变截面压电智能梁的频率分析

建立了变截面压电智能梁的动态模型,分析了表面粘贴压电元件的均质梁的固有频率。在分析中考虑了压电元件和粘结层的影响,同时,还考虑了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,粘结层剪切的弹性模量对一阶频率影响较小;当考虑梁的剪切变形和转动惯量时,则对梁的高阶频率影响较大。     

含多个压电元件智能悬臂梁的横向振动特性

本文以含多个压电元件的悬臂梁为例,基于Bernoulli-Euler梁的阶梯折算法,结合压电智能悬臂梁段的等效弹性模量理论,计算了多个压电元件的悬臂梁的固有频率和振型,并与有限元和等截面梁的计算结果进行比较。计算分析表明,压电材料尺寸和位置变化对智能悬臂梁结构的横向振动特性具有显著的影响,分析结论对高速飞行器结构设计和主动振动控制中压电元件的优化布置有实用价值。     

考虑粘贴层影响的智能结构梁分布力模型

以线性应变理论为基础,提出了考虑粘贴层影响的智能结构梁分布力模型。分别导出了单面粘贴驱动器和双面粘贴驱动器时的分布力模型的计算公式。通过数值模拟,分析了压电驱动器的驱动性能及其影响因素。     

传递矩阵分析轴向受力智能梁的振动和稳定性

主要针对受轴向压力的智能梁,研究压电片的尺寸、位置变化以及轴向力变化对智能梁固有特性及其稳定性的影响.利用复合材料力学的等效弹性模量理论,将表面均匀对称分布压电材料的智能梁等效为非均质变截面梁.用传递矩阵法分析轴向受力智能梁的振动和稳定性.基于Bemoulli-Euler梁振动分析的传递矩阵法,导出轴向受压的智能梁的频率方程、模态函数及临界载荷方程.以受轴向压力的智能简支梁为例,分别用传递矩阵法和基于ANSYS的有限元法计算其动态特性和稳定性.计算结果表明,压电片尺寸、位置以及轴向力对智能梁的固有特性和稳定性都有显著影响,所得结论对高速飞行器结构设计和主动振动控制中压电元件的优化布置有一定的实用价值.     

含MFC智能层的复合材料层合板自由振动研究

在一阶剪切变形板理论的基础上,提出一种考虑之子函数影响的位移场。根据给定的位移场,利用瑞利-里兹法和切比雪夫多项式,考虑机电耦合特性,分别求出含有智能压电宏观纤维复合材料层(macro fiber composite,简称MFC)的碳纤维增强复合材料层合悬臂板在开路与通路两种电学边界条件下自由振动的固有频率,讨论不同铺层方式、宽厚比、长宽比以及不同的外电压状态下,MFC智能层对碳纤维增强复合材料层合板固有频率的影响。研究结果表明,MFC智能层对所研究系统的固有频率影响显著,可以通过控制MFC智能材料的通电电压来实现对复合材料层合板振动特性的控制。     

智能结构中压电材料厚度的设计

研究了在振动控制中压电元件和主结构体之间厚度的匹配关系。通过对智能复合材料的分析,得出了对称粘贴、功能不对称的压电元件所感受的有效弯矩,给出了压电元件产生最大弯矩时的最佳厚度,并讨论了材料弹性模量的影响。     

压电智能梁的拉伸-弯曲耦合模型

利用虚功原理,建立了单面粘贴有压电致动器的梁结构的拉伸－弯曲耦合模型,在分析过程中,考虑了梁与致动器之间粘贴层的影响。通过分析可得,粘贴层剪切应力的分布与致动器端部附近的应变分布有相似的特征。随着粘贴层的剪切模量的增加或其厚度的减小,则剪切力在靠近压电致动器端部区域迅速增大。     

压电智能梁的拉伸—弯曲耦合模型

利用力平衡原理,建立了单面粘贴有压电致动器的梁结构的拉伸—弯曲耦合模型,在分析过程中,考虑了梁与致动器之间粘贴层的影响。通过分析可得,粘贴层切应力的分布与致动器端部附近的应变分布有相似的特征,随着粘贴层的切变模量的增加或其厚度的减小,切应力在靠近压电致动器端部区域迅速增大。     

利用压电层提高变截面Beck杆的稳定性研究

对一定边界条件下的变截面Beck杆,通过在其表面特定位置粘贴压电片,并施加电场于压电片来提高其稳定性。建立了含端部集中质量的压电层合变截面Beck杆的计算模型,导出分段表示的运动微分方程。利用微分求积法分析了压电片几何物理参数对Beck杆的动态稳定性的影响。研究结果表明,粘贴压电片可以有效提高Beck杆的稳定性。     

智能悬臂梁横向振动的行波解

介绍智能梁的行波建模方法及其横向振动固有频率的计算方法.行波建模方法主要步骤包括,①求出Timoshenko梁横向振动方程的谐波解.②根据弯曲波的传播特性,给出弯曲波的传递关系;在智能梁上截面尺寸改变处和边界处,根据其连续条件和平衡条件,给出波的反射关系和透射关系.③通过联立智能梁内所有的传递、反射、透射关系,求得整体智能梁的特征方程.文中以智能悬臂梁为算例,通过解析法(包括Timoshenko梁模型和Euler-Bernoulli梁模型)与有限元法得到横向振动频率的比较,验证行波建模方法的有效性.此外,为考虑压电片材料对智能梁整体模型的影响,引入等效弹性模量.     

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。     

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.     

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.     

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.     

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.     

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.     

Static, dynamic, and buckling analysis of partial interaction composite members using Timoshenko's beam theory

The static, dynamic, and buckling behavior of partial interaction composite members is investigated in this paper by taking into account for the influences of rotary inertia and shear deformations. The governing differential equations obtained are very comprehensive, covering and extending the current models for the problems that are based on Euler–Bernoulli beam theory. The analytical solutions of the deflection are then found for the beam with uniformly distributing load under common boundary conditions. The free vibration and buckling behavior are also studied and the analytical expressions of the frequencies of the simply supported beam are obtained explicitly, as are the buckling loads. For other boundary conditions, the eigen-equations are transcendental and thus some numerical examples are presented to demonstrate the effects of the shear deformation and rotary inertia on the resonant frequencies and buckling loads.     

A more comprehensive modeling of atomic force microscope cantilever

This paper focuses on the development of a complete model of an atomic force microscope (AFM) micro-cantilever beam, based on considering the effects of four major factors in modeling the cantilever. They are: rotary inertia and shear deformation of the beam and mass and rotary inertia of the tip. A method based on distributed-parameter modeling approach is proposed to solve the governing equations. The comparisons generally show a very good agreement between the present results and the results of other investigators. As expected, rotary inertia and shear deformation of the beam decrease resonance frequency especially at high ratio of cantilever thickness to its length, and it is relatively more pronounced for higher-order frequencies, than lower ones. Mass and rotary inertia of the tip have similar effects when the mass-ratio of the tip to the cantilever is high. Moreover, the influence of each of these four factors, thickness of the cantilever, density of the tip and inclination of the cantilever on the resonance frequencies has been investigated, separately. It is felt that this work might help the engineers in reducing AFM micro-cantilever design time, by providing insight into the effects of various parameters with the micro-cantilever.