旋转圆环动态特性的行波解

基于固体弹性介质中的行波理论,对旋转圆环的固有频率进行了计算.以扩张弯曲梁微元体的运动方程为基础,分析了运动条件下该波导中行波的色散关系.通过分离正行波数和负行波数,解决了行波法计算旋转圆环的固有频率问题.同时给出了波数分离的判断依据,并结合简谐波动的相位封闭原理和传递矩阵建立了旋转圆环的特征方程.数值模拟研究了旋转体...     

旋转弹性体的有限元线法分析

本文将有限元线法应用于一般荷载作用下的旋转弹性体的分析。文中将任意荷载沿环向展开为Ｆｏｕｒｉｅｒ级数，利用正交性，将问题转变为一系列旋转子午面上二维问题的叠加。文中对任一环向谐波建立了旋转面上的曲线曲边单元，导出了相应的常微分方程体系，并对由柱坐标引起的ｒ＝０处的奇异性问题做了完备合理的处理。文中给出了具有代表性的数值算例，用以展示本法的出色的表现     

多自由度参数振动受迫响应的三角级数逼近

针对多自由度的参数振动系统,研究了参数周期与激励力周期不相同情况下受迫振动稳态响应的三角级数解。首先根据调制反馈原理将受迫振动响应表示为各谐波成分线性组合的三角级数形式;然后运用谐波平衡及分块带状矩阵求逆算法,求解得到各个谐波项的系数向量;最后将本文提出的级数逼近法与标准的Runge-Kutta法进行了对比。结果表明:两种方法得到的相图结果高度一致,而本文方法在分析和计算上更具有优势:1)用三角级数来表达振动受迫响应,可以直接得到各频率成分的谐波系数,利于参数振动的时域、频域分析;2)所有的谐波系数向量都可以通过计算机进行数值计算,采用该方法得到的逼近误差与级数项数有关,随着级数项数的增加精度会进一步提高;当级数项数取15项时,逼近误差为8.12×10-3;3)对于同样的10万数据点的计算量,Runge-Kutta法耗时69.51s,而本文采用了大型稀疏矩阵快速算法的级数逼近法计算耗时仅0.1317s,计算效率显著提高。     

旋转相似载荷下轴对称结构弹性响应的快速算法:旋转叠加法及其应用

基于叠加原理,采用坐标旋转和线性叠加的方法,建立了求解旋转相似载荷下轴对称结构弹性响应的快速算法--旋转叠加法.文章首先给出了"旋转相似载荷"的定义,推导了相关计算公式,然后给出了一个应用实例,验证了算法的正确性和有效性,最后对相关问题进行了讨论.旋转叠加法巧妙利用了叠加原理和结构的轴对称性,对同一结构只需一次分析,即...     

考虑横向剪切变形和旋转惯性的层合正交异性球壳的动态响应

本文建立了计及横向剪切变形的旋转惯性的复合材料轴对称层合圆柱正交异性球壳的运动方程。在此基础上，用有限差分法计算了球壳在轴对称动力载荷下的动态响应，并讨论了材料参数、结构参数和横向剪切变形的影响。     

基于Nataf变换的层递响应面法分析结构可靠度

针对现有的随机响应面法(SRSM)和层递响应面法(CRSM)存在的局限性,本文结合预处理随机Krylov子空间法,建立了基于Nataf变换的向量型层递响应面法,并应用于含非高斯型互相关随机变量的结构可靠度分析。首先,利用预处理随机Krylov子空间的层递基向量近似展开结构的总体节点位移向量,建立向量型层递响应面;然后,根据Nataf变换建立非高斯型互相关随机变量与独立标准正态随机变量之间的关系式,将独立标准正态空间内由Hermite多项式的根组合形成的概率配点变换成非高斯空间内的概率配点,并通过回归分析确定层递响应面的待定系数。计算结果表明,本文建立的CRSM属于向量型响应面法,能较好地处理含非高斯型互相关随机变量的结构可靠度分析问题,计算精度和效率均较高,且具有良好的全域性。     

旋转FGM圆环形截面柔性梁的振动特性

工程实际中直升机的旋翼和风力机的叶片等可简化为旋转柔性悬臂梁的动力学问题。针对旋转FGM圆环形截面柔性悬臂梁的横向振动问题,基于Euler-Bernoulli梁理论和Hamilton原理,建立了自由振动时的运动微分方程。对运动微分方程和边界条件进行量纲归一化处理,采用微分求积法对其进行离散化,得到了系统的广义特征方程。分析了旋转FGM圆环形截面柔性梁的前三阶量纲为一的固有频率随梯度指标和不同梯度指标、径长比下量纲为一的固有频率随轮毂量纲为一的角速度的变化关系。数值计算结果表明,在给定某些参数情况下,旋转FGM环形截面悬臂梁的前三阶量纲为一的固有频率随轮毂量纲为一的角速度的增大而增大,第二阶、第三阶量纲为一的固有频率随梯度指标的增大而增大的趋势较为明显。     

样条配点法分析结构动力响应的无条件稳定计算格式

本文以三次B样条函数作为位移时域函数,应用配点法,在任一时间步长中列出两个时刻的结构物运动方程式残值为零的条件并使结果满足了稳定条件得到一个计算结构物动力响应无条件稳定的计算格式。 这个计算格式于参数θ符合0.15<θ<0.05时是绝对无条件稳定的,研究证明,本文所提出的格式的精度根据三项指标:振幅衰减率 AD,周期伸长率 PE 及算法阻尼比都比较Wilson-θ法,Newmark法及Houbolt法的为优,例题计算也证明此点,即本文方法精度较上述三法为高,本文格式简单,准确,工作量不多,可以作为计算结构动力响应有效方法之一。     

基于微分变换法分析热弹耦合旋转圆板的振动特性

研究了热弹耦合匀速旋转圆板的振动特性和稳定性问题。基于Kirchhoff薄板理论和考虑变形影响时的热传导方程,建立了热弹耦合旋转圆板的运动微分方程,采用微分变换法导出了系统的复特征方程;分析了周边固支、简支和自由边界条件下,热弹耦合系数和量纲为一的角速度对旋转圆板复频率的影响。结果表明:周边简支和固支热弹耦合旋转圆板量纲为一的复频率实部,随着量纲为一的角速度的增加而减小并逐渐趋于0,一阶临界发散量纲为一的角速度分别为3.95和39.58,热弹耦合系数的变化不改变其发散失稳的类型;周边自由热弹耦合旋转圆板,当量纲为一的角速度达到25之后,热弹耦合系数的增大对复频率实部曲线的影响逐渐减小,不存在失稳现象。     

基于最优概率配点的向量型层递响应面法分析结构可靠度

概率配点的选取策略是响应面法研究的关键问题之一.论文提出了配点矩阵行满秩原则,据此筛选层递响应面的最优概率配点.首先利用结构总体刚度矩阵和荷载列阵定义预处理随机Krylov子空间,并利用该空间的层递基向量近似展开结构的总体节点位移向量,建立层递响应面表达式;然后利用层递基向量所对应的基本随机变量组合构造随机行向量,并形成配点矩阵,根据配点矩阵行满秩原则筛选确定层递响应面的最优概率配点,进而通过回归分析确定层递响应面的待定系数.分析表明,层递响应面法具有良好的全域性且待定系数极少;基于配点矩阵行满秩原则筛选最优概率配点能够排除大部分作用不大的配点,大幅减少概率配点数目,与传统响应面法及随机响应面法相比,层递响应面法能够取得更好的计算效率和精度.     

Vibration analysis of a multi-span rotating ring with ray tracing method

A ray tracing method is applied to analyze both the free and forced responses in a rotating multi-span section ring. In this paper, element coordinates are established and coupled by dispersion and transmission matrices. Structure vibration displacements are expressed in a wave form with a combination of propagation, fast-attenuating and near-field waves. Meanwhile, an exciting force is considered as a point discontinues with different elements on both sides. The wave reflection and transmission matrices are introduced through coupling different elements by applying wave transmission coefficients and transfer matrices. For numeric computation, the reflection and transmission matrices are assembled, independent waveguide elements are integrated and the responses of rotating rings with non-uniform section area are derived. The structure modeling and a numeric computation with corresponding solutions illustrate the validity of the presented approach. The investigation result also shows that the presented approach can be extended to compute accurately on the dynamic characteristics of a rotating complex structure (high speed bearing cage).     

环形陀螺敏感结构的平面振动分析

在薄壁圆环振动特性基础上,研究了振动环式微机械陀螺的支撑梁对环的振动模态及自然频率的影响。对一种外支撑式环形微机械陀螺敏感结构进行了ANSYS模态仿真,得到工作振动模态的变形量。以薄壁环2节点变形模态函数为参考函数对仿真变形量用最小二乘法拟合,拟合误差在4.5%以内,各函数系数一致性误差小于1.5%。基于支撑梁对环结构的模态函数影响较小的条件,用能量法和速度积分法得到结构的应变能和动能函数,进一步得到具有支撑梁环结构自然频率的近似解。选取4组支撑梁尺寸,其近似解与仿真结果的相对误差在±3%以内。     

In-plane vibration of a circular ring with arbitrary concentrated elements by an analytical method

Archive of Applied Mechanics - This paper investigates the vibration characteristics of a circular ring with an arbitrary number of concentrated elements based on the Hamilton principle. The shear...     

In-plane free vibration of a single-crystal silicon ring

In this paper the natural frequencies and the associated mode shapes of in-plane free vibration of a single-crystal silicon ring are analyzed. It is found that the Si(1 1 1) ring is two-dimensionally isotropic in the (1 1 1) plane for elastic constants but three-dimensionally anisotropic, while the Si(1 0 0) ring is fully anisotropic. Hamilton’s principle is used to derive the equations of vibration, which is a set of partial differential equations with coefficients being periodic in polar variable. Expressing the radial and tangential displacements in sinusoidal form with non-predetermined amplitudes, and through the integration with respect to the circumferential variable, the original governing equations in partial differential form can be converted into the amplitude equations in ordinary differential form. The exact expressions for frequencies and mode shapes are obtained. It is found that for Si(1 0 0) rings the frequencies of a pair of modes, which are equal for an isotropic ring, split due to the anisotropic effect only for the second in-plane vibration mode. The phenomena of frequency splitting and degenerate modes can be proved either based on the conservation of averaged mechanical energy or by the concept of crystallographic symmetry groups. When the single-crystal silicon is replaced by the polycrystalline silicon, which is isotropic in elastic constants, the derived equations for frequencies correctly predict the vanishing of the phenomenon of frequency splitting.     

In-plane bending vibration analysis of a rotating beam with multiple edge cracks by using the transfer matrix method

Meccanica - In this study, the effects of cracks on the natural frequencies of a rotating Bernoulli–Euler beam are investigated using a new numerical method in which these effects can be...     

In-plane vibration analysis of plates in curvilinear domains by a differential quadrature hierarchical finite element method

Free in-plane vibration analysis of plates is carried out by a differential quadrature hierarchical finite element method (DQHFEM). The NURBS (Non-Uniform Rational B-Splines) patches of geometries were first transformed into differential quadrature hierarchical (DQH) patches, and then the elastic field was discretized by the same DQH basis. The DQHFEM solved the compatibility problem caused by different parametrization of neighbouring patches of isogeometric analysis using NURBS. And mesh refinement in DQHFEM does not propagate from patch to patch. The DQHFEM matrices also have the embedding property as the hierarchical finite element method (HFEM). In-plane vibration analyses of plates of several planforms showed that the DQHFEM is similar as the fixed interface mode synthesis method that can analyse a structure using a few nodes on the boundary of substructure elements and only several clamped modes inside each substructure element, but the DQHFEM does not need modal analysis and is of high accuracy. The accuracy and convergence of the DQHFEM were validated through comparison with exact and approximate results in literatures and computed by the authors.     

In-plane forced vibration of curved pipe conveying fluid by Green function method

The Green function method(GFM) is utilized to analyze the in-plane forced vibration of curved pipe conveying fluid, where the randomicity and distribution of the external excitation and the added mass and damping ratio are considered. The Laplace transform is used, and the Green functions with various boundary conditions are obtained subsequently. Numerical calculations are performed to validate the present solutions, and the effects of some key parameters on both tangential and radial displacements are further investigated. The forced vibration problems with linear and nonlinear motion constraints are also discussed briefly. The method can be radiated to study other forms of forced vibration problems related with pipes or more extensive issues.     

FGM环扇形板的面内自由振动分析

假定功能梯度材料(FGM)的物性参数沿环扇形板径向按照幂律梯度变化,基于平面线弹性理论,建立了FGM环扇形板面内自由振动的运动控制微分方程。采用二维微分求积法(DQM)对FGM环扇形板面内自由振动的无量纲运动控制微分方程进行离散,数值求解了不同边界条件下FGM环扇形板面内自由振动的无量纲固有频率,同时也给出了FGM环扇形板扇形角为!/4时有限元商用软件ANSYS的部分计算结果,验证了本文方法的正确性。结果表明,在相应边界条件下,FGM环扇形板的梯度指标、内外半径比以及扇形角对无量纲固有频率均有影响,其计算结果和分析方法可供设计和研究参考。     

非均匀Winkler弹性地基上变厚度矩形板自由振动的DTM求解

针对非均匀Winkler弹性地基上变厚度矩形板的自由振动问题,通过一种有效的数值求解方法——微分变换法（DTM）,研究其无量纲固有频率特性。已知变厚度矩形板对边为简支边界条件,其他两边的边界条件为简支、固定或自由任意组合。采用DTM将非均匀Winkler弹性地基上变厚度矩形板无量纲化的自由振动控制微分方程及其边界条件变换为等价的代数方程,得到含有无量纲固有频率的特征方程。数值结果退化为均匀Winker弹性地基上矩形板以及变厚度矩形板的情形,并与已有文献采用的不同求解方法进行比较,结果表明,DTM具有非常高的精度和很强的适用性。最后,在不同边界条件下分析地基变化参数、厚度变化参数和长宽比对矩形板无量纲固有频率的影响,并给出了非均匀Winkler弹性地基上对边简支对边固定变厚度矩形板的前六阶振型。     

变截面欧拉梁自由振动分析的重采样微分求积法

采用重采样微分求积法求解了变截面欧拉梁的自由振动问题。推导了变截面梁的控制方程离散格式,采用重采样矩阵方法对边界条件进行处理,给出了变截面梁自由振动算法。采用本文方法对不同类型截面形式和不同边界条件的变截面梁进行自由振动分析,并和其他解法进行比较。计算结果表明,本文方法可以适用于不同变截面类型和不同边界条件,计算精度与解析解吻合良好,具有良好的收敛性能。在同等精度条件下网格点数少于现有计算方法。重采样转换矩阵边界处理方法相比于传统边界处理方法具有更快的收敛性能。