Numerical studies of a non-linear aeroelastic system with plunging and pitching freeplays in supersonic/hypersonic regimes

The flutter and post flutter of a two-dimensional double-wedge lifting surface with combined freeplay and cubic stiffness nonlinearities in both plunging and pitching degrees-of-freedom operating in supersonic/hypersonic flight speed regimes have been analyzed. In addition to the structural nonlinearities, the third-order piston theory aerodynamics is used to evaluate the unsteady non-linear aerodynamic force and moment. Such model accounts for stiffness and damping contributions produced by the aerodynamic loads. Responses involving limit cycle oscillation and chaotic motion are observed over a large number of parameters that characterizes the aeroelastic system. Results of the present study show that the freeplay in the pitching degree-of-freedom and soft/hard cubic stiffness in the pitching and plunging degrees-of-freedom have significant effects on the LCOs exhibited by the aeroelastic system in the supersonic/hypersonic flight speed regimes. The simulations also show that the aeroelastic system behavior is greatly affected by physical structural parameters, such as the radius of gyration and the frequency ratio, especially in post-flutter regimes, when accounting for all system nonlinearities. It has been shown that at high Mach numbers the non-linear aerodynamic stiffness yields detrimental effects from the aeroelastic point of view, while the damping one do not.     

Aeroelastic response of a 2-D airfoil in a compressible flow field and exposed to blast loading

This paper deals with the generation and use of proper aerodynamic indicial functions toward the aeroelastic formulation of two-dimensional lifting surfaces in the subsonic compressible, linearized transonic, supersonic and hypersonic flight speed regimes. The indicial function approach enables one to treat in an unified way (i.e. in the time and frequency domains) the subcritical aeroelastic response and the flutter instability of lifting surfaces. Validations of the aerodynamic model are documented and excellent agreements are reported. In addition, closed form solutions and aerodynamic derivatives for different flight speed regimes are obtained; comparisons, and results displaying the aeroelastic response to blast loads are presented, and pertinent conclusions are outlined.     

Nonlinear Aeroelastic Response of High-aspect-ratio Flexible Wings

The aeroelastic analysis of high-altitude, long-endurance (HALE) aircraft that features high-aspect-ratio flexible wings needs take into account structural geometrical nonlinearities and dynamic stall. For a generic nonlinear aeroelastic system, besides the stability boundary, the characteristics of the limit-cycle oscillation (LCO) should also be accurately predicted. In order to conduct nonlinear aeroelastic analysis of high-aspect-ratio flexible wings, a first-order, state-space model is developed by combining a geometrically exact, nonlinear anisotropic beam model with nonlinear ONERA (Edlin) dynamic stall model. The present investigations focus on the initiation and sustaining mechanism of the LCO and the effects of flight speed and drag on aeroelastic behaviors. Numerical results indicate that structural geometrical nonlinearities could lead to the LCO without stall occurring. As flight speed increases, dynamic stall becomes dominant and the LCO increasingly complicated. Drag could be negligible for LCO type, but should be considered to exactly predict the onset speed of flutter or LCO of high-aspect-ratio flexible wings.     

Adaptive aeroelastic vibration suppression of a supersonic airfoil with flap

This paper concerns the flutter, post-flutter and adaptive control of a non-linear 2-D wing-flap system operating in supersonic/hypersonic flight speed regimes. An output feedback control law is implemented and its performance toward suppressing flutter and limit cycle oscillations (LCOs) as well as reducing the vibrational level in the subcritical flight speed range is demonstrated. This control law is applicable to minimum phase systems and we provide conditions for stability of the zero dynamics. The control objective is to design a control strategy to stabilize the pitch angle while adaptively compensating for uncertainties in all the aeroelastic model parameters. It is shown that all the states of the closed-loop system are asymptotically stable.     

Nonlinear aeroelastic analysis of the folding fin with freeplay under thermal environment

The nonlinear aeroelastic behavior of a folding fin in supersonic flow is investigated in this paper. The finite element model of the fin is established and the deployable hinges are represented by three torsion springs with the freeplay nonlinearity. The aerodynamic grid point is assumed to be at the center of each aerodynamic box for simplicity. The aerodynamic governing equation is given by using the infinite plate spline method and the modified linear piston theory. An improved fixed-interface modal synthesis method, which can reduce the rigid connections at the interface, is developed to save the problem size and computation time. The uniform temperature field is applied to create the thermal environment. For the linear flutter analyses, the flutter speed increases first and then decreases with the rise of the hinge stiffness due to the change of the flutter coupling mechanism. For the nonlinear analyses, a larger freeplay angle results in a higher vibration divergent speed. Two different types of limit cycle oscillations and a multiperiodic motion are observed in the wide range of airspeed under the linear flutter boundary. The linear flutter speed shows a slight descend in the thermal environment, but the effect of the temperature on the vibration divergent speed is different under different hinge stiffnesses when there exists freeplay.     

高速流场中变刚度复合材料层合板颤振分析

变刚度复合材料层合板在高速流场中的颤振行为是设计中需要考虑的问题。本文研究了高速流场中的曲线纤维变刚度层合复合材料壁板非线性颤振响应,分析了边界条件和纤维方向对颤振特性的影响。利用von-Karman大变形应变-位移关系,采用气动力活塞理论,根据虚功原理和有限元法建立变刚度复合材料壁板颤振的气动弹性力学模型,采用Newmark法对壁板的颤振方程求解。给出了不同边界条件和纤维方向条件下层合复合材料壁板的颤振特性。计算结果表明：随着纤维在板中心处或在边界±a/2处与x方向夹角（T₀或T₁）的增大,颤振临界动压减小;相同动压下,随着T₀或T₁的增大,极限环振幅增大。研究表明采用曲线纤维进一步提高了复合材料层合板的可设计性,通过调整曲线纤维路径可以改变复合材料壁板的颤振特性。     

超声速气流中受热壁板的二次失稳型颤振

研究了超声速气流中受热壁板的非线性气动弹性响应,发现了一种新的动态失稳现象——二次失稳型颤振。基于von Karman非线性应变-位移关系、Reissner-Mindlin板理论和一阶活塞理论建立超声速气流中三维壁板的有限元模型。通过数值算例,研究了超声速气流中受热壁板发生二次失稳型颤振的条件,并运用非线性振动理论分析了二次失稳型颤振的机理。研究表明,超声速气流中受热壁板在平衡态的稳定性未发生变化时,也会因系统参数的变化引起气动弹性响应性质的突变,导致壁板的二次失稳型颤振。二次失稳型颤振能否发生不仅受到气流速压和壁板温升的影响,而且还与初始扰动有关。当扰动引起壁板的初始变形较小时,不能激发出二次失稳型颤振,壁板的气动弹性响应最终收敛到屈曲平衡态。应用二次失稳型颤振理论和分析方法,确定了前人给出的一个金属壁板模型的热颤振边界的风洞试验结果,而且计算结果与试验结果符合良好,从而对这一壁板热颤振现象的风洞试验结果作出了较合理的理论解释。     

Supersonic flutter control and optimization of metamaterial plate

A metamaterial plate is designed by embedding a periodic array of local nonlinear resonators for its supersonic flutter control. Based on the von Karman large deformation theory and supersonic piston aerodynamic theory, the nonlinear aeroelastic equations of the metamaterial plate are obtained by using the Hamilton principle. The comparisons for aeroelastic behaviors of the metamaterial plate and pure plate show that the proposed metamaterial plate can lead to an enlarged flutter boundary and lower vibration amplitude. Furthermore, a parametric optimization strategy for local nonlinear resonators is proposed to improve the nonlinear flutter behaviors of the metamaterial plate, and a significant enhancement of passive control performance can be achieved through optimization design. The present study demonstrates that the design of the metamaterial plate can provide an effective approach and potential application for nonlinear flutter suppression of supersonic plate.     

吸气式高超声速飞行器多学科动力学建模

高超声速飞行器一体化设计中存在气动/热/推进/结构弹性相互耦合的问题,首先根据飞行器的机体/发动机一体化设计思想构造了二维高超声速飞行器模型,并基于激波/膨胀波原理和动量定理建立了气动力模型,采用Chavez和Schmidt建立的超燃冲压发动机推进系统模型;在飞行器结构方面,引入变截面和变质量分布的自由梁结构模型,并采用Eckert参考焓方法分析的气动加热过程中承力梁不同轴向位置温度随时间变化特征,在此基础上运用模态法计算了燃料消耗和气动加热条件下结构的固有频率和振型特征,获得结构弹性变形的模型;最后建立了考虑热气动弹性和推进系统作用的飞行动力学方程。研究结果表明:质量变化对结构弹性特性影响比较显著,而气动加热的影响主要表现在振动频率方面,且会随着加热过程的持续而逐渐增强;结构变形会改变飞行器静配平状态,特别是在机体质量较大的最初飞行阶段,气动加热会强化结构变形对配平特征的影响;线性化系统的动力学特征分析表明,质量减小和结构变形均会增加短周期模态和振荡模态的不稳定特性,而对高度特性的影响不大,气动加热效应会进一步增加飞行力学和气动弹性的耦合特征,并导致弹性模态的稳定性降低。     

Hypersonic flutter and flutter suppression system of a wind tunnel model

The aeroelastic behavior of a thin flat rudder model was numerically simulated and experimentally investigated in a hypersonic wind tunnel. In particular, a flutter suppression system taking advantage of collision within small gaps was proposed and a novel system for the flutter simulation of the whole nonlinear aeroelastic system including the flutter suppression system was developed. First, the critical flutter dynamic pressure of the rudder without the flutter suppression system was calculated with different methods. Then, the whole nonlinear aeroelastic system, including theflutter suppression system, was simulated to design the gap size. Finally, the flutter suppression system was experimentally validated in a hypersonic wind tunnel operating at Mach number 5. The typical phenomenon of Limit Cycle Oscillation(LCO) was observed, avoiding the structural failure of the model and the consistency between numerical and experimental results was demonstrated.The proposed suppression system can improve the design and reusability of test models of hypersonic flutter experiments.     

一种基于亚临界响应的颤振稳定性边界预测新方法

基于地面模态试验事先获取的结构模态参数,通过弹性机翼在气流中的亚临界响应,解算出作用在机翼上的非定常模态气动力系数。以弹性机翼的模态位移作为系统输入,模态气动力系数作为系统输出,通过辨识方法获得弹性机翼振动的气动力模型。在时域内耦合结构运动方程和气动力模型,建立基于试验数据的气动弹性稳定性分析模型。通过分析系统稳定性随动压的变化规律,获得弹性机翼的颤振稳定性特性。与经典颤振边界外推方法的主要区别在于该方法实质上只需要一次亚临界响应试验即可预测颤振临界点,可极大降低颤振试验的风险和成本。该方法既可用于颤振风洞试验,也可用于颤振试飞。     

颤振边界高效精确预测分析

高效精确地确定多种飞机构型的颤振边界在飞机设计过程中具有重要意义。为了提高计算效率和计算结果的准确性,针对亚声速和跨声速两种马赫数区域,提出分别采用线性和非线性方法进行非定常气动力分析。非线性分析在引入精确的定常气动力的基础上,采用高效率跨声速小扰动方程进行求解;颤振求解统一采用g 法。对大型飞机的梁架—减缩刚度组合模型的空机及三种典型燃油构型进行涵盖飞行包线的全马赫数变高度颤振分析,结果表明：四种构型的颤振边界与颤振试飞边界一致,与其他分析方法相比,效率有明显提高,尤其是对多种飞机构型能够高效地获得准确的颤振边界,即说明本文采用的方法是目前适用于工程上的一种高效精确的预测大型飞机颤振边界的方法。     

基于超燃冲压发动机的HIFiRE项目飞行试验研究进展

飞行器在临近空间内的气动特性及发动机性能一直是各国高超声速项目研究的重点,为探索边界层转捩、激波边界层相互作用以及气动加热效应,美澳牵头于2006年联合启动了HIFiRE项目,采用探空火箭发射进行重点技术验证的模式开展了系列创新性研究。项目重点关注20~38km空域,4~8速域飞行马赫数,试验方案通过单项验证、系统集成的思路逐步深入,将一体化设计的乘波体从无动力滑翔推进到有动力巡航,最终完成带超燃冲压发动机高升阻比飞行器的总体性能测试。研究结果表明:①试验飞行器的边界层转捩高度在35~25km;②乘波体飞行器在飞行马赫数为7时最大升阻比为5.6;③超燃冲压发动机的飞行试验中,在86.2kPa的恒定动压下,飞行马赫数从5.5加速到8.5,试验中发动机实现了从亚燃到超燃的模态转换。      

The flutter of an airfoil with cubic structural and aerodynamic non-linearities

The flutter of a two-dimensional airfoil in a supersonic flow field, with cubic structural and aerodynamic non-linearities, is investigated using an efficient algorithm of normal form, which combines the normal form theory and the center manifold theory together. First, the stability of the linearized system is analyzed in the neighborhood of an equilibrium point, which shows that the flutter instability is resulted by the Hopf bifurcation. Then the normal form of Hopf bifurcation is deduced by applying the symbolic procedure of the new normal form algorithm to the perturbation equations. Analyzing the obtained coefficients of normal form shows that for a given system, the Hopf bifurcation can change from super-critical type to sub-critical type, consequently the flutter instability changes from “benign” type to “catastrophic” type, as the flight Mach number increases. Numerical simulations verify the dependence of response on initial conditions. Finally, the effects of the structural and aerodynamic parameters on the character of flutter instability are analyzed.     

高超声速飞行器热颤振研究现状与展望

高超声速飞行器在飞行过程中承受严酷的气动载荷以及气动加热,因此其结构在设计中要充分考虑气动力及气动热效应引起的结构动稳定性和动响应等问题,热颤振是其中较为关键的一环。本文梳理了热颤振研究的发展历程,总结了用于热颤振研究的多种现有方法,包括热模态试验、热颤振仿真分析以及风洞试验等。在此基础上,进一步分析了可用于热颤振研究...     

考虑机翼几何非线性的气动弹性建模与分析

大展弦比柔性机翼结构重量轻、气动效率高,广泛应用于高空长航时无人机(UAVs)。飞行过程中,这类机翼在气动力作用下发生大变形,线性结构模型不再适用,需要建立考虑几何大变形的结构模型。采用牛顿力学方法推导了考虑结构几何非线性的机翼结构动力学模型,该方法推导过程简洁、物理意义明确,可以与Hodges基于哈密顿原理的推导方法相互补充,相互验证。为了能够更准确地求解大展弦比柔性机翼的非定常气动力,建立了能够考虑机翼三维效应且适用于机翼空间大变形的非定常气动力模型。基于建立的非线性结构模型和非定常气动力模型,采用松耦合方法建立了非线性气动弹性模型,并通过算例验证了气弹模型的准确性。研究结果表明,大展弦比柔性机翼颤振速度对来流迎角和机翼的展长均较为敏感;当来流速度大于颤振速度时,由于几何非线性,机翼振动并未发散而是形成稳定的极限环振荡(LCO);随着来流速度进一步增加,机翼再次穿过临界稳定点,由不稳定系统变为稳定系统,直到随着速度的增加系统再次达到临界稳定状态。     

切尖三角翼极限环振荡的气动弹性模拟

 建立了高精度的气动弹性计算模型,对切尖三角翼风洞试验中的极限环振荡（LCO）现象进行数值模拟。结构部分引入大变形产生的几何非线性和塑性引起的材料非线性,气动部分采用Euler方程描述跨声速流动。结构/气动交界面精确匹配,并选取三维插值进行界面载荷传递。依据所建模型分析切尖三角翼的颤振和LCO,并与试验值进行比较。在小来流动压情况下,结构几何非线性引起了切尖三角翼的LCO,计算结果和试验值吻合较好。在大来流动压情况下,结构材料非线性导致了LCO幅值的急剧增大,其变化趋势与试验观察相符。研究结果显示,切尖三角翼的LCO不仅与结构几何非线性密切相关,而且受到结构材料非线性的显著影响。     

Stall flutter prediction based on multi-layer GRU neural network

The modeling of dynamic stall aerodynamics is essential to stall flutter, due to the flow separation in a large-amplitude pitching oscillation process. A newly neural network based Reduced Order Model (ROM) framework for predicting the aerodynamic forces of an airfoil undergoing large-amplitude pitching oscillation at various velocities is presented in this work. First, the dynamic stall aerodynamics is calculated by solving RANS equations and the transitional SST-γ model. Afterwards, the stall flutter bifurcation behavior is calculated by the above CFD solver coupled with structural dynamic equation. The critical flutter speed and limit-cycle oscillation amplitudes are consistent with those obtained by experiments. A newly multi-layer Gated Recurrent Unit (GRU) neural network based ROM is constructed to accelerate the calculation of aerodynamic forces. The training and validation process are carried out upon the unsteady aerodynamic data obtained by the proposed CFD method. The well-trained ROM is then coupled with the structure equation at a specific velocity, the Limit-Cycle Oscillation (LCO) of stall flutter under this flow condition is predicted precisely and more quickly. In order to predict both the critical flutter velocity and LCO amplitudes after bifurcation at different velocities, a new ROM with GRU neural network considering the variation of flow velocities is developed. The stall flutter results predicted by ROM agree well with the CFD ones at different velocities. Finally, a brief sensitivity analysis of two structural parameters of ROM is carried out. It infers the potential of the presented modeling method to depict the nonlinearity of dynamic stall and stall flutter phenomenon.     

考虑间隙非线性的控制舵非线性气动弹性分析

间隙结构的气动弹性系统非线性颤振问题是飞行器气动弹性力学工程领域的研究热点和难点,研究 考虑间隙非线性的控制舵系统的气动弹性特性具有重要意义。基于最小状态拟合方法获得时域降阶气动力模 型,并通过Lagrange方程获得系统非线性气动弹性方程;对比分析三种不同非线性控制舵系统的极限环颤振 及非线性动力学响应特性,并与等效线化法和时域仿真的结果进行一致性对比。结果表明:俯仰和扑动弹簧刚 度的变化对系统颤振边界有显著影响,当俯仰和扑动两个方向同时含有间隙非线性时,系统在线性颤振速度内 存在倍周期、混沌等复杂非线性动力学现象。     

增程飞行器高超声速飞行的动态特性

研究了增程飞行器高超声速飞行时的动态特性.短程导弹和火箭弹等高超声速飞行来源于增程的实际需要,从超声速到高超声速飞行所遇到的主要飞行动力学问题是,尽管在增程前低超声速时具有良好稳定性,但在高超声速飞行中会丧失稳定性并导致复杂的锥动.通过飞行和风洞实验表明:高超声速飞行时增程飞行器固有的横侧向稳定特性丧失,带有弱滚转阻尼的不稳定荷兰滚振荡将导致滚转-偏航耦合,此外还存在由耦合导致的轻微不稳定拟周期模态和滚动共振.