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。     

A moderate deflection composite helicopter rotor blade model with an improved cross-sectional analysis

The compatibility between a composite beam cross-sectional analysis based on the variational asymptotic approach, and a helicopter rotor blade model which is part of a comprehensive rotorcraft analysis code is examined. It was found that the finite element cross-sectional analysis code VABS can be combined with a moderate deflection rotor blade model in spite of the differences between the formulations. The new YF/VABS rotor blade model accounts for arbitrary cross-sectional warping, in-plane stresses, and moderate deflections. The YF/VABS composite rotor blade model was validated against experimental data and various rotor blade analyses by examining displacements and stresses under static loads, as well as aeroelastic stability of a composite rotor blade in hover, and forward flight vibratory hubloads of a four bladed composite rotor.     

Tightly coupled aeroelastic model implementation dedicated to fast aeroelastic tailoring optimisation of high aspect ratio composite wing

This paper presents the development of a code, called GEBTAero, dedicated to very flexible aircraft (VFA) aeroelasticity and especially the evaluation of aeroelastic tailoring effect on critical speeds. GEBTAero is an open source code consisting in a tightly coupling between a geometrically exact beam theory -and a finite state induced flow unsteady aerodynamic model, including an homogenisation tool. This model has been implemented in Fortran using GEBT code and optimised open source libraries with particular focus on computation speed. Besides a non linear transient dynamic simulation capacity, a particular focus is put on the fast critical speed computation strategy using a non-iterative modal approach about the geometrically non linear deformed shape of the wing with the computation of only a few aeroelastic modes. Computation speed and accuracy of this implementation is assessed using widely used aeroelastic test cases and compared successfully to other aeroelastic codes. Configurations using aeroelastic tailoring, which are the core target of this solver, are then evaluated numerically on a representative high aspect ratio anisotropic composite wing and a simple 2-ply composite laminates with both variable ply orientations. It illustrates the strong correlation between the structural bending/twisting coupling of an unbalanced composite laminates and its critical aeroelastic speed. It also shows the high sensitivity of ply orientation on the aeroelastic behaviour.     

AEROELASTIC OPTIMIZATION DESIGN OF COMPOSITE WING WITH CONSIDERATION OF STRUCTURAL INSTABILITY

从工程数学求解和有限元分析角度对复合材料结构的稳定性分析方法进行研究,基于这两个方面分别建立了同时考虑壁板稳定性约束和气动弹性约 束的气动弹性优化技术,并以大展弦比复合材料机翼为对象,进行气动弹性综合优化设计。研究表明,机翼气动弹性优化中若不考虑稳定性约束条件,虽然可以获得较小结构重量,但往往不满足稳定性要求;相比从有限元角度考虑结构失稳特征的气动弹性综合优化设计方法,通过工程数学方法对机翼结构进行分区失稳分析优化可以更加精准地控制变量,在满足各项性能指标,特别是稳定性约束的同时,进一步减轻了结构重量,提高了结构失稳因子。     

Aeroelastic analysis of helicopter rotor blade in hover using an efficient reduced-order aerodynamic model

This paper presents a coupled flap–lag–torsion aeroelastic stability analysis and response of a hingeless helicopter blade in the hovering flight condition. The boundary element method based on the wake eigenvalues is used for the prediction of unsteady airloads of the rotor blade. The aeroelastic equations of motion of the rotor blade are derived by Galerkin's method. To obtain the aeroelastic stability and response, the governing nonlinear equations of motion are linearized about the nonlinear steady equilibrium positions using small perturbation theory. The equilibrium deflections are calculated through the iterative Newton–Raphson method. Numerical results comprising steady equilibrium state deflections, aeroelastic eigenvalues and time history response about these states for a two-bladed rotor are presented, and some of them are compared with those obtained from a two-dimensional quasi-steady strip aerodynamic theory. Also, the effect of the number of aerodynamic eigenmodes is investigated. The results show that the three-dimensional aerodynamic formulation has considerable impact on the determination of both the equilibrium condition and lead-lag instability.     

Numerical investigation of structural geometric nonlinearity effect in high-aspect-ratio wing using CFD/CSD coupled approach

An efficient and robust fluid–structure coupled methodology has been developed to investigate the linear and non-linear static aeroelastic behavior of flexible high-aspect-ratio wing. A three-dimensional open source finite element solver has been loosely coupled with an in-house Reynolds-averaged Navier–Stokes solver, designed for hybrid-unstructured meshes, to perform aero-structural coupled simulations. For volume mesh deformation and two-way data interpolation over non-matching grids interface, a radial basis function methodology combined with a data reduction algorithm has been used. This technique is efficient in handling large deflections and provides high-quality deformed meshes. Structural geometric nonlinearity has been considered to predict the deformations in the vertical and torsional directions caused by gravitational and aerodynamic loading. A multi-material finite element model has been generated to match the experimental configuration. Computational aeroelastic simulations were performed on an experimental high-aspect-ratio aeroelastic wing model with a slender body at the tip to get non-linear static deflections, twist and structure natural frequencies. The effect of the geometric nonlinearity is significant for large deformation analysis and has been highlighted in the predicted maximum tip deflection and twist. Good qualitative and quantitative agreement has been achieved between the predicted results and the available experimental data.     

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.     

Nonlinear transient response of strain rate dependent composite laminated plates using multiscale simulation

The effects of strain rate dependency and inelasticity on the transient responses of composite laminated plates are investigated. A micromechanics model which accounts for the transverse shear stress effect, the effect of strain rate dependency and the effect of inelasticity is used for analyzing the mechanical responses of the fiber and matrix constituents. The accuracy of the micromechanics model under transverse shear loading is verified by comparing the results with those obtained using a general purpose finite element code. A higher order laminated plate theory is extended to capture the inelastic deformations of the composite plate and is implemented using the finite element technique. A complete micro–macro numerical procedure is developed to model the strain rate dependent behavior of inelastic composite laminates by implementing the micromechanics model into the finite element model. Parametric studies of the transient responses of composite plates are conduced. The effects of geometry, ply stacking sequence, material models, boundary conditions and loadings are investigated. The results show that the strain rate dependency and inelasticity influence the transient responses of composite plates via two significantly different mechanisms.     

变角度纤维复合材料圆柱壳的轴压屈曲

变角度纤维复合材料的纤维方向角可沿铺层面内连续变化,因此相应结构的性能具有更高的设计灵活性和更大的优化空间．本文假设纤维方向角沿圆柱壳的轴向呈正弦函数变化,对变角度纤维复合材料圆柱壳在两端简支边界条件下的轴压屈曲问题进行研究．基于Donnell经典壳体理论,推导变角度纤维复合材料圆柱壳的前屈曲控制方程并运用伽辽金法进行求解,然后采用瑞利里兹法求解屈曲问题．通过和现有文献及有限元数值结果的对比,验证了本文模型的收敛性和正确性,通过数值算例分析了纤维起始角和终止角的变化对圆柱壳的屈曲临界荷载的影响．本文的研究结果可为变角度纤维复合材料圆柱壳的分析和设计提供一定的参考．     

Aeroelastic instability of composite wings by the consideration of different structural constitutive assumptions

The aeroelastic instability of composite wings modeled as Circumferentially Asymmetric Stiffness (CAS) thin-walled composite beams with closed cross-section is carried out. The objective has been to investigate the effects of different assumptions of constitutive equations on the aeroelastic instability behavior. Non-classical effects such as restrained warping and transverse shear are included in the beam model. The unsteady incompressible airloads are presented using Wagner׳s function. A comparison of the results based on different constitutive equations for a number of configurations including three types of stacking sequence for a box cross-section and two types of stacking sequence for a biconvex cross-section, is performed. The effects of the values of twist as well as twist-bending stiffness coefficients have been studied carefully on the results. As an outcome of this investigation it is revealed that the different choices of structural constitutive equations which result in different values of stiffness quantities; namely, twist and twist-bending stiffness, significantly affect the predicted results. For example, a difference of up to 45% in the aeroelastic critical speed has been observed between different sets of constitutive equations in some cases.     

Aeroelastic analysis of swept pre-twisted wings

In this paper, aeroelastic modeling of aircraft wings with variations in sweep angle, taper ratio, and variable pre-twist angle along the span is considered. The wing structure is modeled as a classical beam with torsion and bending flexibility. The governing equations are derived based on Hamilton’s principle. Moreover, Peters’ finite state aerodynamic model which is modified to take into account the effects of the wing finite-span, the wing sweep angle, and the wing pre-twist angle, is used to simulate the aerodynamic loads on the wing. The coupled partially differential equations are discretized to a set of ordinary differential equations using Galerkin’s approach. By solving these equations the aeroelastic instability conditions are derived. The results are compared with some experimental and analytical results of previous published papers and good agreement is attained. Effects of the wing sweep angle, taper ratio, bending to torsional rigidity, and pre-twist angle on the flutter boundary in several cases are studied. Results show that these geometrical and physical parameters have considerable effects on the wing flutter boundary.     

Reduced order nonlinear aeroelasticity of swept composite wings using compressible indicial unsteady aerodynamics

Nonlinear dynamic aeroelasticity of composite wings in compressible flows is investigated. To provide a reasonable model for the problem, the composite wing is modeled as a thin walled beam (TWB) with circumferentially asymmetric stiffness layup configuration. The structural model considers nonlinear strain displacement relations and a number of non-classical effects, such as transverse shear and warping inhibition. Geometrically nonlinear terms of up to third order are retained in the formulation. Unsteady aerodynamic loads are calculated according to a compressible model, described by indicial function approximations in the time domain. The aeroelastic system of equations is augmented by the differential equations governing the aerodynamics lag states to derive the final explicit form of the coupled fluid-structure equations of motion. The final nonlinear governing aeroelastic system of equations is solved using the eigenvectors of the linear structural equations of motion to approximate the spatial variation of the corresponding degrees of freedom in the Ritz solution method. Direct time integrations of the nonlinear equations of motion representing the full aeroelastic system are conducted using the well-known Runge–Kutta method. A comprehensive insight is provided over the effect of parameters such as the lamination fiber angle and the sweep angle on the stability margins and the limit cycle oscillation behavior of the system. Integration of the interpolation method employed for the evaluation of compressible indicial functions at any Mach number in the subsonic compressible range to the derivation process of the third order nonlinear aeroelastic system of equations based on TWB theory is done for the first time. Results show that flutter speeds obtained by the incompressible unsteady aerodynamics are not conservative and as the backward sweep angle of the wing is increased, post-flutter aeroelastic response of the wing becomes more well-behaved.     

Aeroelastic instability of a composite wing with a powered-engine

In this paper the aeroelastic instability of a wing, modeled as an orthotropic composite beam with a concentrated mass subjected to the engine thrust, is investigated in an incompressible flow. The wing is modeled using classical beam theory. Wagner function is used to model the unsteady aerodynamic loads, while the engine thrust is modeled as a follower force and a concentrated mass is used to model the engine mass. The numerical results of the developed generic and simple model are compared with published results, and an excellent agreement is observed. The fiber orientation, engine thrust, mass magnitude and its location are reported to have had significant effects on the aeroelastic instability boundaries.     

A non‐linear coupled fluid–structure aeroelastic analysis of a slender bridge deck

This paper presents a new numerical methodology for the integral aeroelastic instability analysis of slender structures, based on the appropriate conjugation of an algorithm for dynamic and geometrically non‐linear analysis of structures based on the finite element method with another algorithm of computational fluid dynamics (Finite volume method). It is considered a viscous incompressible unsteady turbulent bidimensional air flow solved on a structured control volume mesh. The computer code developed on the basis of this methodology is applied to the aeroelastic study of a simply supported slender bridge deck in order to find out the critical wind velocity leading to instability. Some of the most significant results associated with the analysis of the corresponding aeroelastic behaviour are presented. Copyright 2004 John Wiley & Sons, Ltd.     

3-D inviscid self-excited vibrations of a blade row in the last stage turbine

Presented here is a three-dimensional (3-D) nonlinear time-marching method for the aeroelastic behaviour of an oscillating turbine blade row. The approach has been based in the solution of a coupled fluid–structure problem where the aerodynamic and structural dynamic equations are integrated simultaneously in time. This provides the correct formulation of a coupled problem, as the interblade phase angle (IBPA) at which stability (instability) would occur is also a part of solution. The ideal gas flow around multiple interblade passages (with periodicity in the entire annulus) is described by the unsteady Euler equations in conservative form, which are integrated by using the explicit monotonic second-order accurate Godunov–Kolgan finite-volume scheme and a moving hybrid H–O (or H–H) grid. The fluid and the structural equations are solved using the modal superposition method. An aeroelasticity prediction of a turbine blade of 0.765 m is presented. The natural frequencies and modal shapes of the blade were calculated by using 3-D finite element models. The instability regions for five mode shapes and the distribution of the aerodamping coefficient along the blade length were shown for harmonic oscillations with an assumed IBPA. The coupled fluid–structure oscillations in which the IBPA is part of the solution are shown.     

Aeroelastic response of a coupled rotor/fuselage system in hovering and forward flight

Summary The aeroelastic response analysis of a coupled rotor/fuselage system is approached by iterative solution of the blade aeroelastic response in the non-inertial reference frame fixed on the hub, and the periodic response of the fuselage in the inertial reference frame. A model of the coupled system hinged with the flap and lag hinges, the pitching bearing which may not coincide with the hinges, and the sweeping-blade configuration is established. The moderate-deflection beam theory and the two-dimensional quasi-steady aerodynamic model are employed to model the aeroelastic blade, all the kinetic and inertial factors are taken into account in a unified manner. A five-nodes, 15-DOFs pre-twisted nonuniform beam element is developed for the discretization of the blade, three rigid-body-motion DOFs are introduced for the motion of the hinges and the bearing. The Hamilton's principle is employed to evaluate the equation of motion of the blade. The derived nonlinear ordinary differential equations with time-dependent periodic coefficients are solved by a modified quasi-linearization method, which is developed for the higher DOF periodic system. The resulting periodic forces and moments exerted on the fuselage by all the blades are evaluated every time, when the converged nonlinear periodic response of the blade is obtained under the consideration of the equilibrium of the blades. The fuselage structure is simplified to be a beam structure, the governing equation is established in the inertial reference frame and a two-nodes beam element is used to discretize the flexible fuselage. The periodic response of the fuselage is solved by a simple shooting method. The iteration of the rotor/fuselage response is continued, until the aeroelastic responses of the blade and the fuselage converge simultaneously. Both the hovering and the forward flight states can be considered. The results of a computed numerical example by the developed program are presented to verify in practice the economy of the modeling as well as the reliability and efficiency of the corresponding solving methods. Received 4 May 1998; accepted 11 August 1998     

Nonlinear aeroelastic behavior of an oscillating airfoil during stall-induced vibration

In this paper, nonlinear aeroelastic behavior of a two-dimensional symmetric rotor blade in the dynamic stall regime is investigated. Two different oscillation models have been considered here: pitching oscillation and flap–edgewise oscillation. Stall aeroelastic instability in such systems can potentially lead to structural damage. Hence it is an important design concern, especially for wind turbines and helicopter rotors, where such modes of oscillation are likely to take place. Most previous analyses of such dynamical systems are not exhaustive. System parameters like structural nonlinearity or initial conditions have not been studied which could play a significant role on the overall dynamics. In the present paper, a parametric study on the aeroelastic instability and the nonlinear dynamical behavior of the system has been performed. Emphasis is given on the effect of structural nonlinearity and initial conditions. The aerodynamic loads in the dynamic stall regime have been computed using the Onera model. The qualitative influence of the system parameters is different in the two systems studied. The effect of structural nonlinearity on the bifurcation pattern of the system response is significant in the case of pitching oscillation. The initial condition plays an important role on the aeroelastic stability as well as on the bifurcation pattern in both the systems. In the forced response study, interesting dynamical behavior, like period-3 response, has been observed in the pitching oscillation case. On the other hand, for the flap–edgewise oscillation case, super-harmonic and quasi-harmonic response have been found.     

考虑几何非线性的复合材料机翼气动弹性分析

本文研究结构几何非线性与气动力非平面效应对大展弦比复合材料机翼的气动弹性行为的影响．将非线性有限元法与曲面涡格法结合,计算机翼静气动弹性变形;通过曲面偶极子格网法结合静气动弹性平衡位置处的结构切线刚度,建立气动弹性方程并求解得到机翼颤振速度．针对板模型机翼,分析了迎角对机翼几何非线性气动弹性特性的影响．结果表明：本文复合材料板模型机翼的颤振形式不受水平弯曲模态影响,属于经典弯扭颤振;在几何非线性的影响下,机翼扭转频率随结构变形增大而明显减小,颤振速度随迎角增大而减小．     

Numerical identification of mechanisms triggering 2D choke flutter in transonic fan

Blade vibration may trigger a self-induced aeroelastic instability (flutter). In turbomachinery choke flutter appears when a strong shock-wave chokes the blade passage. The aim of this study is to identify mechanisms responsible for the instability. An innovative methodology relying on the splitting of the emitter and receiver role of the blade is presented. It is successfully applied to 2D linearized RANS computations of choke flutter. The emission splitting shows that the vibration of the blades downstream of the shock-wave generates a backward traveling pressure wave triggering the aeroelastic instability. The reception splitting demonstrates the destabilising contribution of the shock-wave / separated boundary layer interaction. The source of flutter is finally a combination of inviscid (regressive waves) and viscous (unsteady separation) mechanisms.     

直升机旋翼/机体动稳定性研究进展

首先对直升机旋翼/机体动不稳定性问题的种类进行了简要概述,包括旋翼挥舞/变距、变距/摆振、挥舞/摆振和挥舞/摆振/变距耦合等孤立旋翼动不稳定性问题,以及直升机地面共振和空中共振等旋翼/机体耦合动不稳定性问题,然后分别从气动力与结构的高精度数值模型、动稳定性的计算分析方法和实验模型测试3 个方面详细介绍了直升机旋翼/机体动不稳定性问题的研究现状,并着重讨论了直升机旋翼/机体动稳定性分析技术最近的主要研究方向:耦合CFD(computational fluid dynamics)/CSD(computational structuraldynamics) 的直升机旋翼气弹动稳定性分析、复合材料旋翼动稳定性分析及其材料不确定性影响、带减摆器的旋翼/机体动稳定性分析和先进直升机构型的旋翼/机体动稳定性分析,最后对直升机旋翼/机体动稳定性研究的发展趋势进行了展望.