磁力调频压电电磁复合发电设计与实验

开展了基于环境振动发电作为微电源弥补传统化学电池供能缺陷的研究。基于非线性磁力调频开发了低宽频振动能采集压电电磁复合发电系统。介绍了发电装置工作原理;利用ANSYS和Ansoft Maxwell有限元分析软件仿真分析了压电和电磁发电的输出特性;最后,搭建了压电电磁复合宽频发电装置实验测试系统,测试了发电系统在磁力自调过程中的输出特性。实验结果显示:复合发电系统在谐振频率60Hz时输出开路电压峰值为5.8V,高于压电系统(5.5V)和电磁系统(410mV)独立发电的开路电压峰值。施加磁力拓宽装置后,当压电悬臂梁沿竖直方向上下移动0~15mm时,系统适应谐振频带拓宽为45~76Hz;悬臂梁沿水平方向平移0~30mm时,谐振频带拓宽为51~70 Hz。结果表明仿真分析与实验测试结果吻合很好。该宽频带能量采集技术可用于低频振动环境的能量采集,可在频变环境中为微型低功耗系统提供低电能。     

Identification of pseudo-natural frequencies of an axially moving cantilever beam using a subspace-based algorithm

This study focuses on extraction of frequency information of a linear time-varying system using free response data. Frequency information is obtained from the pseudo-modal parameters that were defined in a previous study. A subspace-based identification algorithm is introduced. An improved version is proposed to make the algorithm less sensitive to measurement noise. An axially moving cantilever beam is used as the experimental system. A dynamic model is presented to show that lateral vibration of the axially moving cantilever beam is governed by a linear time-varying model. A computer simulation is conducted to compare the true pseudo-modal parameters and approximate ones that can be identified using the improved algorithm. The experimental study focuses on the capabilities of the algorithm and the factors that affect the identification results. A method of grouping identified structural pseudo-natural frequencies is proposed. Limitations of the algorithm are discussed.     

疲劳裂纹对悬臂梁振动特性影响的理论分析

研究了疲劳裂纹对悬臂梁的固有频率及强迫振动响应的影响,使用余弦函数描述疲劳裂纹的开合过程。计算结果表明,疲劳裂纹不仅使悬臂梁的固有频率下降,而且引起非线性强迫振动响应。     

Study of the tip mass and interaction force effects on the frequency response and mode shapes of the AFM cantilever

The vibrational characteristics of an atomic force microscope (AFM) cantilever beam play a key role in dynamic mode of the atomic force microscope. As the oscillating AFM cantilever tip approaches the sample, the tip–sample interaction force influences the cantilever dynamics. In this paper, we present a detailed theoretical analysis of the frequency response and mode shape behavior of a cantilever beam in the dynamic mode subject to changes in the tip mass and the interaction regime between the AFM cantilever system and the sample. We consider a distributed parameter model for AFM and use Euler–Bernoulli method to derive an expression for AFM characteristics equation contains tip mass and interaction force terms. We study the frequency response of AFM cantilever under variations of interaction force between AFM tip and sample. Also, we investigate the effect of tip mass on the frequency response and also the quality factor and spring constant of each eigenmodes of AFM micro-cantilever. In addition, the mode shape analysis of AFM cantilever under variations of tip mass and interaction force is investigated. This will incorporate the presentation of explicit analytical expressions and numerical analysis. The results show that by considering the tip mass, the resonance frequencies of the cantilever are decreased. Also, the tip mass has a significant effect on the mode shape of the higher eigenmodes of the AFM cantilever. Moreover, tip mass affects the quality factor and spring constant of each modes.     

Mechanical and dynamic characteristics of double and single beam cantilevers for MEMS manipulation

Micro and millimeter-scaled cantilever beams are commonly used to apply and measure microforce and manipulate micro-objects, biological cells, and tissues. In manipulating micro-objects and actuating micro-devices by cantilever beams, sudden application and release of forces are typical, and subject to static and dynamic modes of operation. Therefore, the cantilever’s mechanical behavior and vibration characteristics are vital since they are also used in force sensors and probes. The dynamic behavior of the double beam cantilever (DBC) in micro and millimeter-scaled is explored by varying the length without changing the stiffness and compared with the single beam cantilever (SBC). The dynamic attributes such as mode shape, natural frequency, resonance, and response under the impulse force and Coulomb friction are evaluated numerically. This study will assist in selecting the appropriate type and length of cantilevers in micro and millimeter-scale to manipulate micro-objects, biological cells and tissues, and use in MEMS sensors.

     

Crack detection in beams using experimental modal data and finite element model

In this paper, an analytical, as well as experimental approach to the crack detection in cantilever beams by vibration analysis is established. An experimental setup is designed in which a cracked cantilever beam is excited by a hammer and the response is obtained using an accelerometer attached to the beam. To avoid non-linearity, it is assumed that the crack is always open. To identify the crack, contours of the normalized frequency in terms of the normalized crack depth and location are plotted. The intersection of contours with the constant modal natural frequency planes is used to relate the crack location and depth. A minimization approach is employed for identifying the cracked element within the cantilever beam. The proposed method is based on measured frequencies and mode shapes of the beam.     

RESEARCH ON MODELING AND CHARACTERISTICS OF THE SPINDLE DYNAMIC COUPLING ABSORBERING SYSTEM OF A SUPER－PRECISION SURFACE GRINDING MACHINE

The bearing is described by constrain matrix, and the spindle system of a NC surface grinding machine is simplified as elastic-coupling beam, then modal synthesis method is used to establish the dynamic model of beam. Moreover, the response of the end of rotor is analyzed, and the natural frequency, principle mode and other dynamic characteristics of the coupling system are studied, the law of bearing stiffness to coupling frequency and amplitude of rotor is also found. Finally, according to the actual condition, a dynamic absorber is designed. The simulation and experimental results show that the amplitude of spindle can be declined effectively when the dynamic absorber is attached.     

移动质量激励下梁动态响应分析与试验研究

以移动质量激励下的梁为研究对象,建立了移动质量-简支梁和移动质量-悬臂梁耦合振动模型.考虑了移动质量的重力、Corilous加速度和惯性加速度对梁横向振动的影响,利用得到的级数解编制程序分析了移动质量参数变化对梁动态响应的影响.建立了移动质量激励下的梁动态响应试验平台,通过试验得到了各种规格质量块以不同运动速度激励作用下的梁动态响应曲线.试验结果表明了移动质量激励下梁动态响应模型的正确性.     

裂纹扩展过程中电磁谐振疲劳试验系统动态特性分析*

电磁谐振疲劳裂纹扩展试验系统是一种工作在谐振状态下测试金属材料断裂特性的试验装置,要求在裂纹扩展过程中精确跟踪系统的固有频率和控制试验载荷,为达到这一目的,需要对裂纹扩展过程中系统的动态特性进行精确的分析。据此,建立3自由度有阻尼电磁谐振疲劳试验振动系统的数学模型,采用ANSYS有限元法计算CT紧凑拉伸试件的刚度,研究不同材料试件刚度、系统固有频率,试验载荷幅频曲线、共振振幅在裂纹扩展过程中的变化规律,并进行相关试验,试验结果表明：系统固有频率计算值与试验测量值之间的最大偏差为1.9 Hz;系统动态特性仿真结果与试验结果能够较好地吻合。该研究结果为电磁谐振式疲劳试验载荷的高精度控制提供了理论依据。     

Four-beam model for vibration analysis of a cantilever beam with an embedded horizontal crack

As one of the main failure modes, embedded cracks occur in beam structures due to periodic loads. Hence it is useful to investigate the dynamic characteristics of a beam structure with an embedded crack for early crack detection and diagnosis. A new four-beam model with local flexibilities at crack tips is developed to investigate the transverse vibration of a cantilever beam with an embedded horizontal crack; two separate beam segments are used to model the crack region to allow opening of crack surfaces. Each beam segment is considered as an Euler-Bernoulli beam. The governing equations and the matching and boundary conditions of the four-beam model are derived using Hamilton's principle. The natural frequencies and mode shapes of the four-beam model are calculated using the transfer matrix method. The effects of the crack length, depth, and location on the first three natural frequencies and mode shapes of the cracked cantilever beam are investigated. A continuous wavelet transform method is used to analyze the mode shapes of the cracked cantilever beam. It is shown that sudden changes in spatial variations of the wavelet coefficients of the mode shapes can be used to identify the length and location of an embedded horizontal crack. The first three natural frequencies and mode shapes of a cantilever beam with an embedded crack from the finite element method and an experimental investigation are used to validate the proposed model. Local deformations in the vicinity of the crack tips can be described by the proposed four-beam model, which cannot be captured by previous methods.     

基于非线性动响应的夹持松动特性研究

根据夹持结构存在的局部非线性特点,研究基于非线性动响应的夹持松动识别方法。利用悬臂梁结构在夹持边界条件下自由振动的非线性动响应理论解,将结构非线性响应的二次谐波振幅与基频振幅响应的比例系数r作为松动判别特征量,研究夹持结构的松动特性规律。以夹持悬臂梁结构为研究对象,建立接触有限元模型来计算夹持结构的非线性动响应;同时开展了试验研究,通过不同夹持力下结构振动响应特性来验证该方法的有效性。仿真和试验结果表明,随着夹持力的增加,结构非线性动响应信号的二次谐波振幅呈下降趋势,振幅比值r呈幂指数下降。二次谐波振幅与基频振幅的比值r可以作为表征结构松动状态的判据。     

基于μ综合的压电柔性结构振动主动控制

利用模态理论和μ综合方法,对智能柔性悬臂梁进行振动主动控制研究。以压电陶瓷为作动器,电阻应变计为传感器,采用有限元方法和实验模态测试方法建立结构动力学模型,对两种方法所得结果进行比较分析可知有限元模型与实际系统存在误差。考虑外部扰动和量测噪声的不确定性,同时考虑系统固有频率、阻尼比和作动器参数的不确定性,选择模态位移信号为评价量,根据信号的频率特性选择合适的加权函数,利用μ综合方法设计振动控制器。从频域角度分析控制器的有效性,结果表明该控制器能抑制不确定干扰对输出应变的影响,能在系统不确定性情况下满足控制要求,说明控制器具有鲁棒性。进行了振动主动控制实验研究,结果表明,所设计的控制器能有效抑制结构的振动响应。     

动质量对悬臂梁振动抑制的数值分析和实验研究

在简谐激励下,实验研究端部动质量对悬臂梁共振响应的抑制能力,发现抑振效果与质量位置和质量比有直接关系,动质量和梁的高频碰撞振动现象。提出包含碰撞效应的数学模型,用振型叠加法,将耦合的非线性偏微分方程变为时变非线性微分方程。计算无量纲梁端部位移和碰撞力。结果显示,提出的模型基本上描述了系统的动态特性,在一定程度上理论和实验结果是一致的。     

基于固有频率的呼吸式裂纹梁损伤识别方法

将呼吸裂纹梁简化为由扭转弹簧连接的两段弹性梁,在假定振动响应随振幅变化的基础上推导出呼吸裂纹梁的固有频率方程;考虑振动过程中呼吸裂纹的开合情况,假定裂纹梁的刚度是振幅的非线性函数,建立了呼吸裂纹梁的多项式刚度模型;结合等高线裂纹识别理论和方法,提出了一种基于固有频率的呼吸裂纹梁损伤识别方法,算例验证了方法的可行性与有效性。研究表明,该方法的识别精度取决于实验固有频率的精度。     

多频响应的压电振动能量采集器的性能分析与测试

为了提升压电悬臂梁采集振动能量的能力,研究了一种具有多频振动响应的振动能量采集器。在压电悬臂梁与振动激励源之间增加一个附加梁,压电悬臂梁和附加梁的末端分别安装一个质量块,压电悬臂梁和附加梁垂直连接。附加梁的末端质量被设计为远大于压电梁的末端质量,而压电梁的一阶谐振频率在附加梁的前两阶谐振频率之间。采用该设计,压电悬臂梁的振动响应是多个谐振频带的叠加。通过建立机电解析模型,描述了所提出的振动能量采集器的振动响应和发电特性,同时制作了一个振动能量采集器样机进行试验,结果表明,与传统的悬臂梁振动能量采集器相比,所提出的振动能量采集器可以在更宽的频带范围内采集更多的振动能量。     

含集中参数弹性梁振动特性解析与实验识别

基于Laplace变换推导出含集中质量与集中刚度弹性梁的振型函数和典型边界条件对应的频率方程,针对有一个集中质量与一个集中刚度的悬臂梁,求解出其固有特性,并利用基于自然激励技术(natural excitation technique,简称NExT)的特征系统实现算法(eigensystem realization algorithm,简称ERA),即NExT-ERA法对相应结构系统进行了模态识别。通过对比解析结果和实验结果,分别讨论了集中质量与集中刚度大小变化和位置变化时对梁振动特性的影响,得出了集中质量和集中刚度在悬臂梁上位置和大小变化时,悬臂梁固有频率的相应变化规律,为工程中具有集中质量和集中刚度等直弹性梁的振动分析方法和集中参数布置设计提供了参考。     

Modal testing of nanocomposite materials through an optimization algorithm

An efficient identification method for modal testing of viscoelastic composite materials is demonstrated in this paper, through the analytical–experimental transfer function method. The procedure for the identification of analytical–experimental transfer functions is carried out using a genetic algorithm (GA) by minimizing the difference between the measured response from tests and the calculated response, which is a function of the modal parameters. The analytical transfer functions provide a sub-structuring process to identify modes, as a function of damped natural frequencies and loss factors of a complex structure and it is insensitive to experimental noise as well as the modal coupling effect. The proposed method is verified with the calculation of the elastic modulus and modal properties of a cantilever steel beam with the FEM and compared with the identification results of the proposed algorithm. The effectiveness of the proposed method is demonstrated by investigating the static and dynamic behavior of epoxy cantilever beam specimens reinforced with silica nanoparticles. Analytical–experimental transfer functions accurately identified the viscoelastic and dynamic response of the studied specimens, while the results indicated that the inclusion of nanosilica particles increased the stiffness of the epoxy network and the damping response of the reinforced specimens is improved.     

Dynamic characteristics of a beam angular-rate sensor

This paper gives a bandwidth and sensitivity analysis for a vibrating square beam angular-rate sensor. A skew-symmetric gyroscopic inertia matrix results from rotating about an axis orthogonal to the plane of a forced-vibration elastic system giving unique characteristics permitting measurement of its rotation rate. The quality factor has a huge influence on the forced response at the resonant frequencies governing the dynamic operating range in its use as an angular-rate sensor. Fourier-type solution for the cantilever beam with electrostatic excitation reveals characteristics analogous to those occurring for more complex systems. The deflection-dependent nature of the electrostatic excitation induces the parametric excitation into the system, yielding a Hill-type equation. Although it causes the behavior to be more complex, linear sensitivity curves can be obtained, provided that the displacement of the beam is small compared with the gap in static equilibrium. Finally, it is seen that the system provides the applicability of the rotating beam for use as an angular-rate sensor within a certain small range of parametric excitation. Design rules are suggested by observing that sensor sensitivity decreases with increasing sensor bandwidth.     

Dynamic analysis of an axially moving robot manipulator supported by bearings

In this study, a robot manipulator is modelled as a cantilever beam, which moves in an axial direction, has a lumped mass at the end, and is supported by intermediate springs. Considering the tip mass and intermediate springs in the modeling, we derive the equations of motion in which the rigid-body motion is coupled with the flexible motions, and then analyze the transverse vibrations of the beam. Furthermore, we study the tip mass effects on the natural frequencies and the corresponding mode shapes. The natural frequency loci veering is analyzed for variations in the tip mass and the spring position/stiffness. In addition, we investigate the exchange and localization of modes around these veering regions as well as the parameter effects on the mode shapes. Using a Short-time Fourier transform (STFT), the relationship between the dynamic characteristics and dynamic responses are described. It is found that the dynamic characteristics of the beam are dependent on the veering distance. It is also shown via dynamic responses that the mode exchanges occur when a veering distance is close.     

智能Timoshenko梁强迫振动响应的行波解

运用行波法求解智能Timoshenko梁的强迫振动响应.基于梁的振动行波法分析理论,介绍周期力和周期力矩激励下激励点处波的传播关系,推导在逆压电效应下,智能Timoshenko梁上某一点的响应函数,并以智能Timoshenko悬臂梁为例,得到梁不同位置的拾振点处的幅频和相频特性及不同受力状况下的智能梁的幅频特性,还得到了受迫振动的时域响应信号波形,最后将求解结果与有限元法求解结果做对比分析.分析结果表明,行波法分析可用于精确计算智能梁的强迫振动响应.