A finite element analysis for the vibration modes of a bladed disc

The coupled vibration modes of a rotating blade-disc system are calculated by a finite element method. It is assumed that a large number of identical blades are present, such that the resulting blade loadings on the disc can be considered continuously distributed around the rim of the disc. The disc may have arbitrary profile, and the blades may be tapered and twisted, thus closely representing practical axial flow turbomachine configurations. The effects of rotation, thermal stress, and transverse shear and rotatory inertia in discs of moderately thick profile are readily incorporated into the finite element model. Calculated values of frequencies are compared with experimental data obtained on non-rotating models, and the convergence of the solution is examined by comparison with exact solutions, which can be obtained for configurations of simple geometry. Excellent agreement with experimental data is obtained when using remarkably few elements in the mathematical model, and convergence of the solution is extremely rapid.     

A finite element for the vibration analysis of Timoshenko beams

A Timoshenko beam finite element is presented which has three nodes and two degrees of freedom per node, namely the values of the lateral deflection and the cross-sectional rotation. The element properties are based on a coupled displacement field; the lateral deflection is interpolated as a quintic polynomial function and the cross-sectional rotation is linked to the deflection by specifying satisfaction of the governing differential equation of moment equilibrium in the absence of the rotary inertia term. Numerical results confirm that this procedure does not preclude convergence to true Timoshenko theory solutions since rotary inertia is included in lumped form at element ends. The new Timoshenko beam element has good convergence characteristics and where comparison can be made in numerical studies it is shown to be generally more efficient than previous elements.     

振动切削刀杆参数化有限元设计研究

基于振动切削刀杆的结构特点,从其动力学问题的基本方程出发,建立了三阶梯对称刀杆的参数化有限元动力学模型;利用有限元分析软件ANSYS的参数化设计语言APDL对其进行二次开发,编制程序绘制了阶梯刀杆尺寸对其谐振频率和夹紧间距影响的三维关系曲线,完成了三阶梯对称弯曲谐振刀杆的参数化有限元设计。对比本文有限元计算和文献1的解析计算与实验结果的差别,谐振频率和夹紧间距的计算误差分别为2.5%和3.5%,而相同的刀杆尺寸范围内解析法的计算误差分别是3%和5%。说明本文提出的方法能更好地逼近实验结果,从而为振动切削刀杆的设计提供了更加方便、准确的手段。     

Anterior-posterior biphonation in a finite element model of vocal fold vibration

In this paper, a finite-element model is used to simulate anterior-posterior biphonation [Neubauer et al., J. Acoust. Soc. Am. 110(6), 3179-3192 (2001)]. The anterior-posterior stiffness asymmetric factor and the anterior-posterior shape asymmetric factor describe the asymmetry properties of vocal folds. Spatiotemporal plot, spectral analysis, anterior-posterior fundamental frequency ratio, cross covariation function, and correlation length quantitatively estimate the spatial asymmetry of vocal fold oscillations. Calculation results show that the anterior-posterior stiffness asymmetry decreases the spatial coherence of vocal fold vibration. When the stiffness asymmetry reaches a certain level, the drop in spatial coherence desynchronizes the vibration modes. The anterior and posterior sides of the vocal fold oscillate with two independent fundamental frequencies (f(a) and f(p)). The complex spectral characteristics of vocal fold vibration under biphonation conditions can be explained by the linear combination of f(a) and f(p). Empirical orthogonal eigenfunctions prove the existence of higher-order anterior-posterior modes when anterior-posterior biphonation occurs. Then, it is found that the anterior-posterior shape asymmetry also decreases the spatial coherence of vocal fold vibration, and shape asymmetry is a possible reason for anterior-posterior biphonation.     

Free vibration analysis of a cracked beam by finite element method

In this paper, the natural frequencies and mode shapes of a cracked beam are obtained using the finite element method. An ‘overall additional flexibility matrix’, instead of the ‘local additional flexibility matrix’, is added to the flexibility matrix of the corresponding intact beam element to obtain the total flexibility matrix, and therefore the stiffness matrix. Compared with analytical results, the new stiffness matrix obtained using the overall additional flexibility matrix can give more accurate natural frequencies than those resulted from using the local additional flexibility matrix. All the elements in the overall additional flexibility matrix are computed by 128-point (1D) or (128×128)-point (2D) Gauss quadrature, and then further best fitted using the least-squares method. The explicit form best-fitted formulas agree very well with the numerical integration results, and are very convenient for use and valuable for further reference. In addition, the authors constructed a shape function that can perfectly satisfy the local flexibility conditions at the crack locations, which can give more accurate vibration modes.     

A finite element method for analysis of vibration induced by maglev trains

This paper developed a finite element method to perform the maglev train–bridge–soil interaction analysis with rail irregularities. An efficient proportional integral (PI) scheme with only a simple equation is used to control the force of the maglev wheel, which is modeled as a contact node moving along a number of target nodes. The moving maglev vehicles are modeled as a combination of spring-damper elements, lumped mass and rigid links. The Newmark method with the Newton–Raphson method is then used to solve the nonlinear dynamic equation. The major advantage is that all the proposed procedures are standard in the finite element method. The analytic solution of maglev vehicles passing a Timoshenko beam was used to validate the current finite element method with good agreements. Moreover, a very large-scale finite element analysis using the proposed scheme was also tested in this paper.     

Analysis of in-plane vibration of shear walls by a finite element method

The purpose of this paper is to present the application of a finite element technique in the free vibration analysis of shear-wall-type structures. An in-plane plate element with six degrees of freedom per node is developed and the results are compared with those for other plate elements.     

Analysis of inplane vibration of box-type structures by a finite element method

Application of the finite element technique in the analysis of box-type structures is described in this paper. The box is developed from plate elements with two degrees of freedom per node and only inplane free vibration is considered.     

A finite element method prediction of the vibration of a bridge subjected to a moving vehicle load

This paper is concerned with the analysis of dynamic deflection and acceleration of a concrete bridge which is subjected to a moving vehicle load. The bridge, to be constructed across the River Brahmaputra in India, consists of 20 main spans, and each main span is assumed to be double cantilever type with a small suspended span. The moving vehicle is modeled as one degree of freedom. The deflections and accelerations at specific locations on the bridge when the vehicle moves at constant speed are analyzed by using the finite element method.     

BOR-FDTD subgridding based on finite element principles

In this paper a recently developed provably passive and stable 3D FDTD subgridding technique, based on finite elements principles, is extended to body-of-revolution (BOR) FDTD. First, a suitable choice of basis functions is presented together with the mechanism to assemble them into an overall mesh consisting of coarse and fine mesh cells. Invoking appropriate mass-lumping concepts then leads to an explicit leapfrog time stepping algorithm for the amplitudes of the basis functions. Attention is devoted to provide the reader with insight into the updating equations, in particular at a subgridding boundary. Stability, grid reflection and dispersion are also discussed. Finally, some numerical examples for toroidal and cylindrical cavities demonstrate the stability and accuracy of the method.     

Free vibration analysis of a flat plate using the hierarchical finite element method

The hierarchical finite element method is used to determined the natural frequencies and modes of a flat, rectangular plate. Ten different boundary conditions—including free edges and point supports—are considered in this paper. Extensive results are presented for each case (including the variation of frequency with the aspect ratio and the Poisson ratio), and these are shown to be in very good agreement with the work of other investigators. This confirms both the applicability and accuracy of solution of the HFEM to problem of this type.     

A 3D finite element model for the vibration analysis of asymmetric rotating machines

This paper suggests a 3D finite element method based on the modal theory in order to analyse linear periodically time-varying systems. Presentation of the method is given through the particular case of asymmetric rotating machines. First, Hill governing equations of asymmetric rotating oscillators with two degrees of freedom are investigated. These differential equations with periodic coefficients are solved with classic Floquet theory leading to parametric quasimodes. These mathematical entities are found to have the same fundamental properties as classic eigenmodes, but contain several harmonics possibly responsible for parametric instabilities. Extension to the vibration analysis (stability, frequency spectrum) of asymmetric rotating machines with multiple degrees of freedom is achieved with a fully 3D finite element model including stator and rotor coupling. Due to Hill expansion, the usual degrees of freedom are duplicated and associated with the relevant harmonic of the Floquet solutions in the frequency domain. Parametric quasimodes as well as steady-state response of the whole system are ingeniously computed with a component-mode synthesis method. Finally, experimental investigations are performed on a test rig composed of an asymmetric rotor running on nonisotropic supports. Numerical and experimental results are compared to highlight the potential of the numerical method.     

激光测振有限元反演优化方法测量黏弹材料动态力学参数

基于非接触式光学测振和有限元反演对黏弹材料复模量的测量进行了理论和实验研究。针对反演精度受测点选择影响显著的问题进行了误差分析,推导了灵敏度矩阵的计算公式;得到了反演误差的计算方法;找出了影响反演精度的主要误差来源;通过测点优化,提高了泊松比测试精度。利用温频等效原理,在常压、变温条件下对橡胶样品进行了温频等效测量,实验研究表明,该系统可以以较少的温度台阶获得材料主曲线,反演结果与动态机械分析仪(DMA)测试结果误差在10%以内,进一步印证了反演系统的有效性。     

干摩擦引起自激振动现象研究

对干摩擦引起自激振动现象进行分析,得到了其解析表达式,对振动过程进行了详细的分析,画出了振动曲线和相图,说明这就是弦弓乐器发出优美声乐的物理原因.     

Free vibration analysis of functionally graded curved panels using a higher-order finite element formulation

Free vibration analysis of functionally graded curved panels is carried out using a higher-order formulation. A C⁰ finite element formulation is used to carry out the analysis. The element consists of nine degrees of freedom per node with higher-order terms in the Taylor's-series expansion, which represents the higher-order transverse cross-sectional deformation modes. The formulation includes Sanders’ approximation for doubly curved shells considering the effects of rotary inertia and transverse shear. A realistic parabolic distribution of transverse shear strains through the shell thickness is assumed and the use of shear correction factor is avoided. Material properties are assumed to be temperature independent and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. Heat conduction between ceramic and metal constituents is neglected. The accuracy of the formulation is validated by comparing the results with those available in the literature. Effects of panel geometry parameters and boundary conditions are studied.     

基于接触有限元方法的镜面面形仿真技术研究

为考察在外载作用下某镜体镜面面形的变化是否满足设计要求,研究在预紧力及重力作用下镜面面形的变化规律,使用接触非线性有限元方法对镜体组件进行了仿真,采用基于Zernike多项式的光机集成仿真接口程序对面形数据进行了处理,得到了消除刚体位移后表征面形变化的参数和表示刚体位移系数的分布曲线。结果表明在预紧力和重力作用下刚体位移明显,镜面平移占据了刚体位移的主要方面,基于集成仿真技术的面形处理程序可有效地消除刚体位移;预紧力存在在不同方向重力作用下对面形的影响略有不同,与预紧力相比,重力作用对面形的影响较小。在预紧力作用下面形仿真数据对于镜体设计、装调具有一定指导意义,也说明基于接触方法面形仿真的工程适用性。     

干式变压器有限元仿真模型的电磁和振动分析

随着电力需求的逐年增长,干式变压器的数量也在不断增加。干式变压器在运行时存在着振动和噪声的问题,为了对干式变压器振动的规律与特点进行研究,本文建立了干式变压器本体振动的有限元仿真模型,通过电磁分析获得相应的磁场分布,然后利用结构动力学分析得到其本体振动的相关规律。通过对处于运行状态的变压器振动数据进行实测分析,得到变压器振动的特征频率,然后对仿真结果进行对比分析,可以发现振动幅度与频率之间存在的关系。本文的研究结果可对干式变压器的减振降噪研究提供参考。