基于结构动力学的框架结构固有频率估算方法

对框架结构的一阶固有频率与单门框的一阶固有频率的关系进行了推导,找出一种通过部件模态参数估算整体系统的模态参数的方法．通过ANSYS有限元分析对该估算方法进行了验证,并在石油钻机井架底座的有限元模态分析中应用该方法对系统固有频率进行了估计,误差均不超过1％．结论表明,该方法对于框架串联结构的固有频率估算是方便且可行的．     

机抖激光陀螺动力学分析及优化设计

利用有限元分析软件ANSYS,建立了机抖激光陀螺有限元模型并进行了模态分析和随机振动分析,通过与试验结果对比,验证了模型的合理性和精确性,指出了现有结构的薄弱环节。利用灵敏度分析技术分析了安装盒底部、四壁和支柱等几何尺寸和约束位置对机抖激光陀螺固有频率的影响。计算表明:影响固有频率的主要因素是安装盒的支柱高度、底面厚度和约束位置,而安装盒四壁厚度对固有频率影响很小。最后对结构进行了优化设计,优化后结构一阶固有频率提高35.7%,二阶以上固有频率提高63%以上。     

辅助质量块—单裂纹悬臂梁耦合系统固有频率的理论研究及其应用

论文研究了辅助质量块—单裂纹悬臂梁耦合系统的固有频率,用无缺陷悬臂梁固有振型叠加一个多项式来近似拟合含单裂纹悬臂梁的振型,由动力学方法推导了辅助质量块—单裂纹悬臂梁系统的固有频率方程的解析形式,系统频率随着质量块在梁上位置改变而改变,即可得到固有频率曲线,此频率曲线包含了缺陷信息,因此可对固有频率曲线进行平稳小波变换来识别梁上的缺陷.同时用有限元计算结果对上述固有频率理论推导进行验证,有限元结果与论文理论推导结果相一致.最后论文数值计算了质量块大小、缺陷深度、位置等因素对系统固有频率的影响,也探讨了平稳小波变换用于识别损伤,结果验证了该理论推导的可靠性和损伤识别的准确性.     

复杂承载钢结构模态参数识别与综合性能评价

提出了根据动力特性试验识别结构的模态参数,运用优化算法修改动力有限元模型,进而评价复杂承载钢结构练合性能的方法.针对复杂承载钢结构的结构特点和激振形式,推导了模态参数识别公式;介绍了有限元模型动力修正的一阶搜索优化算法.利用近似平稳随机激励,对井架钢结构进行了现场模态试验,识别出前三阶固有频率和前二阶振型,分析了该结构的实际运行状况.仅依据前二阶固有频率,应用一阶搜索的优化算法,对动力有限元模型进行了修正,重分析表明:该修正模型实现了前三阶固有频率和应力特征的精确反演,能够用于进一步的静、动力分析和综合性能评价.     

碳纤维双马树脂基圆锥壳的热振动特性研究

本文针对碳纤维双马树脂基圆锥壳在自由边界条件下的热振动特性展开了研究.通过热模态试验获得了圆锥壳在不同温度时的前三阶固有频率,结果表明:圆锥壳的固有频率随温度升高而降低.结合有限元方法,分析了温度对圆锥壳的热振动特性的影响机理,结果表明:随着温度升高,一方面圆锥壳的弹性模量会降低,使固有频率减小;另一方面,复合材料单层...     

薄板振动特征值问题的一种改进积分方程解法

本文根据一种改进的边界元/有限元混合法求解薄板振动固有频率问题,既避开了标准的边界元法所导致的求解非代数特征值方程的困难,亦能够基本上消除通常的边界元/有限元混合法结果精度受区域内部单元划分影响较大的弊端。文中讨论了迭代算法的收敛问题,并用于薄板固有频率分析。数值结果表明,即便是在域内单元很粗疏划分的情况下,本文的方法仍能给出相当满意的结果。     

环形桁架结构模态实验及有限元仿真分析

针对大型可展开环形桁架天线结构开展了模态实验和有限元仿真分析。首先设计加工了环形桁架实验模型,采用锤击法对自由边界条件下环形桁架结构进行了实验模态分析,得到环形桁架结构的前六阶固有频率及其对应模态振型,并通过模态置信准则对实验结果进行了可靠性分析。其次,建立了环形桁架实验模型的有限元模型并进行模态分析,仿真得到其前六阶固有频率和模态振型。最后详细对比分析了实验结果与有限元仿真结果。结果表明:二者固有频率误差小于5%,且实验模态振型与有限元仿真模态振型一致,证明了本文分析结果真实可靠;同时,分析得到了环形桁架结构第一、二阶振型为椭圆形,第三、四阶振型为三角形,第五、六阶振型为四边形。     

半球谐振陀螺仪谐振子振动特性的有限元分析

应用 ANSYS 软件对半球谐振陀螺仪谐振子的振动特性进行了有限元分析,建立了Ψ型半球壳谐振子的有限元模型,计算出了谐振子的固有频率及振型。在理论分析的基础之上,提出了对于Ψ型半球壳谐振子的结构设计的合理建议。     

氮化硅陶瓷平板振动模态参数的研究

本文采用压电陶瓷片测振技术,试验分析了氮化硅陶瓷平板的固有频率及模态阻尼比,试验结果与有限元计算结果比较吻合。本文还对氮化硅陶瓷平板与普通钢平板做了对比试验,结果表明氮化硅陶瓷平板的固有频率及模态阻尼比都较高。     

基于固有频率向量的结构损伤检测方法

基于损伤前后结构固有频率的变化,引入了固有频率向量及固有频率向量置信准则的概念,提出了基于固有频率向量的结构损伤检测方法.首先建立完好结构的有限元模型,并模拟出结构的若干种损伤模式,分别求出完好结构与各损伤模式结构的固有频率向量,从而构建出结构损伤特征数据库,随后对具有某种未知损伤的结构,根据该结构的固有频率向量与损伤数据库中每一个固有频率向量之间的相关程度--固有频率向量置信准则,由最大置信准则来判定对应的损伤模式.应用该方法对一个八层剪切空间框架模型的损伤进行了仿真检测,对于无测量误差的情况,在任何一层的支柱损伤大于最低可检损伤的情况下,都能准确的检测出损伤的位置及程度;考虑了固有频率测量的随机误差之后,应用损伤检测概率进行评估,该方法也具有较高的损伤检测概率.     

基于高阶梁理论的功能梯度材料自由振动分析

本文基于一种新型的高阶梁理论,研究了功能梯度材料梁的自由振动问题。首先对该新型高阶梁理论进行了介绍,然后对该理论进行了有限元实现,并利用Hamilton原理推导得到了离散的动力学平衡方程,构造了2节点8自由度的C1型高阶梁单元。参照文献作了均质悬臂梁的模态分析,验证了该梁单元的精度。然后利用该单元进行功能梯度梁的模态分析,并构造了一种材料相关性很弱的无量纲固有频率。由该无量纲固有频率引入了功能梯度梁与均质梁固有频率之间的转换关系,并通过算例分析了该转换关系的适用条件。     

Free vibration characteristics of sectioned unidirectional/bidirectional functionally graded material cantilever beams based on finite element analysis

Advancements in manufacturing technology, including the rapid development of additive manufacturing (AM), allow the fabrication of complex functionally graded material (FGM) sectioned beams. Portions of these beams may be made from different materials with possibly different gradients of material properties. The present work proposes models to investigate the free vibration of FGM sectioned beams based on onedimensional (1D) finite element analysis. For this purpose, a sample beam is divided into discrete elements, and the total energy stored in each element during vibration is computed by considering either the Timoshenko or Euler-Bernoulli beam theory. Then, Hamilton's principle is used to derive the equations of motion for the beam. The effects of material properties and dimensions of FGM sections on the beam's natural frequencies and their corresponding mode shapes are then investigated based on a dynamic Timoshenko model (TM). The presented model is validated by comparison with three-dimensional (3D) finite element simulations of the first three mode shapes of the beam.     

Monitoring structural damage of components using an effective modulus approach

This paper describes a novel nondestructive damage detection method that was developed to study the influence of a crack on the dynamic properties of a cantilever beam subjected to bending. Experimental measurements of transfer functions for the cracked cantilever beam revealed a change in the natural frequency with increasing crack length. A finite element model of a cracked element was created to compute the influence of severity and location of damage on the structural stiffness. The proposed model is based on the response of the cracked beam element under a static load. The change in beam deflection as a result of the crack is used to calculate the reduction in the global component stiffness. The reduction of the beam stiffness is then used to determine its dynamic response employing a modal analysis computational model. Euler–Bernoulli and Timoshenko beam theories are used to quantify the elastic stiffness matrix of a finite element. The transfer functions from both theories compare well with the experimental results. The experimental and computational natural frequencies decreased with increasing crack length. Furthermore the Euler–Bernoulli and Timoshenko beam theories resulted in approximately the same decrease in the natural frequency with increasing crack length as experimentally measured.     

Dynamic analysis of a spinning composite “deep” hyperbolic coupling

A dynamic analysis of a “deep” hyperbolic composite coupling is presented. A model is developed based on “shell/beam” assumptions, the energy approach, and the application of the extended Lagrange’s Equations. The mathematical model is solved, using the finite element method, to study the effect of the minimum diameter of a specific “deep” coupling on its dynamic characteristics. The results of the developed finite element program are compared with the corresponding 3D-ANSYS ones. The effect of the spinning speed is also investigated. Results indicate that the developed model is very accurate in predicting the axial and meridional/tangential natural frequencies. The model, however, over predicts the flexural natural frequency. The model also successfully captures the branching phenomenon of the flexural natural frequency exhibited with spinning.     

一类刚-柔耦合系统的建模与稳定性研究

对于由中心刚体带有柔性梁附件组成的这一类简单刚 柔耦合系统，目前文献广泛采用的Ｅｕｌｅｒ Ｂｅｒｎｏｕｌｉ梁模型中考虑的刚 柔运动耦合项有严重的缺陷．本文对于物理本构关系线性的有限变形梁，分别采用微元法和变分法建立了该系统大挠度非线性动力学方程组．本文使用严格的方法来研究此非线性耦合动力学模型，采用能量 动量矩组合方法构成Ｌｉａｐｕｎｏｖ函数，严格证明了此非线性系统平凡解的积分范数稳定性以及具有鲜明物理意义的最大模范数稳定性．本文对文献中引用的三类线性化模型，采用假设模态法，对中心刚体匀速转动时梁的振动作了数值仿真，进一步验证了本文的结论．上述结果，对选择刚 柔耦合系统正确的动力学模型是有益的．     

On the Transfer of Energy between Widely Spaced Modes in Structures

An experimental and theoretical study of the response of aflexible cantilever beam to an external harmonic excitation nearthe beam's third natural frequency is presented. For a certain range ofthe excitation frequency, we observed experimentally that the responseincludes a large contribution due to the first mode of the beamaccompanied by a slow modulation of the amplitude and phase of the thirdmode. In addition, we noted that the energy transfer between the thirdand first modes is very much dependent upon the closeness of themodulation (or Hopf bifurcation) frequency to the first-mode naturalfrequency. In earlier studies by Nayfeh and coworkers, the modulationfrequency was close to the first-mode natural frequency, and thereforelarge first-mode swaying was observed. But for higher forcingamplitudes, the present experiments show that the modulation frequencytends to shift away from the first-mode natural frequency, andsubsequently very little swaying is observed. We also developed areduced-order analytical model by discretizing the integralpartial-differential equation of motion, derived by Crespo daSilva and Glenn, using the Galerkin procedure with a four-modeapproximation. The reduced-order model demonstrates the energy transferfrom the third mode to the first mode.     

基于粗粒化方法的类超级碳纳米管自由振动研究

超级碳纳米管是在碳纳米管结构基础上，将每一根碳-碳键替换为碳纳米管而形成的新型结构。类超级碳纳米管是超级碳纳米管对应的宏观结构，在保持外观结构的基础上将尺度放大到宏观尺度。本文建立了类超级碳纳米管的粗粒化模型。基于粗粒化方法，研究了类超级碳纳米管的自由振动。分析了内外管半径以及长度对类超级碳纳米管振动行为的影响。与原结构有限元进行对比，结果表明粗粒化方法能有效的计算类超级碳纳米管的振动行为。     

基于粗粒化方法的类超级碳纳米管自由振动研究

超级碳纳米管是在碳纳米管结构基础上,将每一根碳-碳键替换为碳纳米管而形成的新型结构。类超级碳纳米管是超级碳纳米管对应的宏观结构,在保持外观结构的基础上将尺度放大到宏观尺度。本文建立了类超级碳纳米管的粗粒化模型。基于粗粒化方法,研究了类超级碳纳米管的自由振动。分析了内外管半径以及长度对类超级碳纳米管振动行为的影响。与原结构有限元进行对比,结果表明粗粒化方法能有效的计算类超级碳纳米管的振动行为。     

任意边界条件下Timoshenko梁及其修正理论的自振特性分析

提出一种求解任意边界条件下经典Timoshenko梁以及修正Timoshenko梁自振频率和振型的新方法。利用改进的傅立叶级数消除传统傅立叶级数的边界不收敛问题,然后通过Rayleigh-Ritz法导出Timoshenko梁的拉格朗日泛函,根据Hamilton原理将原问题转化为求解矩阵广义特征值问题。通过与解析解对比,本文采用的方法具有较好的收敛性以及较高的计算精度;通过数值计算发现,经典Timoshenko梁的自振频率略高于修正的Timoshenko梁,随着振型阶数的提高,经典Timoshenko梁的计算结果逐渐偏离文献解和有限元结果,而修正的Timoshenko梁能够保持较好的一致性;对于不同边界条件下修正Timoshenko梁的计算结果均能与有限元的计算结果吻合得很好。最后运用MATLAB编程软件将程序设计为App,对于不同情形的梁只需要修改参数即可,可为实际工程提供高效便捷的计算方案和可靠理论依据。