变截面智能压电梁的动态特性研究

建立变截面智能压电梁的动态模型,分析表面粘贴压电元件的均质梁的固有频率。在分析时考虑坟电元件、粘贴层、梁的剪切变形和转动惯量。研究表明,压电元件的刚度和惯量对梁的频率影响很大,变截面智能压电梁的一除非 固有频率总是高于等截面梁的固有频率。粘结层剪切 对一阶频率影响较 剪切变 转动惯量时,对梁的高阶频率影响较大。考虑梁的惊动国惯量和剪切谱形时,智能阶梯梁的频率比没有时的要低。     

基于能量等效的行波型超声波电动机解析模型

提出一种基于能量等效的行波型超声波电动机稳态特性分析计算的解析模型.首先通过能量等效原则将压电复合定子环简化成复合等直梁模型,综合考虑压电复合定子的转动惯量和剪切变形的影响,利用铁木辛柯梁振动理论得到电动机定子振动的频率方程和强迫振动稳态解:其次,对电动机定、转子接触面的滑动状况进行分析,利用弹性接触理论确定了定、转子接触面的力传递模型和效率表达式,通过把定、转子接触面的摩擦损耗和转子的输出功率视为定子强迫振动的等效阻尼损失,由此建立电动机的机械特性和输出功率表达式;最后,仿真和试验分析了不同电动机结构和材料参数以及定子预压力、驱动频率和摩擦层厚度等对电动机振动特性和机械特性的影响,试验证明了该模型的有效性和适用范围.     

连续移动集中力作用下的梁振动分析

对连续移动集中力作用下梁的有阻尼振动进行了分析,考虑了转动惯量和剪切变形对振动的影响,基于有限差分法给出了振动方程的数值解法,所给出的数值解适用于梁的不同边界条件,利用该数值解法具体求解了一个简单边界条件问题,并以此算例分别讨论了载荷移动速度和载荷间距的变化对梁振动的影响.     

基于压电悬臂梁的驱动器与传感器性能分析的精确解析模型

三层压电梁结构在电场作用下发生变形后会产生诱发电势,进而改变材料整体电势分布,本文考虑此变形和电势耦合效应,基于欧拉-伯努利梁变形理论,推导出能够准确预测压电智能悬臂梁传感器与驱动器性能的解析表达式。考虑压电梁结构弯曲变形后产生的电场影响,建立了三层压电梁结构的控制方程;建立了压电梁作为驱动器时端部输出位移、驱动力矩与输入电压之间联系的解析表达式,以及作为传感器时输出电压与端部作用力之间联系的解析表达式。通过与ANSYS有限元模拟结果以及传统的驱动器和传感器性能表达式的对比,验证了所推导的解析表达式的准确性。     

连续移动集中力作用下的梁振动分析

对连续移动集中力作用下梁的有阻尼振动进行了分析，考虑了转动惯量和剪切变形对振动的影响，基于有限差分法给出了振动方程的数值解法，所给出的数值解适用于梁的不同边界条件，利用该数值解法具体求解了一个简单边界条件问题，并以此算例分别讨论了载荷移动速度和载荷间距的变化对梁振动的影响。     

考虑粘结层的悬臂压电振子发电性能分析

利用压电振子将环境中的振动能量转换为电能是近年研究的热点,研究发现,叠层压电振子中,粘结层厚度对压电振子的发电性能以及抗剪强度均有较大影响。针对矩形、梯形截面形状悬臂梁叠层压电振子,利用ANSYS有限元分析软件仿真分析了其粘结层厚度不同时对于叠层压电振子发电性能及抗剪强度的影响关系。结果表明:随着粘结层厚度的增加,虽然梯形截面叠层压电振子对低频振动的环境能量转换效率要高,但梯形截面压电振子会比矩形截面更容易发生剪切破坏;综合分析表明当粘结层厚度控制在基底层厚度的(1/4~1/5)左右时,叠层压电振子的发电性能及抗剪强度较为理想。     

高速机床主轴支承位置配置对主轴单元振动特性影响的研究

采用考虑剪切变形和转动惯量的Timoshenko梁作为该主轴系统的简化模型,通过对比分析确定前端组配轴承之间的最优跨距后,在施加不同预紧力的情况下,分析不同位置添加支承对于主轴低阶固有频率的影响,为设计和研究人员今后的工作提供一定的理论依据和可行的分析方法.     

行波超声马达带齿定子固有振动频率解析

提出了一种用于计算行波超声马达带齿定子固有振动频率的解析算法。该法重点考虑了带齿梁弯曲变形的具体特点及高阶振动时定子齿的转动惯量对定子固有频率的影响 ,推导了相应的振动微分方程 ,解算出了带齿定子梁的固有振动频率 ,实验证明是一种行之有效的方法。该方法便于分析固有振动频率对各参数变化的敏感性 ,对马达最终驱动频率的确定、定子尺寸的设计及材质选取等优化问题具有指导意义     

Timoshenko模型轴向运动梁的横向振动特性分析

通过对梁微单元体的受力分析,导出Timoshenko模型的轴向运动梁横向振动的运动方程, 并利用复模态分析方法及半解析半数值方法, 研究两端铰支条件下轴向运动梁横向振动的振动模态及固有频率.文中还讨论运动梁前两阶固有频率随轴向运动速度变化的情况.最后利用数值算例对Timoshenko梁、Euler梁、Rayleigh梁及剪切梁的固有频率进行比较, 分析转动惯量及剪切变形的影响.     

超声波电动机胶粘技术及其对定子特性的影响

针对行波型超声波电动机定子压电陶瓷(Piezoelectric,PZT)的胶粘问题,通过对定子的机电耦合效应有限元动力学模型的分析与计算,研究了胶粘层材料特性、厚度对超声波电动机定子振动特性的影响。重点分析不同激励条件下定子边缘缺胶和夹有气泡对胶层的抗剪切能力和定子振动特性的影响;分别从改进电动机定子结构和PZT粘结工艺方面探讨了提高胶粘层抗剪切能力的措施,确定了胶层最佳参数和电动机定子胶粘工艺及结构优化设计思想。结果表明：胶层厚度对电动机定子频率影响不大,但对其振动特性的影响较大,在保证可靠的粘结强度下降低胶层厚度有利于提高电动机性能。基于该工艺和设计思想研制的直径80 mm行波型超声波电动机性能稳定,堵转力矩达到1.2 N·m,空载转速80 r/min,研究结果有助于超声波电动机的产业化。     

考虑翘曲影响的Bernoulli-Euler薄壁梁的弯扭耦合振动

通过直接求解均匀薄壁梁单元弯扭耦合振动的运动偏微分方程，推导其自由振动时的精确动态传递矩阵。采用考虑翘曲影响的Bernoulli-Euler梁理论，且假定薄壁梁单元的横截面是单对称的。动态传递矩阵可以用于计算薄壁梁集合体的精确固有频率和模态形状。针对两个薄壁梁算例，采用自动Muller法和结合频率扫描法的二分法求解频率特征方程，并讨论翘曲刚度对弯扭耦合：Bernoulli-Euler薄壁梁固有频率的影响。数值结果验证了本文方法的精确性和有效性，并指出翘曲刚度可以显著改变薄壁开口截面梁的固有频率。     

A finite thin circular beam element for in-plane vibration analysis of curved beams

In this paper, the stiffness and the mass matrices for the in-plane motion of a thin circular beam element are derived respectively from the strain energy and the kinetic energy by using the natural shape functions of the exact in-plane displacements which are obtained from an integration of the differential equations of a thin circular beam element in static equilibrium. The matrices are formulated in the local polar coordinate system and in the global Cartesian coordinate system with the effects of shear deformation and rotary inertia. Some numerical examples are performed to verify the element formulation and its analysis capability. The comparison of the FEM results with the theoretical ones shows that the element can describe quite efficiently and accurately the in-plane motion of thin circular beams. The stiffness and the mass matrices with respect to the coefficient vector of shape functions are presented in appendix to be utilized directly in applications without any numerical integration for their formulation.     

Effects of shear deformation and rotary inertia on the natural frequencies of axially loaded beams

The purpose of this study is to investigate how the axial load in beams influences the relationships between the natural frequencies and the effects of shear deformation and rotary inertia. Four beam theories are considered in this study. Finite element equations of motion for the beams under a tensile load are formulated to allow the application of various axial loads as well as to impose any type of boundary conditions. The results demonstrate that the stiffening effect by a tensile load may not reduce the frequency error of the Euler beam theory, unlike the results reported in other studies.     

Dynamic finite element method for generally laminated composite beams

A dynamic finite element method for free vibration analysis of generally laminated composite beams is introduced on the basis of first-order shear deformation theory. The influences of Poisson effect, couplings among extensional, bending and torsional deformations, shear deformation and rotary inertia are incorporated in the formulation. The dynamic stiffness matrix is formulated based on the exact solutions of the differential equations of motion governing the free vibration of generally laminated composite beam. The effects of Poisson effect, material anisotropy, slender ratio, shear deformation and boundary condition on the natural frequencies of the composite beams are studied in detail by particular carefully selected examples. The numerical results of natural frequencies and mode shapes are presented and, whenever possible, compared to those previously published solutions in order to demonstrate the correctness and accuracy of the present method.     

Finite elements for dynamical analysis of helical rods

Finite elements are presented for dynamical analysis of helical rods. The element stiffness and mass matrices are based on the exact differential equations governing static behaviour of an infinitesimal element. Natural frequencies obtained by use of the element, which allows for both shear deformation and rotary inertia, are compared to the frequency spectra of helical compression springs. The element performance is compared with that of other finite elements.     

可调频旋磁激励式压电发电机的设计与试验

为提高旋转式压电发电机的安全性与有效带宽,提出一种可调频旋磁激励式压电发电机,并从理论、仿真与试验三个方面对发电机的工作特性进行了研究。建立了压电梁在端部外载荷作用下的刚度/频率偏移模型,并通过仿真获得了刚度、动磁铁数量对发电机响应特性的影响规律。结果表明,压电梁刚度随端部拉/压力的增大而线性增大/减小,固有频率相应地提高且趋于平缓/降低且速率增大,而动磁铁数量将影响发电机的谐振峰数量与放大比。在此基础上进行了相关试验,试验表明,压电梁受拉伸/压缩都将提高发电机的固有频率并降低输出电压幅值,且受压时减幅更大;此外,动磁铁数量除仿真中影响因素外对发电机的固有频率也具有一定影响;通过改变动磁铁数量与调节量,实现了发电机固有频率在39.2～112Hz内的调整,最大频率偏移为185.7%。     

压电式振动发电机的建模及应用

振动式压电发电机是一种可为旋转机械故障诊断中的无线传感节点供电的微能源。本文设计了由压电悬臂梁、质量块和固定装置组成的振动式压电发电机,并建立了安装在恒速旋转机械上的悬臂梁式发电机的数学模型。分析了轴向分力对悬臂梁刚度和发电机频率的影响,在考虑悬臂梁受到轴向力影响的基础上,给出了发电机固有频率、输出电压和输出功率的公式。对一个安装于转动框架上的振动式压电发电机进行了测量,结果表明,当框架转动频率为14.25 Hz时,发电机的输出功率约为35 μW,随着旋转机械转动频率偏离发电机固有频率,发电机的输出功率很快降低。     

Coupled bending and torsional vibration of axially loaded thin-walled Timoshenko beams

A dynamic transfer matrix method of determining the natural frequencies and mode shapes of axially loaded thin-walled Timoshenko beams has been presented. In the analysis the effects of axial force, warping stiffness, shear deformation and rotary inertia are taken into account and a continuous model is used. The bending vibration is restricted to one direction. The dynamic transfer matrix is derived by directly solving the governing differential equations of motion for coupled bending and torsional vibration of axially loaded thin-walled Timoshenko beams. Two illustrative examples are worked out to show the effects of axial force, warping stiffness, shear deformation and rotary inertia on the natural frequencies and mode shapes of the thin-walled beams. Numerical results demonstrate the satisfactory accuracy and effectiveness of the presented method.