变截面压电层合梁自由振动分析

考虑压电材料的质量效应和刚度效应,将表面粘贴或埋入式压电悬臂梁看作变截面梁,研究压电材料对智能结构固有特性的影响。基于一阶剪切变形理论导出压电层合梁的抗弯刚度和横向剪切刚度,计及梁的剪切变形和转动惯量,采用Timoshenko理论推导变截面压电层合梁的频率方程。给出了T300/970压电层合梁和硬铝压电层合梁的前3阶固有频率,并和有限元结果、等截面梁的计算结果进行比较。计算表明,压电材料对压电结构固有频率和固有振型的影响显著,在以振动控制为目标的压电结构动力学建模过程中,有必要考虑压电材料的质量和刚度。     

用动态刚度法分析旋转变截面梁横向振动特性

通过引入动态刚度法分析旋转变截面梁的振动特性。首先基于欧拉-伯努利梁理论给出旋转变截面梁自由振动方程,然后通过动态刚度法推导该旋转梁的动态刚度矩阵,最后运用MATLAB中的fzero函数求解特征值方程得到旋转梁横向振动的固有频率和模态振型。数值计算结果证明了动态刚度法的精度和有效性,同时分析了轮毂半径、转速以及渐变系数对固有频率的影响。     

Static and dynamic analysis of wind turbine blades using the finite element method

Analysis of forces and stresses of horizontal axis propellers and turbines has been the subject of increased interest in recent years because of the need to develop adequate analytical tools for the design and evaluation of-wind turbine rotors. Most of the structural failures of wind turbines occur in the blade root section. Hence, a three-dimensional analytical model to compute the deflection, stresses and eigenvalues in the rotor blades is proposed using bending triangular plate finite elements. Both membrane and bending stiffness are considered in deriving the element stiffness matrix. The consistent mass matrix is used in generating the overall mass matrix. Lift and drag forces created in steady wind conditions are analysed as normal and tangential forces on the blade sections at certain angles of attack. These forces are applied as boundary loads to the computer program to analyse statically and dynamically rotor blades of symmetrical aerofoil NACA 0015 series. Constant chord, tapered and twisted blades were analysed at rated and survival wind speeds. The validity of the computer program used was verified by applying it to a standard cantilever box beam using the beam theory. The results showed that maximum stresses occurred at the root of the blades for all configurations in the spanwise direction and that a tapered blade, in addition to saving material weight, diminished the stresses obtained. The twisting of the blade leads to an increase in stiffness and a decrease in the stresses.     

旋转几何非线性复合材料薄壁梁的自由振动分析

研究具有几何非线性的旋转复合材料薄壁梁的自由振动。梁的变形引入了Von Kármán几何非线性, 基于Hamilton原理和变分渐进法 (Variational-Asymptotical Method -VMA),导出旋转复合材料薄壁梁的非线性振动偏微分方程组。采用Galerkin法将振动方程离散化为常微分方程组。借助于谐波平衡法 (Harmonic Balance Method -HBM) 建立自由振动的振幅-非线性固有频率关系方程。将上述方程化为非线性特征值问题,采用迭代算法进行求解。将所建立的旋转复合材料薄壁梁非线性自由振动分析模型和计算方法,应用于周向均匀刚度配置(Circumferentially Uniform Stiffness –CUS) 构型复合材料薄壁梁,通过数值计算揭示了纤维铺层角、旋转速度对非线性振动固有频率-振幅关系的影响。     

复合材料变截面旋转薄壁悬臂梁自由振动分析

基于拉格朗日方程推导出复合材料封闭变截面旋转薄壁梁的自由振动方程。与基于哈密顿原理的动力学建模方法相比,该文所采用的方法更为简洁。此外,在薄壁梁的结构模型中还考虑除横向剪切外的扭转、拉伸和弯曲引起的翘曲,具有考虑翘曲因素多的特点。给出了两种刚度配置下的变矩形截面旋转悬臂直梁的自由振动方程简化形式及其相应的迦辽金法求解的固有频率。基于大型通用有限元软件ANSYS,计算了薄壁变截面旋转悬臂梁的固有频率,并且与迦辽金法的求解结果进行了对比。分析了复合材料的弹性耦合、铺层角度、截面变化和旋转速度对薄壁梁的自由振动的影响。     

弹性螺旋桨-轴系建模及振动特性的解析方法研究

为考虑螺旋桨自身弹性对桨-轴系统振动特性的影响,建立了一套基于Timoshenko梁理论的解析方法。将螺旋桨、轴系均用Timoshenko梁建模,结合桨叶与轴系连接处的协调条件及其边界条件,给出系统横向、纵向自由振动的控制方程;在同有限元结果对比表明本方法具有良好精度基础上,分析了桨叶弹性对系统模态的影响及桨-轴系统的力传递特性。研究表明:桨-轴系统的模态振型中螺旋桨叶片和轴系的弹性变形同时发生且相互影响,叶片弯曲模态会加剧轴系振动;作用于桨叶的激励引起的桨-轴系统轴承处的纵向传递力被桨叶弯曲和轴系纵振两阶模态显著放大,而横向传递力主要由桨叶及轴系的弯曲模态控制。     

Free vibration analysis of pre-twisted rotating FGM beams

The natural frequencies of vibration of a rotating pre-twisted functionally graded cantilever beam are investigated. Rotating cantilever beam with pre-twist made of a functionally gradient material (FGM) consisting of metal and ceramic is considered for the study. The material properties of the FGM beam symmetrically vary continuously in thickness direction from core at mid section to the outer surfaces according to a power-law form. Equations of motion for free vibration are derived using Lagrange’s equation and the natural frequencies are determined using Rayleigh–Ritz method. The effect of parameters such as the pre-twist angle, power law index, hub radius and rotational speed on the natural frequencies of rotating functionally graded pre-twisted cantilever beams are examined through numerical studies and comparison is made with the numerical results obtained using other methods reported in literature. The effect of coupling between chordwise and flapwise bending modes on the natural frequencies has also been investigated.     

Non-linear dynamic analysis of a wind turbine blade

ABSTRACT

Wind turbine blades’ dynamic behavior must be well investigated during the design process in order to avoid resonance. Modal analysis and nonlinear dynamic analysis of a rotating wind turbine blade are presented in this paper to study the effects of rotation speed on the natural frequencies and displacements. Accordingly, an enhanced finite element formulation based on uncoupled translational and rotational displacements’ kinetic energy was developed. A twisted wind turbine blade was discretized using beam elements with different cross sections; each has six degrees of freedom per node. At rest, the model results were validated using ABAQUS software. Furthermore, the effects of geometrically non-linear phenomena produced by blade displacement on the vibration characteristics of the rotating blade have been discussed. The blade non-linear problem was solved by applying the Newmark method combined with the Newton-Raphson schema. Results show that the blade natural frequencies and displacements increase under angular rotation speed augmentation. This work highlights the significant sensitivity of the blade vibration characteristics to the geometric non-linearity. Accordingly, a modal and a linear analysis are insufficient to precisely estimate the dynamic behavior of a rotating turbine blade.     

In Situ Detection of Turbine Blade Vibration and Prevention

Turbine blades are the most critical components in any power plant. Failure in even one rogue blade out of hundreds of blades fixed on the rotor leads to colossal damage to the machine. Statistics have shown that low-pressure turbine blades in steam power plants are generally more susceptible to failure compared to high- or intermediate-pressure blades. The mechanism of failures is different in each case and is generally very complex. As a result, a large number of blade failures are not fully understood. Two primary forces acting on the blades are the steady centrifugal force due to rotation and the fluctuating steam bending force. In view of no direct access to monitor the health of the blades through vibration or other means, indirect method using non-contacting probes have been attempted and some are in use in special cases. Largely these methods are expensive and intrusive in nature. They involve placing of sensors in the narrow space inside the turbine casing, routing special signal cables with sealing arrangement and involves difficulties in analyzing shot duration signals from each rotating blades. Unless a diagnostic technique is made simple to implement and whose reliability is proven, power plants will not find it attractive to invest on upgrade for safe operation of the machine. This article is about an innovative method of detecting the presence of blade vibration in operating turbine through vibration signal analysis and prevention through process control. The method is based on vibration analysis of the turbine casing. The casing vibration includes signals associated with the blades of different stages called as blade passing frequency (BPF). When the rotating blades vibrate, the analysis of changes in the BPF is a novel way of diagnosing blade vibrations. Signals captured from operating plants have been analyzed and blade vibrations have been detected and verified with Campbell diagram. Laboratory experiments were carried out on a rotating fan to demonstrate robustness of the diagnostics tool for turbine blades.     

汽轮机叶片动频的转子调频非接触测量法

叶片的共振断裂是叶片损伤的主要形式,为了避免叶片共振,如何准确地测得叶片的动频是保证叶片安全工作的关键。本文提出采用转子调频非接触测量法测量汽轮机叶片的动频。采用该方法只需要在叶片顶部固定支架上安装两只光学传感器及在转子的适当位置安装一只转子旋转同步传感器,就可以测量工作轮上所有叶片的动步,从而克服了传统接触应变片法仅能测量某几个叶片动频、应变片寿命短等缺点,同时也避免了安装多只传感器工艺复杂、费用较高等问题。本文通过实验验证了该方法的可行性。     

两侧受液时悬臂梁的自由振动分析

本文研究悬臂梁在两侧受有液体作用时的横向自由振动问题,给出了两侧液深不等时悬臂梁自由振动的振型函数和固有频率的精确计算公式,结果可由计算机解出。分析表明,液体对悬臂梁自由振动的影响等效一附着于梁上的广义分布质量。     

Vibration and optimum design of rotating laminated blades

The vibration and optimum design of a rotating laminated blade subject to constraints on the dynamic behavior are investigated. Restrictions on multiple natural frequencies as well as the maximum dynamic deflections of rotating laminated blades are considered as constraints on the dynamic behavior of the system. Aerodynamic forces acting on the blade are simulated as harmonic excitations. The optimality criterion method and the modified method of feasible directions have been successfully developed for optimizing the weight of the rotating laminated blade. Effects of radius of the disk, aspect ratio, and rotating speed on the system dynamic behaviors and/or the optimum design are also studied. The vibration analysis shows that most of the bending modes can be significantly affected by the rotating speed and the radius of the disk. Results also show that the optimum weight with constraints on the dynamic response is higher than that with frequency constraints. Moreover, results show that the weight of the rotating laminated blade can be greatly reduced at the optimum design stage.     

Experimental-numerical investigation of the dynamic stability of flexural-torsional vibrations of compressor blades under conditions of attached and separated flow. part 3. mutual aerodynamic couplings

The paper considers the results of a study of mutual aerodynamic couplings which give rise to nonstationary aerodynamic interactions between the translational and angular components displacements of neighboring ring blades in the case of variation of attack angle, reduced vibration frequency and the geometric parameters of the blade cascade. The effect of mutual aerodynamic couplings between neighboring blades on the aerodynamic stability of flexural-torsional vibrations of the blades of the peripheral section of the shrouded fan blade ring of gas turbine engine for an attack angle of 15° has been estimated.     

Free vibration analysis of sandwich beams using improved dynamic stiffness method

In this paper, free vibration of three-layered symmetric sandwich beam is investigated using dynamic stiffness and finite element methods. To determine the governing equations of motion by the present theory, the core density has been taken into consideration. The governing partial differential equations of motion for one element contained three layers are derived using Hamilton’s principle. This formulation leads to two partial differential equations which are coupled in axial and bending deformations. For the harmonic motion, these equations are combined to form one ordinary differential equation. Closed form analytical solution for this equation is determined. By applying the boundary conditions, the element dynamic stiffness matrix is developed. They are assembled and the boundary conditions of the beam are applied, so that the dynamic stiffness matrix of the beam is derived. Natural frequencies and mode shapes are computed by the use of numerical techniques and the known Wittrick–Williams algorithm. After validation of the present model, the effect of various parameters such as density, thickness and shear modulus of the core for various boundary conditions on the first natural frequency is studied.     

大型水平轴风力发电机桨叶稳定性研究

大型水平轴风力发电机桨叶为流-刚-柔耦合的周期时变多体系统。本文暂未考虑风载荷,分析了重力载荷和桨叶预锥角、转速等因素的变化对稳定性的影响。力学建模中,考虑了桨叶挥舞、摆振、扭转和轴向运动以及根部铰的挥舞、摆振和变矩等刚体运动。利用有限元法形成5节点18自由度的刚-柔混合梁单元模型,应用Hamilton原理建立桨叶动力学方程,求得对应的摄动方程,采用Newmark隐式积分方法求解。根据Floquet理论判断运动稳定性,计算了相关转换矩阵的特征值。结果表明预锥角对桨叶运动稳定性影响不容忽视。在通常的工况下,桨叶能够稳定地运转。     

Nonlocal nonlinear bending and free vibration analysis of a rotating laminated nano cantilever beam

In this article, we present the nonlocal, nonlinear finite element formulations for the case of nonuniform rotating laminated nano cantilever beams using the Timoshenko beam theory. The surface stress effects are also taken into consideration. Nonlocal stress resultants are obtained by employing Eringen’s nonlocal differential model. Geometric nonlinearity is taken into account by using the Green Lagrange strain tensor. Numerical solutions of nonlinear bending and free vibration are presented. Parametric studies have been carried out to understand the effect of nonlocal parameter and surface stresses on bending and vibration behavior of cantilever beams. Also, the effects of angular velocity and hub radius on the vibration behavior of the cantilever beam are studied.     

中低频集中质量悬臂式簧片仪基频分析方法研究

簧片仪是一种中低频冲击响应谱测量装置,设计时可将其简化为端部附带集中质量的悬臂梁。簧片仪的振型方程中存在超越函数,对于等截面簧片仪来说,可使用二分法等数值方法求解,计算量较大,该方法不适用于复杂截面簧片仪基频设计。首先利用悬臂梁自由端受集中力的挠度公式,推导出其等效刚度等效单自由度的弹簧振子系统,利用弹簧振子相关频率公式解决求解集中质量等截面悬臂梁的基频问题,该方法与振型方程求解的基频对比,发现在10 Hz以下的中低频区域,可以很好的保证等截面悬臂梁的基频精度,大于10 Hz的中频段,误差随频率的升高而迅速增大。接下来,通过Mohr积分的方法,推导出等强度集中质量悬臂梁自由端的最大挠度,并给出其基频的设计公式,该方法与试验进行对比,发现误差与等截面悬臂梁有相同趋势,因此利用瑞利能量法修正设计公式中的质量参数,修正后与实验误差在5%左右。经理论与试验验证,所提出的簧片仪设计方法简单可行、计算结果可信。     

Vibration analysis of rotating composite beams using a finite element model with warping degrees of freedom

A finite element beam formulation that properly takes into account the warping of the cross-sections has been extended to the free vibration analysis of rotating and nonrotating composite beams. The formulation allows transverse shear deformation and the warping effects are incorporated by superimposing warping displacements that are parallel to the beam axis in the deformed configuration. For modeling of thin and moderately thick walled sections, the strain is assumed to be linear through the wall thickness. Numerical tests were conducted to calculate the natural frequencies of cantilever composite beams with various ply layups. Correlations of the calculated natural frequencies with experimentally measured values demonstrate the validity of the present approach. Although only rectangular solid and box beams were considered for numerical tests, the formulation allows modeling of beams with complicated cross-sections, tapers, pretwists and arbitrary planforms.     

基于格林函数的多跨钻柱系统的振动特性分析

随着油气勘探开发向着深层、深水及非常规等复杂领域的不断扩展,钻井面临的井况与约束条件更加苛刻,钻柱的动力学特性更加复杂,失效问题频发。该文应用格林函数理论对多跨旋转钻柱双向耦合动力学特性进行了定量分析和研究。考虑多稳定器及不同约束条件,以钻柱整体为研究对象,基于Euler-Bernoulli梁模型和Hamilton原理建立了具有广义边界约束条件及多稳定器的旋转钻柱双向耦合动力学方程。采用分离变量法、Laplace变换及Laplace逆变换求解所获得的振动微分方程,得到了旋转钻柱系统横向振动的格林函数解以及以格林函数为基础的多跨旋转钻柱系统的闭合形式的模态函数及隐式的频率方程。定量地分析了稳定器位置、弹簧刚度系数与稳定器个数对钻柱系统振动特性的影响。数值结果表明:稳定器位置与固有频率的关系曲线中有相应阶次数目的峰值;随着等效弹簧的刚度系数的增大,系统的固有频率随之增大,但当刚度增加到一定值时,系统的一阶和二阶频率将趋于稳定。研究结果有助于深化对多跨旋转钻柱的动力学特性规律的认识,为提高钻速、减少钻柱失效及钻柱钻井技术的应用提供了新的研究方法和理论依据。     

损伤叶片动力参数变化规律的数值模拟与试验研究

风力发电机叶片的结构动力特性是叶片结构设计时考虑的重要方面,其动力特性对于整个风力机的安全运行具有重要意义.为了研究损伤引起的结构自振频率的变化规律,从有限元模拟以及试验两方面结合进行了研究.通过对比两种研究方法所得的固有频率值的变化规律,找出他们的共性,从而互相印证结果的正确性.结果表明,叶片的固有频率值受损伤位置、...