Nonlinear vibrations of blade with varying rotating speed

This paper investigates the nonlinear dynamic responses of the rotating blade with varying rotating speed under high-temperature supersonic gas flow. The varying rotating speed and centrifugal force are considered during the establishment of the analytical model of the rotating blade. The aerodynamic load is determined using first-order piston theory. The rotating blade is treated as a pretwist, presetting, thin-walled rotating cantilever beam. Using the isotropic constitutive law and Hamilton??s principle, the nonlinear partial differential governing equation of motion is derived for the pretwist, presetting, thin-walled rotating beam. Based on the obtained governing equation of motion, Galerkin??s approach is applied to obtain a two-degree-of-freedom nonlinear system. From the resulting ordinary equation, the method of multiple scales is exploited to derive the four-dimensional averaged equation for the case of 1:1 internal resonance and primary resonance. Numerical simulations are performed to study the nonlinear dynamic response of the rotating blade. In summary, numerical studies suggest that periodic motions and chaotic motions exist in the nonlinear vibrations of the rotating blade with varying speed.     

Aerothermoelastic behavior of supersonic rotating thin-walled beams made of functionally graded materials

In this study, a thin-walled beam made of functionally graded material (FGM) which is used as rotating blades in turbomachinery under aerothermoelastic loading is investigated. The governing equations, which are based on first-order shear deformation theory, include the effects of the presetting angle, the secondary warping, temperature gradient through the wall thickness of the beam and also the rotational speed. Moreover, quasi-steady aerodynamic pressure loadings are determined using first-order piston theory, and steady beam surface temperature is obtained from gas dynamics theory. Then, the blade partial differential equations are transformed into a set of ordinary differential equations using the extended Galerkin method. Finally, having solved the resulting structural–fluid–thermal eigenvalue system of equations, the effects of Mach number and geometric parameters on natural frequencies are presented. The results demonstrate that the natural frequencies decrease under aerothermoelastic loading at high Mach numbers.     

DYNAMIC ANALYSIS OF A SPATIAL COUPLED TIMOSHENKO ROTATING SHAFT WITH LARGE DISPLACEMENTS

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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.      

伽辽金有限元素法对旋翼气弹稳定性的应用

采用伽辽金加权余数有限元素法发展了一种悬停状态下无铰旋翼桨叶气弹稳定性的分析方法。分析模型包括预锥角、下垂角、预掠角、总距角、桨根预安装角、桨叶预扭角、变距轴偏置、根部外伸量和操纵线系刚度等结构参数，对无铰旋翼桨叶气弹稳定性研究有普遍适用意义。试验证明该理论可行并能用于研究无铰旋翼结构参数对桨叶气弹稳定性的影响，也能用于直升机旋翼的型号设计。     

基于径向基点插值法的旋转Mindlin板高次刚柔耦合动力学模型

将无网格径向基点插值法(radial point interpolation method,RPIM)用于中心刚体?旋转柔性板的动力学分析.基于浮动坐标系方法和一阶剪切变形理论即Mindlin板理论,考虑剪切变形的影响,并计入板面内变形的非线性耦合变形项,采用径向基点插值法描述板的变形场,保留动能中有关非线性耦合变形项...     

Nonlinear aeroelastic stability analysis of wind turbine blade with bending–bending–twist coupling

In this study, the nonlinear aeroelastic stability of wind turbine blade with bending–bending–twist coupling has been investigated for composite thin-walled structure with pretwist angle. The aerodynamic model used here is the differential dynamic stall nonlinear ONERA model. The nonlinear aeroelastic equations are reduced to ordinary equations by Galerkin method, with the aerodynamic force decomposition by strip theory. The nonlinear resulting equations are solved by a time-marching approach, and are linearized by small perturbation about the equilibrium point. The nonlinear aeroelastic stability characteristics are investigated through eigenvalue analysis, nonlinear time domain response, and linearized time domain response.     

Delayed presetting of helical springs

Abstract

This article establishes the calculation of remaining deformation and residual stress for helical springs after long-lasting presetting process. The article extends the model for the immediate presetting process accounting the creep deformation of the spring. The method is based on plasticity theory for the instant flow overexposed by the relaxation over the long-term presetting. In this article, the following method is used. The plastic deformation of the helical spring with the circular cross section occurs instantly. If the shortening of the spring in the tool holder persists, the relaxation of stresses occurs and the force of the spring reduces. As the consequence, after the elastic unloading of the long-time presetting, the residual stresses spring reduce gradually with the squeezing time as well. The final length of the springs considerably shortens with the increasing preset duration. The advantage of the discovered closed form solutions is the calculation without the necessity of complex finite-element simulation of spring length loss and residual stresses after presetting process. The analytical expressions are proposed and the exact calibration applied for evaluation of factors for presetting processes.     

Free vibration and dynamic stability of rotating thin-walled composite beams

The dynamic stability behavior of thin-walled rotating composite beams is studied by means of the finite element method. The analysis is based on Bolotin’s work on parametric instability for an axial periodic load. The influence of fiber orientation and rotating speeds on the natural frequencies and the unstable regions is studied for symmetrically balanced laminates. The regions of instability are obtained and expressed in non-dimensional terms. The “modal interchange” phenomenon arising in rotating beams is described. The dynamic stability problem is formulated by means of linearizing a geometrically nonlinear total Lagrangian finite element with seven degrees of freedom per node. This finite element formulation is based on a thin-walled beam theory that takes into account several non-classical effects such as anisotropy, shear flexibility and warping inhibition.     

A spiral model for bending of non-linearly pretwisted helicoidal structures with lateral loading

The paper presents a new approach in the bending analysis of helicoidal structures with a large non-linear pretwist and an external lateral loading. It also addresses the issue as to what extent the linearized twisting curvature is applicable in the analysis of pretwisted plates. Employing a non-linear helicoidal model and a natural orthogonal coordinate system, the large non-linear pretwist is formulated and the energy stored in a distorted helicoid subjected to an external pressure normal to the helicoid axis is derived. By integrating the internal strain energy and external pressure work over the helicoidal domain, a non-homogeneous system of equations is presented and numerical solutions are obtained. Significant structural responses such as deformation components and resultant, the effects of width and thickness of helicoid on bending are analyzed and discussed. The analysis can be extended to other areas of interest such as turbomachinery blades, drilling structures, motors in micro-electro-mechanical systems and also DNA biomechanics.     

On the optimal shape of compressed rotating rod with shear and extensibility

In this paper, the optimal shape of a compressed rotating rod which maintains stability against buckling is presented. In the rod modeling, extensibility along the rod axis and shear stress is taken into account. Using Pontryagin's maximum principle, the optimization problem is formulated with a fourth order boundary value problem. The optimally shaped compressed rotating (fixed-free) rod has a finite cross-sectional area on the free end. This shape is qualitatively different from that suggested by the Bernoulli-Euler theory with zero cross-sectional area on the free end. In addition, the Bernoulli-Euler theory overestimates the buckling load, and this effect is more significant in the optimally shaped rod than for the corresponding constant cross-sectional rod consisting of the same material volume and length. In order to show this effect, it is necessary to use a generalized constitutive model which takes real material properties, such as axial extensibility and shear stress into account. Particularly, the solution of this generalized problem, obtained for thin rods, approaches the classical solution predicted by the Bernoulli-Euler theory.     

偶应力理论下拉力型锚固体的受力特性

锚固体的受力特征及其影响因素是锚固体设计的重要依据,直接影响锚固效果。传统的经典弹性理论没有考虑应变梯度的影响。偶应力理论引进弯曲曲率,考虑了弯曲效应对介质变形特性的影响。基于偶应力理论,建立了平面应变问题的有限元计算模型,研究锚固体锚固段界面上的剪应力分布、锚固体轴力分布、偶应力的尺度效应以及弹性模量和围压对锚固力的影响,并将偶应力理论的计算结果和经典弹性理论的计算结果进行了比较。结果表明,在偶应力理论下,锚固体锚固段界面的剪应力有所减小,特别是峰值处的剪应力减小明显;岩土的弹性模量越大,锚固界面局部剪应力越大;锚固力随着围压的增大而增大,偶应力尺度效应明显。     

旋转圆柱绕流流场特性分析

对雷诺数Re = 20000 ~ 90000、相对转速ɑ = 0 ~ 0.72的旋转圆柱后方流场进行了实验测量, 分析了旋转圆柱后方不同剖面处的速度分布规律和湍流度分布规律. 采用LES方法对旋转圆柱绕流问题进行了数值模拟, 分析旋转圆柱周围流场特性和自由剪切层变化规律, 最后通过理论模型对流场变化进行分析, 得出如下结论: 当圆柱逆时针旋转时, 同一雷诺数下随着相对转速的增加, 旋转圆柱尾迹区域下方速度突变处的位置随着相对转速的增加而上移, 而上方速度突变处的位置不变, 雷诺数的增加使旋转圆柱尾迹区域下方速度突变处位置有小幅度的下移. 通过数值模拟发现, 圆柱旋转之后, 圆柱后方下侧涡的位置明显上移, 且幅度较大. 下方的自由剪切层有明显的上移, 上方的自由剪切层位置变化较小. 最后通过理论分析发现, 圆柱后侧下方涡位置的上移对圆柱升力影响十分显著, 在高雷诺数、低相对转速的条件下, 旋转圆柱后侧下方涡位置的改变对旋转圆柱的升力、尾流区自由剪切层的变化起到了重要的影响.      

超高压水射流喷头水动力特性研究

基于对超高压水射流喷头的外部参数定量化分析,给出关于射流核心参数的优选方法,旨在提高水射流效率。首先,根据超高压水射流除锈喷嘴的工作特点,考虑到水的压缩性和空化效应,建立单束定冲角、多束旋转喷头的三维数值模型,通过改变靶距、入射角度、转速等外部特征参数,实施了超高压水射流除锈喷头水动力性能模拟研究。然后,重点分析单束定冲角喷嘴靶距、入射角度对靶面剪切应力、打击压强分布的影响,以及射流等速核长度与最佳射流靶距的关系。发现当靶距等于喷嘴射流等速核长度时,壁面剪切应力达到最佳水平。此外,通过分析高速旋转射流卷吸效应、靶面水垫作用对靶面所受剪切应力、打击压强分布的影响,得到最佳转速范围和对应线速度。初步阐明了射流冲击剥离的机理、单束定冲角以及多束旋转射流的特征参数对射流效果的影响,可为超高压除锈喷头的设计、装配提供参考。     

On the cyclone-anticyclone asymmetry in the stability of rotating shear flows

The manifestations of the cyclone-anticyclone asymmetry on the stability of rotating shear flows are investigated both theoretically and experimentally. The stability of certain classes of shear flows, namely, rotating tangential discontinuities and flows with a constant shear, is analyzed. The dependence of the disturbance growth rate on the sign and absolute value of the shear is determined. The three-dimensional disturbances leading to longitudinal flow modulations are shown to be most dangerous. The results of the observations of the cyclone-anticyclone asymmetry effect in the laboratory conditions are presented.     

Stress diffusion and high order viscoelastic effects in the 3D flow past a sedimenting sphere subject to orthogonal shear

The effect of polymer stress diffusion in the unbounded flow past a sedimenting, freely rotating, rigid sphere subject to shear in a plane perpendicular to the direction of sedimentation is investigated analytically. Steady state, creeping, incompressible, and isothermal flow is assumed. For viscoelastic fluids following the Oldroyd-B constitutive model, three-dimensional results for the velocity vector, pressure, and viscoelastic extra-stress tensor are derived by including an artificial diffusion term in the constitutive equation and using regular perturbation theory with the small parameter being the Deborah number. The analytical solution reveals that the influence of the stress diffusion term on the results may be significant (and sometimes unexpected) and strongly depends on the magnitude of the dimensionless diffusion coefficient. For instance, it is shown that the critical Deborah number, below which a physical solution arises, decreases with the increase in the diffusion coefficient. Also, comparison against simulation results from the literature shows excellent agreement up to shear Weissenberg number (defined as the product of the imposed shear rate with the single relaxation time of the fluid) approximately equal to unity.     

Shear-induced phase separation in cationic surfactant solutions around a rotating sphere

The results of an experimental investigation of the flow of a highly dilute cationic surfactant solution (tetradecyl trimethyl ammonium bromide with added sodium salicylate as counterion, equimolar 2.4mM) around a rotating sphere are presented. The flow and the shear-induced phase transition are visualized by means of a Toepler Schlieren optics. The buildup of the shear-induced structures occurs only above a critical shear rate. Once this critical value is exceeded the shear-induced phase separation starts after a characteristic deformation with the shear rate reduced by the critical one. Further analysis of the obtained data is performed on basis of an analytical calculation of the flow around a rotating sphere in a second order fluid (Thomas and Walters, 1964; Giesekus, 1965). From some characteristic features of the shear-induced structures as induction time and position the parameter describing the elastic properties of the fluid is estimated. Received: 6 January 1998 Accepted: 1 May 1998     

Blowup of solutions for the planar motions of rotating nonlinearly elastic rods

This paper treats the motion of flexible, extensible, shearable nonlinearly elastic rods, described by a geometrically exact theory, when they are confined to a plane rotating about a fixed axis at constant angular speed and when they are confined to a fixed plane with one end rotating at a constant angular speed about an axis perpendicular to the fixed plane. The paper gives restrictions on the constitutive equations and initial conditions that ensure that motions become unbounded at rapid rates as time becomes infinite. The analysis of these constitutive restrictions employs the theory of characteristics for single first-order semilinear partial differential equations.     

Effect of system rotating on turbulent boundary layer flow

This paper experimentally investigated the effect of rotating on the turbulent boundary layer flow using hot-wire. The experiments were completed in a rotating rig with a vertical axis and four measured positions along the streamwise direction in channel, which focuses on the flow flied in the rotating channel. The rotating effects on velocity profile, wall shear stress and semi-logarithmic mean velocity profile are discussed in this paper. The results indicated that: due to the Coriolis force induced by rotating, the phenomenon of velocity deficit happens near the leading side. The velocity deficit near the leading side, do not increase monotonically with the increase of Ro. The trend of the velocity deficit near the leading side is also affected by the normal component of pressure gradient, which is another important force in the cross-section of the rotating channel. The wall shear stress near the trailing side is larger than that on the leading side, and the semi-logarithmic mean velocity profile is also different under rotating effects. The phenomenon reveals that the effect of rotation penetrates into the logarithm region, and the flow near the leading side tends to turn into laminar under the effect of rotation. The rotation correction of logarithmic law is performed in current work, which can be used in the wall function of CFD to increase the simulating accuracy at rotating conditions.     

An aeroelastic model for composite rotor blades with straight and swept tips. Part I: Aeroelastic stability in hover

An analytical model for predicting the aeroelastic behavior of composite rotor blades with straight and swept tips is presented. The blade is modeled by beam type finite elements along the elastic axis. A single finite element is used to model the swept tip. The non-linear equations of motion for the finite element model are derived using Hamilton's principle and based on a moderate deflection theory and accounts for: arbitrary cross-sectional shape, pretwist, generally anisotropic material behavior, transverse shears and out-of-plane warping. Numerical results illustrating the effects of tip sweep, anhedral and composite ply orientation on blade aeroelastic behavior are presented. It is shown that composite ply orientation has a substantial effect on blade stability. At low thrust conditions, certain ply orientations can cause instability in the lag mode. The flap-torsion coupling associated with tip sweep can also induce aeroelastic instability in the blade. This instability can be removed by appropriate ply orientation in the composite construction.