光热激励下微悬臂梁在流体中的振动研究

微悬臂梁结构广泛应用于微纳电子机械系统. 在实际应用中,涂层和工作环境的变化对微悬臂梁结构动态工作模式有着不容忽视的影响. 运用流体中双层微悬臂梁的光热振动模型,研究了在激光光热驱动下,金涂层微悬臂梁在不同流体中的振动特性. 理论上得到了微悬臂梁的温度场,光热驱动力和振动变形场的解析表达式. 研究结果表明,流体环境对微悬臂梁的光热振动谱有显著的影响,主要表现在共振频率的偏移和品质因子的变化两个方面. 相比较于悬臂梁在真空中的响应,当悬臂梁在空气中振动时,共振频率向低频产生微小的漂移（0.7%）,共振峰未发生明显变化;然而,当悬臂梁在液体中振动的时候,共振频率向低频产生巨大的漂移（58%~80%）,而且品质因子发生量级上的减小,共振峰发生了畸变. 本研究对微纳探测以及原子力显微镜等仪器的设计优化,有着一定的理论指导意义.      

Study on the generalized thermoelastic vibration of the optically excited semiconducting microcantilevers

In this paper, the theory of coupled plasma, thermal and elastic wave was used to study the vibration of semiconducting microcantilevers during photothermal process. The generalized thermoelastic model was adopted, along with plasma wave model, to obtain the vibration response of semiconducting microcantilevers under periodical laser excitation. The influence of thermal relaxation time on the vibration was investigated. The conventional and generalized thermoelastic theories for the temperature and deflection of microcantilever were compared. The simulation results for the amplitude and phase versus the modulation frequency revealed that near resonance frequency the generalized hyperbolic thermoelastic model was more suitable to describe the vibration characterization of microcantilevers than the conventional thermoelstic model.     

后临界湍流区间内旋转薄壳结构振动演化与作用机制实测研究

载荷的时变特征可能会对结构振动强度和能量作用机理产生重要影响,火/核电厂最重要的大型建筑结构均为典型的旋转薄壳结构(如冷却塔、烟囱等).为揭示后临界湍流区间内旋转薄壳结构的振动演化特征及其作用机制,实测了后临界雷诺数($Re\ge $3.5$\times $10$^{6}$)条件下8座典型旋转薄壳结构的振动响应.首先,在对实测响应进行降噪滤波处理后进行了不同时距的信号非平稳识别,基于非平稳分析模型对响应的时变均值和极值估计进行研究,并基于多尺度小波变换的演化谱方法开展了响应的频域演变特性研究.在此基础上,探讨了结构风振响应的共振分量占比及其效应,识别了结构的自振频率和阻尼比,并以结构基频为划分依据分别讨论了不同旋转薄壳结构的阻尼作用机制.研究结果表明:(1)旋转薄壳结构在后临界湍流区间内风致振动响应表现为强度非平稳、频率平稳的演化特性;(2)后临界湍流区间内的旋转薄壳结构的风振问题应区分准静力作用点与共振激发点分别进行研究,不同共振激发点的功率谱分布形式较为相近,而准静力作用点的功率谱分布规律差异较大;(3)共振激发点的振动能量分布呈现明显的分段趋势,基于本文大量实测分析结果回归得出适用于共振激发点的三阶段共振谱表达式;(4)借助本文提出的等效阻尼比概念拟合出此类结构的阻尼比预测公式,论证了目前工程中通用的5%阻尼比取值的不合理性.      

Experimental and numerical analysis of vibrating cracked plates at resonant frequencies

Owing to the advantages of noncontact and fullfield measurement, an optical system called the amplitude fluctuation electronic speckle pattern interferometry (AFESPI) method with an out-of-plane setup is employed to investigate the vibration of a cantilever square plate with a crack emanating from one edge. Based on the fact that clear fringe patterns will be shown by the AFESPI method only at resonant frequencies, both the resonant frequencies and the vibration mode shapes can be obtained experimentally at the same time. Three different crack locations will be discussed in detail in this study. One is parallel to the clamped edge, and the other two are perpendicular to the clamped edge. The numerical finite element calculations are compared with the experimental results, and good agreement is obtained for resonant frequencies and mode shapes. The influences of crack locations and lengths on the vibration behavior of the clamped cantilever plate are studied in terms of the dimensionless frequency parameter (λ ²) versus crack length ratio (a/L). The authors find that if the crack face displacements are out of phase, a large value of stress intensity factor may be induced, and the cracked plate will be dangerous from the fracture mechanics point of view. However, there are some resonant frequencies for which the crack face displacements are completely in phase, causing a zero stress intensity factor, and the cracked plate will be safe.     

基于碰撞升频的MEMS压电振动能量采集系统

本文提出了一种基于碰撞升频机制的微型压电能量采集系统，由一对共振频率不同的悬臂梁平行叠放组成。在外界低频振动激励下，底部低频S形金属曲梁产生共振，在运动过程中碰撞顶部高频微型压电直梁，从而将低频环境振动转换为高频压电梁的振动，解决了压电直梁的固有频率与外界激励频率不匹配问题，同时提高能量收集的效率。本文建立了悬臂梁受迫振动和碰撞耦合振动的动力学模型，讨论了压电悬臂梁的电压输出特性。通过实验测试了压电能量收集系统和单个压电悬臂梁的开路电压并计算了输出功率，结果表明当振动加速度为1.0 g时，升频式压电能量采集系统在25 Hz的激振下输出功率达到8.6 μW，高于单个压电悬臂梁的最大输出功率。     

基于局域共振声子晶体结构的低频振动能量回收研究

通过对局域共振型声子晶体的带隙机理及其对能量的局域化作用的分析,提出了一种用于回收环境低频振动能量的新型局域共振结构,并结合有限元方法对此新型结构的振动特性和能量回收能力进行了分析和研究。根据结构的共振模态和“质量-弹簧”系统简化模型,改变结构的材料和几何尺寸可以使结构的前7阶共振频率降到50~250Hz的低频范围。在此基础上发展了一种低频宽带多核结构,在250Hz以下拥有几十甚至更多的共振频率,最低频率低至20Hz,进一步优化了结构的低频宽带共振特性。利用有限元软件对有限结构的频率响应和压电特性进行分析,证实了新型局域共振结构的对环境中低频振动能量的回收能力,并满足了环境振动能量回收的宽带要求。该结构可以应用于各种便携式设备、无线传感器和微机电等自供电系统中,从低频振动环境中的获取能量为自身供电。     

两自由度参数激励摆旋转运动分析和实验

研究具有支撑参数激励摆系统的支撑结构振动对摆旋转的影响,其中支撑结构是受到扭簧约束的刚性悬臂梁,参数激励摆与刚性悬臂梁的悬臂段铰接．首先,通过拉格朗日方程建立了系统两自由度的动力学方程．其次,利用多尺度法对建立的模型进行理论分析,得到悬臂梁的振动与上摆不同运动形式的关系,从而得到上摆不同运动形式下的参数平面分类和悬臂梁在上摆转动时的振动频响．最后,通过建立实验装置,观察理论预测,实验结果验证了理论分析的正确性．实验与理论对照得到,当参数激励频率接近悬臂梁的一阶固有频率时,悬臂梁的振幅变大,会破坏摆的转动稳定性．     

Nonlinear integral resonant controller for vibration reduction in nonlinear systems

A new nonlinear integral resonant controller (NIRC) is introduced in this paper to suppress vibration in nonlinear oscillatory smart structures. The NIRC consists of a first-order resonant integrator that provides additional damping in a closed-loop system response to reduce high-amplitude nonlinear vibration around the fundamental reso-nance frequency. The method of multiple scales is used to obtain an approximate solution for the closed-loop system. Then closed-loop system stability is investigated using the resulting modulation equation. Finally, the effects of different control system parameters are illustrated and an approximate solution response is verified via numerical simulation results. The advantages and disadvantages of the proposed controller are presented and extensively discussed in the results. The controlled system via the NIRC shows no high-amplitude peaks in the neighboring frequencies of the resonant mode, unlike conventional second-order compensation methods. This makes the NIRC controlled system robust to excitation frequency variations.     

实心砖石古塔动力特性与结构损伤分析

为研究"丝绸之路"起点世界文化遗产建筑兴教寺测师塔的动力性能及结构损伤,采用超低频动态测试系统进行了原位动力测试试验.在环境随机激励下,采集了该塔各楼层顶部水平振动的速度响应信号,经滤波后通过积分变换进行自谱及互谱分析,得到了结构沿水平方向的前2阶自振频率与振型.并依据结构测绘结果,建立测师塔数值模型,计算了弹性模量逐渐降低时的振动特性,并与测试结果进行对比,依据结构损伤参数识别的改进形法,进行了测师塔结构损伤分析.结果表明,该塔沿东西与南北两个水平方向的前2阶频率值相近,第1阶振型呈弯曲型,第2阶振型呈弯剪型;与无损砌体弹性模量的取值比较,测师塔结构的等效弹性模量降低较多,其结构整体损伤较为严重.因此,可通过确定无损砌体的弹性模量,采用动力测试及数值计算依据等效弹性模量进行残损砖石古塔结构损伤识别.     

单自由度参数振动系统非线性响应的若干特征

用数值积分方法，分析了无阻尼单自由度参数振动系统在给定的单频刚度激励和单频外载荷激振时的非线性动力学响应特性。研究表明了参数振动问题的主要特征：1)单频激励多频响应；2)多频响应中各谐波的分布具有特殊的规律；3)系统具有多频共振特性。     

双稳杜芬振子的随机共振及其动力学机制

把矩方法应用于高斯白噪声和弱周期信号驱动的双稳杜芬振子,发现矩方法的收敛快慢与阻尼系数的大小有关,即在固定非线性参数的前提下,阻尼系数越大,收敛速度越快。在阻尼系数较大的情形,对于不同频率的弱周期输入信号,系统输出功率谱增益因子的演化防噪声强度呈单峰或双峰结构,亦即对于不同的激励频率,系统可表现出单峰或者重峰随机共振结构。为了解释这些共振结构,通过考察由波动谱密度定义的非零频率峰对噪声强度依赖性,发现重峰随机共振的发生在于噪声一方面抑制了井内运动,另一方面诱发了势垒上振动。研究结果为已有结论的修正,在统计力学等方面具有显著意义。     

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.     

基于应变梯度中厚板单元的石墨烯振动研究

基于应变梯度理论建立了单层石墨烯等效明德林(Mindlin) 板动力学方程,推导了四边简支明德林中厚板自由振动固有频率的解析解. 提出了一种考虑应变梯度的4 节点36 自由度明德林板单元,利用虚功原理建立了单层石墨烯的等效非局部板有限元模型. 通过对石墨烯振动问题的研究,验证了应变梯度有限元计算结果的收敛性. 运用该有限元法研究了尺寸、振动模态阶数以及非局部参数对石墨烯振动特性的影响. 研究表明,这种单元能够较好地适用于研究考虑复杂边界条件石墨烯的尺度效应问题. 基于应变梯度理论的明德林板所获得石墨烯的固有频率小于基于经典明德林板理论得到的结果. 尺寸较小、模态阶数较高的石墨烯振动尺度效应更加明显. 无论采用应变梯度理论还是经典弹性本构关系,考虑一阶剪切变形的明德林板模型预测的固有频率低于基尔霍夫(Kirchho) 板所预测的固有频率.      

绕水翼空化流动及振动特性的实验研究

空化是发生在水力机械内部的一种水动力现象,其发展具有显著的非定常特性.空化流动中空穴的脱落以及溃灭会诱发结构振动,对水力机械的效率、噪声、安全性等造成影响. 研究空化流动中结构的振动特性具有重要的工程意义. 采用实验的方法研究了绕NACA66 水翼空化流动的空穴形态和水翼振动特性. 实验在一闭式空化水洞中进行. 采用高速摄像技术观测不同空化阶段的空穴形态,应用多普勒激光测振仪测量水翼的振动速度,并通过一套同步系统实现了高速相机和多普勒激光测振仪的同步触发和测量. 采用小波分析方法对不同空化阶段下的空穴形态和水翼振动数据在时域和频域中的特性进行了分析.对云状空化阶段的同步测量结果进行了研究,分析了振动与空穴发展过程的联系. 结果表明,随着空化数的降低,流场经历了无空化、初生空化、片状空化和云状空化4个阶段,水翼的振动强度呈逐渐增大趋势. 在片状空化和云状空化阶段,空穴脱落导致水翼振动,诱发的振动频率与空穴脱落频率相同. 对于云状空化,在附着型空穴生长阶段水翼发生高频小幅度振动,在空穴脉动和断裂脱落期间水翼表现为低频大幅振动.      

Transient wave analysis of a cantilever Timoshenko beam subjected to impact loading by Laplace transform and normal mode methods

This study applies two analytical approaches, Laplace transform and normal mode methods, to investigate the dynamic transient response of a cantilever Timoshenko beam subjected to impact forces. Explicit solutions for the normal mode method and the Laplace transform method are presented. The Durbin method is used to perform the Laplace inverse transformation, and numerical results based on these two approaches are compared. The comparison indicates that the normal mode method is more efficient than the Laplace transform method in the transient response analysis of a cantilever Timoshenko beam, whereas the Laplace transform method is more appropriate than the normal mode method when analyzing the complicated multi-span Timoshenko beam. Furthermore, a three-dimensional finite element cantilever beam model is implemented. The results are compared with the transient responses for displacement, normal stress, shear stress, and the resonant frequencies of a Timoshenko beam and Bernoulli–Euler beam theories. The transient displacement response for a cantilever beam can be appropriately evaluated using the Timoshenko beam theory if the slender ratio is greater than 10 or using the Bernoulli–Euler beam theory if the slender ratio is greater than 100. Moreover, the resonant frequency of a cantilever beam can be accurately determined by the Timoshenko beam theory if the slender ratio is greater than 100 or by the Bernoulli–Euler beam theory if the slender ratio is greater than 400.     

IMPEDANCE CONTROL METHOD OF STEPPED SWEPT SINE VIBRATION TEST BASED ON PERIODIC EXTENSION

针对步进式多输入多输出正弦扫频振动试验中相邻信号过渡不平顺以及多点相位控制精度差的问题,分析扫频频率切换机理,在保证试验时间以及多点相位差满足参考容差要求情况下,提出周期延拓法平稳地处理两段不连续信号;提出了阻抗多点控制算法,分析了压缩因子对收敛速度与控制精度的影响,设定频响函数矩阵条件数阈值以避免结构病态频率带来的过激励影响;开展多轴多点正弦扫频振动算法试验,结果验证了算法可靠性与有效性.     

Analysis of frequency-domain vibration response of thin plate attached with viscoelastic free layer damping

To predict the vibration response of viscoelastic composite structure, two key issues need to be conducted, one is introducing the constitutive model of viscoelastic material into the analysis model and the other is describing the real damping behavior of viscoelastic composite structure. The emphasis of this study is to obtain the effects of frequency dependence on the vibration response of viscoelastic composite structure and the method of introducing two kinds of damping (viscoelastic material damping and remaining equivalent viscous damping). Vibration response analysis in frequency domain was investigated for viscoelastically damped plate. A cantilever plate attached with the ZN_1 viscoelastic free layer damping (FLD) was chosen to demonstrate the developed method. Frequency-domain response of the composite plate were solved and the obtained results were compared with the experimental values for the purpose of assessing the rationality of the proposed method. In addition, in order to obtain the effects of viscoelastic material parameters on vibration response of viscoelastic composite structure, a detailed parametric analysis was performed. This study shows that the frequency dependent characteristic of viscoelastic material has significant influence on the vibration response in the resonant region and acceptable results can be achieved in the non-resonant region if frequency dependent parameters are substituted by average values of the viscoelastic parameters reasonably in the analysis process.     

参强联合作用非线性结构动力学实验建模

搭建以L 型梁为实验研究对象的参强联合作用多自由度非线性振动实验系统, 将增量谐波平衡非线性识别理论运用到实验建模方法中, 建立了L 型梁的动力学控制方程. 通过对不同激励频率和不同响应情况下的数值模拟与实验数据的比较, 验证了基于增量谐波平衡识别的实验建模方法对多自由度参强联合作用非线性动力学结构的有效性, 以及动力学控制方程的普适性.     

激光激励微型硅悬臂梁的振动特性研究

本文用光学探测方法研究了半导体硅悬臂梁的振动问题;运用基于外差干涉原理的实验装置得到了悬臂梁在激光激励下的振动响应（振动振幅和相位随调制激光频率的变化）;采用等离子波和热弹性波的数学模型,对悬臂梁的振动进行了理论分析;可看到实验与理论模拟结果吻合很好,同时通过分析可得振动相位与调制激光频率的平方根之间有线性关系。关键词词: 光学探测, 硅悬臂梁,振动.      

黏弹性层合悬臂薄壁圆柱壳的模态特性研究

基于薄壳理论和黏弹性理论, 得出了黏弹性层合悬臂薄壁圆柱壳模态特性的半解析解. 根据乐甫薄壳理论, 建立了基层和黏弹性阻尼层薄壁圆柱壳的一阶状态微分方程, 结合黏弹性阻尼层的变形协调关系和层间作用力关系, 利用传递矩阵法得出了整体结构的传递矩阵, 采用高精度的精细积分法得出了固有频率、模态损耗因子和三维模态振型, 最后通过有限元法进行了比较, 通过算例验证了传递矩阵法对黏弹性层合薄壁圆柱壳模态特性研究的有效性.