拓宽减振频带, 为设计新型吸振器提供了理论依据.      

SMA叠层变刚度水平万向阻尼器滞回性能研究

利用NiTi形状记忆合金(Shape Memory Alloy,简称SMA)的超弹性特性,开发了一种新型SMA叠层变刚度水平万向阻尼器,介绍了其基本构造和工作原理,建立了阻尼器恢复力计算模型并开展了滞回性能参数分析,研究了SMA张拉应变、SMA直径、阻尼器层数以及每层SMA丝根数对阻尼器行程、刚度、耗能、等效阻尼比的影响.研究结果表明：SMA叠层变刚度水平万向阻尼器的恢复力-位移滞回曲线呈饱满的纺锤形,阻尼器具有良好的能量耗散能力、自复位功能、大行程以及变刚度特性;随着SMA张拉应变由0.03不断增大至0.06,阻尼器最大行程不断减小而单位循环耗能呈先增大后减小趋势;随着SMA直径不断增大,阻尼器刚度和耗能能力不断增大而最大行程和等效阻尼比不变;随着叠层层数不断增大,阻尼器最大行程和单位循环耗能不断增加而刚度不断降低;随着每层SMA布置数量由8根增大至16和32根,阻尼器刚度和单位循环耗能不断增大而最大行程和等效阻尼比变化不明显.     

横向荷载作用下弹性地基上梁的主共振分析

基于Winkler地基模型及Euler-Bernoulli梁理论,建立了弹性地基上有限长梁的非线性运动方程.运用Galerkin方法对运动方程进行一阶模态截断,并利用多尺度法求得该系统主共振的一阶近似解.分析了长细比、地基刚度、外激励幅值和阻尼系数等参数对系统主共振幅频响应的影响,然后通过与非共振硬激励情况对比分析主共振对其动力响应的影响.结果表明:主共振幅频响应存在跳跃和滞后现象;阻尼对主共振响应有抑制作用;主共振显著增大系统稳态动力响应位移.     

基于非线性吸能机理的涡激振动减振理论与实验研究

流致振动现象广泛存在于机械、航空、土木和石油等重要工程领域, 为防止工程结构因流致振动行为而造成疲劳破坏, 有必要对稳定性、动力学响应及其振动控制做深入研究. 本文提出了一种由弹簧和质量块构成的非线性吸能器(nonlinear targeted energy transfer, NTET), 研究了该非线性吸能器对弹性支承圆柱体涡激振动的被动控制影响机制. 基于能量法推导了圆柱体涡激振动非线性被动控制的耦合动力学方程, 通过设计非线性弹簧?质量块构型的NTET, 进一步开展了涡激振动控制的实验研究, 并与理论预测结果进行了较好的对比, 获得提升涡激振动控制效果的最佳参数值. 研究发现, NTET的质量、弹簧刚度以及弹簧预应力等参数会对涡激振动控制效果产生显著的影响. 本文研究结果表明, 该耦合系统中圆柱体和NTET均表现出周期性的稳态振动响应, NTET质量的改变会显著影响系统的耦合频率. 在无预应力状态下, NTET质量越大、刚度越小时, 有更好的减振效果. 当弹簧预应力逐渐增大时, NTET的非线性刚度逐渐变弱, 会降低涡激振动控制性能. 参数分析表明: 随着涡激振动控制性能的提升, 圆柱体的振幅逐渐较小, NTET的振幅逐渐增大, 能量传递效率逐渐提高. 研究结果可为工程中涡激振动控制策略的高效设计提供有用的理论支撑和实验数据.      

利用时滞反馈控制自参数振动系统的振动

主要研究采用时滞状态反馈控制自参数动力吸振器减振系统中主系统的振动问题.系统在简谐激励作用下,采用多尺度方法得到了自参数动力吸振器减振系统中饱和控制的范围.当系统处于饱和控制时,引入时滞状态反馈控制主系统的振动.主要分析了反馈增益系数和时滞两控制参数对主系统振动的影响.结果表明,存在反馈增益系数和时滞的调节区域能够减小主系统的振动.对某一反馈增益系数,可以在某段区间内调节时滞以减小主系统的振动.在时滞的调节区间内存在一个时滞的``最大减振点',能够在该反馈增益系数下最大程度地减小主系统的振动.研究还表明,随着反馈增益系数的不断增大,时滞在``最大减振点'时系统的减振能力也不断提高.通过合理的选择反馈增益系数和时滞两参数,主系统的振动几乎可以完全消除.      

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。     

一种含放大机构的负刚度动力吸振器的参数优化

在大多数情况下机械振动是有害的,它不仅产生噪声还会降低设备的工作精度和使用寿命.采用正刚度特性的吸振、隔振系统往往难以达到满意效果,这种情况在低频振动控制系统中尤其明显.放大机构与负刚度元件在振动控制领域均表现出良好性能,但是较少有对同时含有放大机构与负刚度装置的动力吸振系统的研究.以Voigt型动力吸振器为基础提出了一种将放大机构应用于含负刚度弹簧元件的动力吸振器模型,对该模型的最优参数进行了研究.首先建立了系统的运动微分方程并得到了其解析解,发现该系统存在两个固定点,利用固定点理论得到了动力吸振器的最优频率比.根据负刚度的特性,在保证系统稳定的前提下得到了最优负刚度比,并推导了系统的近似最优阻尼比.通过数值仿真验证了解析解的正确性.与多种动力吸振器在简谐激励与随机激励下进行了对比,说明了本文模型相比于已有的动力吸振器,能够大幅降低共振振幅、拓宽减振频带并且降低系统的谐振频率,为设计新型动力吸振器模型提供了理论依据.      

Nonlinear damping in large-amplitude vibrations: modelling and experiments

Experimental data clearly show a strong and nonlinear dependence of damping from the maximum vibration amplitude reached in a cycle for macro- and microstructural elements. This dependence takes a completely different level with respect to the frequency shift of resonances due to nonlinearity, which is commonly of 10–25% at most for shells, plates and beams. The experiments show that a damping value over six times larger than the linear one must be expected for vibration of thin plates when the vibration amplitude is about twice the thickness. This is a huge change! The present study derives accurately, for the first time, the nonlinear damping from a fractional viscoelastic standard solid model by introducing geometric nonlinearity in it. The damping model obtained is nonlinear, and its frequency dependence can be tuned by the fractional derivative to match the material behaviour. The solution is obtained for a nonlinear single-degree-of-freedom system by harmonic balance. Numerical results are compared to experimental forced vibration responses measured for large-amplitude vibrations of a rectangular plate (hardening system), a circular cylindrical panel (softening system) and a clamped rod made of zirconium alloy (weak hardening system). Sets of experiments have been obtained at different harmonic excitation forces. Experimental results present a very large damping increase with the peak vibration amplitude, and the model is capable of reproducing them with very good accuracy.     

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.     

一种含负刚度元件的新型动力吸振器的参数优化

提出了一种含有负刚度弹簧元件的新型动力吸振器模型,对该模型的最优参数进行了详细研究. 通过拉氏变换得到了系统的解析解,发现该系统存在着两个固定点,利用固定点理论得到了动力吸振器的最优阻尼比和最优频率比. 进一步研究发现接地刚度取负值时能够得到更好的减振效果,根据负刚度的特性得到了在保证系统稳定情况下的最优负刚度比. 通过数值解与解析解的对比证明了解析解的正确性. 通过与两种已有的典型动力吸振器模型在简谐激励和随机激励情况下的对比,说明了负刚度模型在主系统减振方面具有很大的优势,减振效果远优于两种已有动力吸振器模型,从而为设计新型动力吸振器模型提出了理论上的依据.      

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...     

Influence of excitation amplitude on the characteristics of nonlinear butyl rubber isolators

The purpose of this study is to explore the advantages and characteristics of nonlinear butyl rubber (type IIR) isolators in vibratory shear by comparison with linear isolators. It is known that the mechanical properties of viscoelastic materials exhibit significant frequency and temperature dependence, and in some cases, nonlinear dynamic behavior as well. Nonlinear characteristics in shear deformation are reflected in mechanical properties such as stiffness and damping. Furthermore, even when the excitation amplitude is small the response amplitude may often be large enough that nonlinearities cannot be ignored. The treatment involves developing phenomenological models of the effective storage modulus and effective loss factor of a rubber isolator material as a function of excitation amplitude. The transmissibility of a nonlinear viscoelastic isolator is compared with that of a linear isolator using an equivalent linear damping coefficient. Forced resonance vibration and impedance tests are used to characterize nonlinear parameters and to measure the normalized transmissibility. It is found that as the excitation amplitude of the nonlinear viscoelastic isolator increases, the response amplitude decreases and the transmissibility is improved over that of the linear isolator for excitation frequency that exceeds a particular value governed by the temperature and excitation amplitude. The method of multiple scales and numerical simulations are used to predict the response characteristics of the isolator based on the phenomenological modeling under different values of system parameters.     

Usefulness of passive non-linear energy sinks in controlling galloping vibrations

The suppression of vibration amplitudes of an elastically-mounted square prism subjected to galloping oscillations by using a non-linear energy sink is investigated. The non-linear energy sink consists of a secondary system with linear damping and non-linear stiffness. A representative model that couples the transverse displacement of the square prism and the non-linear energy sink is constructed. A linear analysis is performed to determine the impacts of the non-linear energy sink parameters (mass, damping, and stiffness) on the coupled frequency and onset speed of galloping. It is demonstrated that increasing the damping of the non-linear energy sink can result in a significant increase in the onset speed of galloping. Then, the normal form of the Hopf bifurcation is derived to identify the type of instability and to determine the effects of the non-linear energy sink stiffness on the performance of the aeroelastic system near the bifurcation. The results show that the non-linear energy sink can be efficiently implemented to significantly reduce the galloping amplitude of the square prism. It is also shown that the multiple stable responses of the coupled aeroelastic system are obtained as well as the periodic responses, which are dependent on the considered non-linear energy sink parameters.     

Numerical optimisation of a classical stochastic system for targeted energy transfer

The paper studies stochastic dynamics of a two-degree-of-freedom system, where a primary linear system is connected to a nonlinear energy sink with cubic stiffness nonlinearity and viscous damping. While the primary mass is subjected to a zero-mean Gaussian white noise excitation, the main objective of this study is to maximise the efficiency of the targeted energy transfer in the system. A surrogate optimisation algorithm is proposed for this purpose and adopted for the stochastic framework. The optimisations are conducted separately for the nonlinear stiffness coefficient alone as well as for both the nonlinear stiffness and damping coefficients together. Three different optimisation cost functions, based on either energy of the system’s components or the dissipated energy, are considered. The results demonstrate some clear trends in values of the nonlinear energy sink coefficients and show the effect of different cost functions on the optimal values of the nonlinear system’s coefficients.     

动力吸振器复合非线性能量阱对线性镗杆系统的振动控制

研究了线性动力吸振器复合非线性能量阱对线性镗杆在外部简谐激励下的振动控制. 忽略镗杆系统中的非线性因素, 建立了附加线性动力吸振器和非线性能量阱的镗杆系统的三自由度运动方程, 研究了附加复合式动力吸振器的镗杆系统的受迫振动. 通过平均法得到了附加复合式动力吸振器的镗杆系统的近似解析解, 并利用数值解验证了近似解析解的准确性, 两者具有很好的一致性. 利用近似解析解详细分析了线性动力吸振器和非线性能量阱的参数对镗杆振动抑制性能的影响. 对给定质量的复合式动力吸振器进行了参数优化, 其中线性动力吸振器参数采用H_∞优化方法的近似解析解进行了优化, 非线性能量阱的阻尼利用系统的近似解析解进行了优化. 分析结果表明, 线性动力吸振器与非线性能量阱组合可以有效抑制线性镗杆系统的振动, 而且采用参数优化后的复合式动力吸振器可以获得更好的减振效果. 通过附加非线性能量阱, 不但可以提高线性动力吸振器的振动抑制效果, 而且还可以提高振动控制系统的鲁棒性.