磁约束双层夹心悬臂梁的振动分析

采用在约束层端部上设置永磁体的新方法可使阻尼层获得比传统约束阻尼处理方法更高的剪应变，从而增强粘弹层的阻尼耗能，降低共振峰。本文应用Hamilton原理，推导了全覆盖双层约束阻尼悬臂梁的运动方程，对模型进行了实验验证；分析了不同物理和几何参数下该方法的减振效果。研究表明，磁约束能提高阻尼减振效果。随着阻尼层厚度的增加，无磁约束的共振峰降低较少，而有磁约束的共振峰急剧降低，减振效果明显。阻尼层剪切模量G的变化对磁约束减振效果的影响较大；当G小于一定值时，减振效果明显，但当G大于一定值时，减振效果急剧降低。在不同的约束层弹性模量和厚度下，磁约束仍起作用。此外，分析了具有较大控制力的主被动混合磁约束振动控制方法的可行性。     

Active and passive magnetic constrained damping treatment

This paper has presented a new class of active and passive magnetic constrained layer damping (APMCLD) treatment for controlling vibration of three-layer clamped–clamped beams. Firstly, optimal placement strategies of discrete patches are investigated. The predictions of model are validated experimentally using three-layer clamped–clamped beams treated with fully or segmented passive magnetic constrained layer damping (MCLD) treatments. The results indicate that full MCLD treatment induces less improvement of damping characteristics. Also, the obtained results illustrate that, the improvement of damping performance using two-patched MCLD treatment becomes more apparent at the first mode compared to the corresponding performance using a single-patched MCLD treatment when the total length of damping layer is from 0.3L to 0.65L under considered magnetic force. Further, damping performances of APMCLD using several control strategies including simple PD controllers are investigated. The analytical results show that it induces less improvement of damping characteristics for higher modes using simple positive proportional feedback controllers whereas higher modes can been suppressed effectively using negative derivative feedback controllers. For broad band control of structural vibration, it is more effective using APMCLD treatments with combined proportional and derivative controllers. Moreover, the MCLD treatment still plays an important role in damping out structural vibrations even though active control systems fail.     

APPROXIMATE SOLUTIONS FOR TRANSIENT RESPONSE OF CONSTRAINED DAMPING LAMINATED CANTILEVER PLATE

The series composed by beam mode function is used to approximate the displacement function of constrained damping of laminated cantilever plates, and the transverse deformation of the plate on which a concentrated force is acted is calculated using the principle of virtual work.By solving Lagrange＇s equation, the frequencies and model loss factors of free vibration of the plate are obtained, then the transient response of constrained damping of laminated cantilever plate is obtained, when the concentrated force is withdrawn suddenly.The theoretical calculations are compared with the experimental data, the results show：both the frequencies and the response time of theoretical calculation and its variational law with the parameters of the damping layer are identical with experimental results.Also, the response time of steel cantilever plate, unconstrained damping cantilever plate and constrained damping cantilever plate are brought into comparison, which shows that the constrained damping structure can effectively suppress the vibration.     

自适应主动共振吸振器的设计和减振性能研究

为了扩大吸振器的工作频带,减小吸振器的阻尼,最终提高吸振器的减振效果,本文设计了一种自适应主动共振吸振器。文中对几种不同种类吸振器的减振原理、动力学特性等进行了理论分析和比较,集成自调谐吸振器和主动吸振器的优点,完成了一种自适应主动共振吸振器的设计,并提出了一种变步长、双寻优的控制算法。在振动台上测试了吸振器的动力学特性并理论分析了吸振器的移频特性和阻尼特性。在两端固支梁上对吸振器的减振效果进行了实验评估。实验结果显示,相比自调谐吸振器,加入主动力控制后,自适应主动共振吸振器的阻尼比从0.04减小至0.02,减振效果得到了显著的提高。     

Force and displacement transmissibility of a quasi-zero stiffness vibration isolator with geometric nonlinear damping

A geometric nonlinear damping is proposed and applied to a quasi-zero stiffness (QZS) vibration isolator with the purpose of improving the performance of low-frequency vibration isolation. The force, stiffness and damping characteristics of the system are presented first. The steady-state solutions of the QZS system are obtained based on the averaging method for both force and base excitations and further verified by numerical simulation. The force and displacement transmissibility of the QZS vibration isolator are then analysed. The results indicate that increasing the nonlinear damping can effectively suppress the force transmissibility in resonant region with the isolation performance in higher frequencies unaffected. In addition, the application of the nonlinear damping in the QZS vibration isolator can essentially eliminate the unbounded response for the base excitation. Finally, the equivalent damping ratio is defined and discussed from the viewpoint of vibration control.     

CALCULATION OF DYNAMIC LOAD IMPACT OF BIMODULOUS BEAM WITH CONSIDERATION OF SHEAR EFFECT AND DAMPING

在考虑剪切效应及阻尼的基础上,采用线性振动理论研究了双模量梁动载荷问题的冲击计算. 建立了双模量梁动载荷问题的振动微分方程,推导出了双模量梁动载荷问题的动位移、动载荷系数、冲击时间的表达式,并讨论分析了剪切效应及阻尼对双模量梁动载荷冲击问题的影响. 算例分析表明,对于某些双模量梁动载荷冲击问题,剪切效应及阻尼的影响是不能忽略的.     

Dynamic characteristics of a cantilever beam with partial self-sensing active constrained layer damping treatment

The equations of motion governing the vibration of a cantilever beam with partially treated self-sensing active constrained layer damping treatment(SACLD) are derived by application of the extended Hamilton principle. The assumed-modes method and closed loop velocity feedback control law are used to analyze and control the flexural vibration of the beam. The influence of the bonding layer and piezoelectric layer thickness, material properties, placements of the piezoelectric patch and feedback control parameters on the actuation ability of the vibration suppression are investigated. Some design considerations for pure passive, pure active control, and self-sensing active constrained layer damping are discussed. The present work is supported by the National Natural Science Foundation of China (No. 59635140).     

负刚度时滞反馈控制动力吸振器的等峰优化

相比于传统动力吸振器, 负刚度动力吸振器同时具有更好的减振能力和更宽的有效减振频带宽度, 为了进一步降低共振峰幅值, 在负刚度吸振器系统耦合时滞反馈控制. 对负刚度时滞反馈控制动力吸振器系统进行等峰优化设计, 优化设计的准则是:第一和第二共振峰的峰值相等; 同时兼顾两个目标, 一个目标是在优化时的最大共振峰幅值小于被动负刚度吸振器系统的反共振峰幅值, 另一目标是在优化时共振峰幅值与反共振峰幅值差小于被动吸振器系统. 接着, 通过设计和调节负刚度系数、吸振器阻尼系数和时滞反馈控制系数对控制系统进行等峰优化设计. 最后, 在降低幅值的同时, 分析结构参数对有效减振频带宽度的影响. 经过等峰优化之后, 选择本文的一组结构参数与两个典型的模型进行对比. 为了定量比较不同模型的降幅效果, 定义了减幅百分比, 研究发现在有效减振频带区间内减幅百分比超过40%以上. 结果表明, 通过等峰优化准则对结构参数进行优化设计和调节增益系数和时滞量, 共振峰幅值的减幅百分比也近似达到40%, 也可以调节增益系数和时滞量, 使得幅频响应曲线具有较宽的有效减振频带和较低的共振峰幅值与反共振峰幅值的差值.      

自感知主被动阻尼悬臂梁动态特性分析

由Ｈａｍｉｌｔｏｎ原理导出了压电层作约束层作约束层的自感知主被动阻尼控制结构的振动控制方程;由自感知电压引入速度负反馈闭环控制,并由假设模态法将位移按模态展开,求解了悬臂梁结构的动态特征;对被动控制、自感知主动控制、自感知主被动控制的控制效果进行了分析比较;分析了粘弹层厚度变化、材料参数变化以及压电层厚度、位置等结构参数变化对控制效果及模态频率的影响;并对自感知主被动阻尼控制结构的特点和设计中应注     

高速铁路连续梁桥的共振响应与振动控制研究

以液体粘滞阻尼器为振动控制外部装置，主桥采用欧拉伯努利梁，通过中国和谐号动车组CRH380AL、日本新干线Shinkansen700和欧洲高速列车HSLMA8三种不同类型的高速列车对比，模拟分析了高速列车作用下桥梁结构共振响应的影响因素，以及粘滞阻尼器的阻尼系数与安装位置对桥梁结构振动响应的减振效果。研究结果表明，（1）合理有效地布置列车荷载轴距，可使桥梁结构发生基频共振的列车时速在运营时速之外，避免了桥梁结构发生较大振动峰值响应，即桥梁结构的基频共振；（2）随着粘滞阻尼器阻尼系数的增大，桥梁的加速度峰值在列车不同时速下均在减少，对桥梁振动有着不同程度的减振效果；（3）通过合理安置液体粘滞阻尼器，可有效降低高速列车作用下桥梁结构的共振响应；（4）随着粘滞阻尼器与主梁的连接点位置逐渐远离支座，粘滞阻尼器的减振效果逐渐明显；（5）随着粘滞阻尼器与桥台的连接点位置逐渐靠近支座，粘滞阻尼器的减振效果略有提升，但不明显。     

Study of the effects of cubic nonlinear damping on vibration isolations using Harmonic Balance Method

In the present study, Harmonic Balance Method (HBM) is applied to investigate the performance of passive vibration isolators with cubic nonlinear damping. The results reveal that introducing either cubic nonlinear damping or linear damping could significantly reduce both the displacement transmissibility and the force transmissibility of the isolators over the resonance region. However, at the non-resonance region where frequency is lower than the resonant frequency, both the linear damping and the cubic nonlinear damping have almost no effect on the isolators. At the non-resonance region with higher frequency, increasing the linear damping has almost no effects on the displacement transmissibility but could raise the force transmissibility. In addition, the influence of the cubic nonlinear damping on the isolators is dependent on the type of the disturbing force. If the strength of the disturbing force is constant and independent of the excitation frequency, then the effect of cubic nonlinear damping on both the force and displacement transmissibility would be negligible. But, when the strength of the disturbing force is dependent of the excitation frequency, increasing the cubic nonlinear damping could slightly reduce the relative displacement transmissibility and increase the absolute displacement transmissibility but could significantly increase the force transmissibility. These conclusions are of significant importance in the analysis and design of nonlinear passive vibration isolators.     

A forced-vibration technique for measurement of material damping

This article describes a technique for measuring material damping in specimens under forced flexural vibration. Although the method was developed for testing fiber-reinforced composite materials, it could be used for any structural material. The test specimen is a double-cantilever beam clamped at its midpoint and excited in resonant flexural vibration by an electromagnetic shaker. Under steady state conditions, material damping is defined in terms of the ratio of input energy to strain energy stored in the specimen. If external losses are negligible, the input energy must equal the energy dissipated in the specimen. Input energy and strain energy are found from measured specimen dimensions, resonant frequency, input acceleration and bending strain. Problems associated with minimization of external energy losses in the apparatus and verification of measurements are discussed in detail. Measured damping of aluminum-alloy calibration specimens shows good agreement with calculated thermoelastic damping. Examples of measured damping showing amplitude and frequency dependence in fiber-reinforced plastic materials are presented.     

减振阻尼材料设计方法研究

减振阻尼材料可以改变结构的阻尼特性从而降低振动响应和声辐射水平,因而被广泛应用于飞机结构的减振降噪。本文针对减振阻尼材料的设计和应用开展了一系列试验研究,首先通过材料改性得到了不同主基料下材料的配方对阻尼性能的影响;其次配制了三种不同的约束阻尼结构,通过DMA测试对比了三种约束阻尼结构的最佳使用温度和频率范围;最后对约束阻尼结构的减振效果和粘贴布局应用进行了试验,试验结果表明,约束阻尼结构具有良好的减振效果。通过研究掌握了减振阻尼材料在材料改性、约束阻尼结构设计、粘贴布局应用等方面的一些设计方法,可为后续的进一步研究提供技术支持和参考。     

圆形空心截面约束层阻尼梁整体单元建模与振动分析

增加阻尼对结构振动抑制具有很重要的意义,为克服三维有限元建模单元数量较大的问题,采用整体单元方法求解圆形空心截面约束阻尼梁的拉伸、弯曲和扭转振动。分析结果同三维有限元分析结果作了比较,证明了该方法的可行性,为圆形截面构件组成的刚架和桁架结构约束阻尼层振动抑制分析提供了简单的计算方法。     

局部约束阻尼开口柱壳的减振分析及优化

为了缩减开口柱壳结构的振动,本文基于Lagrange方程以及Sanders薄壳理论建立了局部约束阻尼开口柱壳的动力学模型,分析了粘弹性单元分段数和厚度、阻尼单元占空比以及约束层敷设角和厚度对结构前三阶模态损耗因子和固有频率的影响,得到了各参数对结构振动特性的影响规律.并以前三阶损耗因子为目标,应用NSGA-Ⅱ遗传算法对...     

Laser-induced vibrations of micro-beams under different boundary conditions

In this study, the vibration phenomenon during pulsed laser heating of a micro-beam is investigated. The beam is made of silicon and is heated by a non-Gaussian laser beam with a pulse duration of 2 ps, which incites vibration due to the thermoelastic damping effect. The coupling between the temperature field and stress field induces energy dissipation and converts mechanical energy into heat energy, which is irreversible. An analytical–numerical technique based on the Laplace transform is used to calculate the vibration of the deflection and thermal moment. A general algorithm of the inverse Laplace transform is developed. The validation of this algorithm is obtained through comparison with numerical results obtained by the FEMLAB software package. The effect of laser pulse energy absorption depth is studied. The size effect and the effect of different boundary conditions are also analyzed. Finally, the damping ratio and resonant frequency shift ratio of beams due to the air damping effect and the thermoelastic damping effect are compared.     

电磁约束阻尼层结构振动主动控制研究

基于弹性、粘弹性、电磁学理论,应用Hamilton原理,导出了覆盖电磁约束层阻尼(EMCLD)主动控制方式的梁的控制方程,并针对覆盖EMCLD的悬臂梁,进行了主动控制仿真模拟,得到了较好的控制效果,分析了控制电流和阻尼层厚度对控制效果的影响.结果表明电磁约束阻尼技术具有结构简单、作动方式合理、耗能低的优点,是一种有效的振动主动控制方式.     

The jump phenomenon effect on the sound absorption of a nonlinear panel absorber and sound transmission loss of a nonlinear panel backed by a cavity

Theoretical analysis of the nonlinear vibration effects on the sound absorption of a panel absorber and sound transmission loss of a panel backed by a rectangular cavity is herein presented. The harmonic balance method is employed to derive a structural acoustic formulation from two-coupled partial differential equations representing the nonlinear structural forced vibration and induced acoustic pressure; one is the well-known von Karman??s plate equation and the other is the homogeneous wave equation. This method has been used in a previous study of nonlinear structural vibration, in which its results agreed well with the elliptic solution. To date, very few classical solutions for this nonlinear structural-acoustic problem have been developed, although there are many for nonlinear plate or linear structural-acoustic problems. Thus, for verification purposes, an approach based on the numerical integration method is also developed to solve the nonlinear structural-acoustic problem. The solutions obtained with the two methods agree well with each other. In the parametric study, the panel displacement amplitude converges with increases in the number of harmonic terms and acoustic and structural modes. The effects of excitation level, cavity depth, boundary condition, and damping factor are also examined. The main findings include the following: (1)?the well-known ??jump phenomenon?? in nonlinear vibration is seen in the sound absorption and transmission loss curves; (2)?the absorption peak and transmission loss dip due to the nonlinear resonance are significantly wider than those in the linear case because of the wider resonant bandwidth; and (3)?nonlinear vibration has the positive effect of widening the absorption bandwidth, but it also degrades the transmission loss at the resonant frequency.     

主动移频式动力吸振器及其动力特性的研究

动力吸振器是振动控制中比较有效的减振装置,只要吸振器(子系统)的振动固有频率与振动物体(主系统)的振动频率相同,即可有效地消除主系统的振动。但传统动力吸振器的控制频率带宽较窄,限制了其稳定性和减振效果的提高。本文通过独特的机械设计,研制了一种可以通过调节自身的几何参数,使得其固有频率随几何参数线性变化的主动移频的新型动力吸振器,并初步设定了相应的控制方法。文中还对其动力学特性进行了理论分析和实验测试,分析了它的机理,评估了它的实际减振效果。研究结果表明该吸振器可以大范围调节自身固有频率,有效拓宽吸振频带,具有良好的减振性能和稳定性。     

分布振子复合板的模态阻尼及多点激励下阻尼减振相关性

分布阻尼振子可拓宽结构减振频带,因此可将振子分布于板中以形成复合板（简称“分布振子复合板”）,进而实现较宽的减振频带．对于多点支撑处受到宽频非一致激励（例如在不同激励点处的激励频率、幅值与相位有差异）的分布振子复合板,目前还缺乏有效简便的优化控制指标．在作者之前的研究中,针对含分布振子的梁推导了基于模态应变能的模态阻尼计算理论,讨论了模态阻尼与单点激励下梁的减振效果的相关性,并应用于宽频减振设计优化．本文进一步将模态阻尼计算理论推广到分布振子复合板,并将研究从梁的单点激励扩展到板的多点非一致激励下的阻尼减振相关性．首先,在利用模态应变能法推导得到分布振子复合板的模态阻尼计算公式后,从理论上讨论了不同边界条件与模态阶次对计算结果的影响,以及计算理论的适用性．而后,进一步通过有限元参数分析了边界条件、频率比、模态阶次与质量比的影响．最后,通过算例分析了无振子板或分布振子复合板在四个激励点具有多种幅值与相位组合情况下的稳态响应．结果表明,推导的模态阻尼计算公式可正确预测不同边界条件下的模态阻尼,且理论预测的模态阻尼与基板的稳态平均加速度减小率、稳态峰值应变能减小率均有较高的相关性．