粘弹性夹芯层合旋转圆板的气动弹性动力稳定性分析

基于哈密尔顿原理,考虑作用于圆板上的空气动力载荷以及粘弹性复模量本构模型,本文建立了含有粘弹性夹芯层的旋转圆板的空气动力学模型,并给出了相应的稳定性的控制方程及边界条件。运用Galerkin方法,文中数值求解并给出了夹芯层合旋转圆板的动力学基本特征,以及结构几何参数、材料参数对于其前、后行波振动频率、阻尼和动力稳定性的影响。结果表明：通过优化合理选取粘弹性夹芯层合旋转圆板的几何参数和材料参数,可提高旋转圆板的临界转速和颤振速度,从而增强其稳定性。     

旋转Rayleigh梁的自由振动及失稳特性

基于Hamilton原理,采用模态坐标得到了旋转梁在固定参考系及旋转参考系下的时域常微分方程,详细分析了两端简支边界条件下旋转Rayleigh梁自由振动的行波特性及临界转速。讨论了长细比等因素对旋转Rayleigh梁的行波振动频率和临界转速的影响,并给出了不同转速下系统自由振动的典型模态坐标时间曲线。研究发现:旋转Rayleigh梁系统存在一次和二次临界转速,固定参考系中一次临界转速对应于旋转参考系中零特征值失稳点,转速在一次临界转速(低速)附近时系统只发生共振失稳,系统真正的失稳发生在转速超过二次临界转速之后。     

基于旋转软化的柔性梁动力学研究

建立了旋转柔性梁的非线性动力学模型,利用能量法及哈密顿原理导出了耦合的动力学方程,分析了转动惯性、Coriolis力、应力刚化、旋转软化、加速度、横向位移、弯曲刚度等作用效应;通过设置应力刚化及旋转软化等刚度矩阵和编制有限元程序,建立了梁单元有限元模型,对柔性梁在旋转软化状态下的振动模态进行了数值模拟与分析。计算表明:梁的旋转软化导致其沿旋转平面的弯振模态(摆振)频率随转速增大而相对下降,且对第一阶摆振频率的影响最显著,呈现非线性;梁的旋转软化对垂直于旋转平面的弯振频率几乎没有影响,此结果表明了旋转柔性梁动态特性的复杂性,因此在计算旋转柔性梁的振动特性时,必须同时设置平动、转动惯性质量矩阵,才能获得准确结果。此外,梁单元模型与实体单元模型计算结果误差小于等于5%,验证了本文梁单元模型求解方法的准确性。     

质量周期分布对偏心旋转环状结构自由振动的影响

工程实际中，某些旋转对称设计结构由于存在制造安装误差常呈现偏心旋转状态，进而影响结构稳定性.针对该类环状周期结构，考虑其偏心运动，研究附加质量周期分布参数以及偏心率对系统固有频率与动力稳定性的影响.首先，在环状结构上建立随动坐标系，利用Hamilton原理建立动力学模型.其次，采用经典振动理论求解系统的特征值，分析不同参数组合下的模态特性和不稳定性.最后，利用数值法计算系统的动态响应，并与解析结果进行对比.结果表明，当附加质量个数与波数满足一定关系时，固有频率发生分裂；对于不同的偏心率和周期分布特征，系统在不同转速下动力性能差异较大，适当提高偏心率、选取合适的附加质量个数及大小可有效抑制不稳定性.此研究有助于分析工程实际中该类结构的动力学稳定性，为其振动控制提供借鉴.     

数学机械化在转子系统分析中的应用

以转子－轴承系统中两圆盘转子为研究对象,在计及陀累力矩的条件下,通过对两圆盘转子临界转速与振型参数的分析,对吴消去法在转子动力学研究中的应用做了初步探索,将吴消去法的特征列思想 Maple软件的符号计算功能相结合,实现了对两圆盘转子临界转速与振型参数的解析计算与分析。     

旋转压电纳米梁的振动分析

本文基于非局部弹性理论，对旋转压电纳米梁模型的振动进行了分析．首先由哈密顿原理导出旋转压电纳米梁的动力学控制方程及相应的边界条件；再通过微分求积法对控制方程和两类边界条件进行离散；最后通过数值计算分析振动特性．通过改变旋转角速度、轮毂半径、非局部参数以及外部电压分析它们对压电纳米梁振动频率的影响关系．数值结果表明这些参数对压电纳米梁固有频率有不可忽略的影响，本文进一步讨论了旋转角速度对结构模态的影响．     

旋转圆盘表面油膜破碎转捩临界特性分析

高速滚动轴承内圈和保持架等旋转运动件表面润滑油膜的流动铺展以及破碎为油带和油矢的特性决定着轴承的润滑与冷却状态.在获得轴承旋转运动件拓扑结构—旋转圆盘表面油膜稳态流动特性的基础上,利用力学平衡和液体表面波不稳定破碎理论,建立表面油膜破碎转捩为油带和油矢的临界特性分析模型,分析和探讨了表面油膜的稳态流动特性以及供油量和润滑油物理特征参数对油膜破碎转捩临界特性的影响.结果表明:表面油膜沿着圆盘径向逐渐变薄,因与圆盘表面存在滑移现象,其流动速度也随之减小;表面油膜破碎的临界波数和临界半径随着圆盘转速的增高而增大,临界厚度则随之减小;表面油膜破碎的临界半径和临界厚度随着润滑油供油量的增加而增大;增大润滑油密度,将延缓表面油膜破碎,破碎临界半径增大,临界厚度减小;增大润滑油的黏度和表面张力系数将促进表面油膜破碎,破碎临界半径减小.与相关的试验结果对比验证了理论分析方法的正确性和可靠性.     

考虑刚体运动与弹性运动耦合影响的旋转叶片振动有限元分析

本文研究了旋转叶片的纵向振动和双向横振动,考虑了刚体运动和弹性振动的耦合关系,利用有限元法推导出离散系统动力学方程,从而引出陀螺特征值问题。本文就某一特例了计算了在不同转速时叶片振动的自然频率,讨论了转速对振动频率的影响。     

叶片振动影响下双盘转子-轴承系统的稳定性与分岔

研究叶片与转子-轴承系统的耦合非线性振动,建立了一个带叶片的双盘转子-轴承系统的非线性动力学模型,其中包含一个弹性转轴、两个滑动轴承、两个刚性圆盘和两组弹性叶片.为了分析叶片的惯性影响,将其简化为单摆模型.采用4阶Runge-Kutta法进行了数值模拟,并利用分岔图、三维谱图、轴心轨迹和Poincaré映射图等方法分析了系统的非线性动力学特性.研究发现,随着转速的变化,系统响应演化出了倍周期运动、概周期运动、混沌运动和倍周期分岔等典型的非线性动力学行为.在与忽略了叶片振动的转子系统对比后发现,叶片振动使转子发生混沌运动的转速区域增大.在某些参数条件下,采用不同的叶片刚度,叶片振动可能引起转子系统产生混沌运动.     

挤压油膜阻尼器-滑动轴承转子系统动力学分析与优化设计

为了对挤压油膜阻尼器-转子系统中挤压油膜阻尼器(SFD)的各项参数进行优化设计,使转子系统的动力学性能达到最佳状态,本文综合运用转子动力学和油膜润滑基本理论以及数值分析方法,对SFD-滑动轴承转子系统的灵敏度及动力学优化进行了系统研究。灵敏度分析结果表明:轴承间隙c1、SFD间隙c2、油粘度η对转子系统的一阶临界转速的影响较大;SFD间隙c2、轴承间隙c1、转轴刚度K2对二阶临界转速的影响较大。据此得到优化的设计变量为c1、c2、η、K2,并采用遗传算法对临界转速进行了优化分析;经过优化后,系统的一阶、二阶临界转速差值由原来的510rad/s变为860rad/s,系统动力学性能得到较大改善。本文的优化设计结果可为此类转子系统的设计提供参考。     

Aeroelastic dynamics stability of rotating sandwich annular plate with viscoelastic core layer

A dynamic model for a rotating sandwich annular plate with a viscoelastic core layer is developed. All fundamental equations and boundary conditions are established based on Hamilton’s principle, and the rotation effect and viscoelastic properties of the sandwich structure are taken into account. The aerodynamics force acting on the plate is described by a rotating damping model, and the constitutive behavior of the viscoelastic core layer is formulated by the frequency-dependent complex modulus. The effects of geometrical and material parameters on frequencies and damping of forward and backward traveling waves and the dynamic stability for the rotating sandwich plate are numerically analyzed by means of Galerkin’s method. The results show that the critical and flutter speeds of the rotating plate can be increased at some certain parameters of the viscoelastic core layer.     

Natural frequencies of rotating functionally graded cylindrical shells

Love’s first approximation theory is used to analyze the natural frequencies of rotating functionally graded cylindrical shells.To verify the validity of the present method,the natural frequencies of the simply supported non-rotating isotropic cylindrical shell and the functionally graded cylindrical shell are compared with available published results.Good agreement is obtained.The effects of the power law index,the wave numbers along the x-and θ-directions,and the thickness-to-radius ratio on the natural frequencies of the simply supported rotating functionally graded cylindrical shell are investigated by several numerical examples.It is found that the fundamental frequencies of the backward waves increase with the increasing rotating speed,the fundamental frequencies of the forward waves decrease with the increasing rotating speed,and the forward and backward waves frequencies increase with the increasing thickness-to-radius ratio.     

Dynamic response of a rotating disk submerged and confined. Influence of the axial gap

In this paper, the natural frequencies and mode shapes of a rotating disk submerged and totally confined inside a rigid casing, have been obtained. These have been calculated analytically, numerically and experimentally for different axial gaps disk-casing. A simplified analytical model to analyse the dynamic response of a rotating disk submerged and confined, that has been used and validated in previous researches, is used in this case, generalised for arbitrary axial gaps disk-casing. To use this model, it is necessary to know the averaged rotating speed of the flow with respect to the disk. This parameter is obtained after an analytical discussion of the motion of the flow inside the casing where the disk rotates, and by means of CFD simulations for different axial positions of the disk. The natural frequencies of the rotating disk for the different axial confinements can be calculated following this method. A Finite Element Model has been built up to obtain the natural frequencies by means of computational simulation. The relative velocity of the flow with respect to the disk is also introduced in the simulation model in order to estimate the natural frequencies of the rotating disk. Experimental tests have been performed with a rotating disk test rig. A thin stainless steel disk (thickness of 8 mm, (h/r<5%) and mass of 7.6 kg) rotates inside a rigid casing. The position of the disk can be adjusted at several axial gaps disk-casing. A piezoelectric patch (PZT) attached on the rotating disk is used to excite the structure. Several miniature and submergible accelerometers have measured the response from the rotating frame. Excitation and measured signals are transmitted from the rotating to the stationary frame through a slip ring system. Experimental results are contrasted with the results obtained by the analytical and numerical model. Thereby, the influence of the axial gap disk-casing on the natural frequencies of a rotating disk totally confined and surrounded by a heavy fluid is determined.     

Distorted wave response of ultrasonic annular stator incorporating non-uniform geometry

The traveling wave ultrasonic stator is normally fabricated with teeth. The tooth geometry improves the driving speed, but it creates natural frequency splitting and mode contamination, especially a distorted traveling wave. A dynamic model of a stepped-plate periodic stator is developed to examine the distortion. The stator is treated as an annular supported by a thin mid plate, and the support stiffness is formulated by using equivalent energy principle. The effects of the tooth and mid plate on the natural frequency and vibration mode are examined by using the perturbation method. The rules governing the frequency splitting, frequency perturbation as well as mode contamination are also identified. The traveling wave response and elliptical trace on stator surface are obtained by using the mode superposition method and they are proved to be distorted due to the tooth geometry. The response at the repeated doublets becomes coupled forward and backward traveling waves, but that at the split doublets becomes coupled forward traveling, standing and backward traveling waves. The results indicate that the tooth mass instead of the stiffness decreases the vibration amplitude and driving speed of the dominant wave, but their effects are different at the repeated and split doublets. Inspection of the model implies that the distortion can be suppressed by using a suitable combination of the wavenumber, tooth count, tooth height and occupying fraction. Numerical calculations are carried out to demonstrate the tooth geometry effect on the transient waveform, driving speed and elliptical trace. The optimization of the tooth geometry that can help achieve a purer traveling wave is discussed.     

On the resonant nonlinear traveling waves in a thin rotating ring

Large amplitude, traveling wave motion of an inextensible, linearly elastic, rotating ring is analyzed. Equations governing the planar dynamics of a thin rod, curved in its undeformed state and moving in a horizontal reference frame which rotates about a fixed axis, are obtained via Hamilton's extended principle. The equations are specialized to study the behavior of a rotating circular ring and approximate solutions are obtained near resonance utilizing a perturbation analysis. Undamped free and viscously damped forced traveling wave motion is considered. The motion is found to consist of a forward and a backward traveling wave which may be coupled due to the non-linear terms present in the equations of motion     

惯性效应对超高速倾斜端面气膜密封稳动态特性影响

研究了惯性效应和端面倾斜对超高速气膜端面密封稳动态特性的影响. 考虑气体惯性效应，建立了气膜端面密封稳动态特性数值分析模型，采用有限差分法求解稳态和微扰雷诺方程，获得端面膜压分布. 数值分析了惯性效应和端面倾斜度对开启力、气膜刚度和泄漏率等稳态性能参数以及刚度系数和阻尼系数等动态特性系数的影响规律，并以获得较大刚度系数为目标，获得了螺旋槽关键几何参数的优选值范围. 结果表明:在超高速条件下，考虑惯性效应后的干气密封泄漏率显著减小，刚漏比明显增大，而开启力、气膜刚度和动特性系数变化不大；倾斜端面气膜密封相较于平行端面气膜密封具有更佳的低频刚度和高频阻尼.      

On the equilibrium configurations of an elastically constrained rotating disk: An analytical approach

According to the linear theory of vibration for spinning disks, the backward traveling waves of some of the modes may have zero natural frequency at what are called the critical speeds. At these speeds, the linear equations of motion cannot properly predict the amplitude response of the spinning disk, and nonlinear equations of motion must be used. In this paper, geometrical nonlinear equations of motion based on Von Karman plate theory are employed to study the dynamics of an elastically constrained disk near its critical speeds. A one-mode approximation is used to examine the effect of elastic constraint on the amplitude response. Presenting the equations in a space-fixed coordinate system, this study aims to find closed-form solutions for some of the equilibrium configurations of an elastically constrained spinning disk. Also, the stability of these configurations is studied using analytical techniques. It is shown that below the critical speed, one neutrally stable equilibrium solution exists, while above it, a bifurcation occurs. In this situation, two more branches of equilibrium configurations emerge, one of which is neutrally stable and the other unstable. Closed-form expressions for the bifurcation points are obtained. Due to the effect of an elastic constraint, a bifurcation occurs and the previously neutrally stable equilibrium configuration turns unstable. Also at this bifurcation point, two more branches of equilibrium solutions emerge.     

考虑剪切效应的旋转FGM楔形梁刚柔耦合动力学建模与仿真

本文对一类中心刚体-柔性梁系统在大范围转动下的刚柔耦合动力学问题进行了研究. 柔性梁为功能梯度材料(functionally graded materials, FGM)楔形变截面梁,材料体积分数在梁轴向呈幂律分布变化. 以弧长坐标来描述柔性FGM梁的几何位移关系,分别使用倾角和拉伸应变变量描述柔性梁的横向弯曲和纵向拉伸变形,并计及剪切效应. 采用假设模态法离散变形场,运用第二类拉格朗日方程进行方程推导,得到系统考虑剪切效应的刚柔耦合动力学模型. 基于全新的刚柔耦合动力学建模理论,研究不同轴向材料梯度分布的FGM楔形梁,通过数值仿真计算,分析讨论不同的转速、梯度分布规律以及变截面参数对系统动力学特性的影响. 结果表明,剪切效应对大高跨比的FGM楔形梁的变形影响较为明显,不容忽略;材料梯度分布规律和截面参数的选取均会对旋转FGM楔形梁的动力学响应和频率产生较大影响. 本文提出的考虑剪切效应的倾角刚柔耦合动力学模型是对以往非剪切模型的进一步完善,可应用于工程中的 Timoshenko梁结构的动力学问题求解.      

Vibration analysis of a spinning disk using image-derotated holographic interferometry

This paper reports on the application of image-derotated holographic interferometry to study the resonant response of a rotating steel disk at speeds up to 8000 rpm. The rotational motion of the disk is optically removed by passing the image of the rotating disk through a prism that is traveling at half the rotational speed of the disk. Off-axis, double-pulsed, laser holography is then used to record the disk resonant-vibratory response. The first five diametrical modes and one complex mode of disk vibration are obtained at various rpm. The effects of disk imbalance, misalignment of optical and mechanical axes of rotation and system-excited modes of vibration are also addressed. Selected experimental results are compared to those obtained using finite element analysis.