Dynamic aeroelastic response and active control of composite thin-walled beam structures in compressible flow

The dynamic aeroelastic response and its active control of composite beam structures in compressible flow and exposed to gust and explosive type loads are examined. Modeling of the structures is based on a refined composite thin-walled beam theory and incorporate a number of nonclassical effects, such as transverse shear, material anisotropy, warping inhibition, and rotatory inertia. The unsteady compressible aerodynamic loads for arbitrary small motion in the time domain are derived based on the concept of indicial functions. The sliding mode control (SMC) and linear-quadratic Gaussian (LQG) control methodology with sliding mode observer are used for the purpose of control. The beam structures are restricted to circumferentially asymmetric lay-up construction and the influence of ply angle, flight speed, and external excitations on the response and its active control are specifically investigated. A number of conclusions are outlined at the end.     

OPTIMUM DESIGN OF A HELICOPTER ROTOR FOR LOW VIBRATION USING AEROELASTIC ANALYSIS AND RESPONSE SURFACE METHODS

An aeroelastic analysis based on finite elements in space and time is used to model the helicopter rotor in forward flight. The rotor blade is represented as an elastic cantilever beam undergoing flap and lag bending, elastic torsion and axial deformations. The objective of the improved design is to reduce vibratory loads at the rotor hub that are the main source of helicopter vibration. Constraints are imposed on aeroelastic stability, and move limits are imposed on the blade elastic stiffness design variables. Using the aeroelastic analysis, response surface approximations are constructed for the objective function (vibratory hub loads). It is found that second order polynomial response surfaces constructed using the central composite design of the theory of design of experiments adequately represents the aeroelastic model in the vicinity of the baseline design. Optimization results show a reduction in the objective function of about 30 per cent. A key accomplishment of this paper is the decoupling of the analysis problem and the optimization problems using response surface methods, which should encourage the use of optimization methods by the helicopter industry.     

大展弦比气弹机翼柔性非线性变形的气动力效应分析与风洞试验

从飞行器刚弹耦合动力学模型出发，引入柔性机翼准定常假设，建立大柔性飞行器非线性静气动弹性气动力方程，利用非线性迭代求解思路模拟了柔性飞行器的静气动弹性响应行为，开展了大展弦比飞机静气动弹性风洞试验验证，采用气动力有限基本解与机翼的耦合计算，发现了大柔性飞机大变形状态下载荷及结构变形形式随风速的变化规律.传统基于小变形假设的线性分析方法和刚体分析由于无法考虑气动面随结构变形的曲面气动力因素和结构变形后的非线性刚度特性，均与风洞试验存在一定的误差.对于大展弦比柔性飞机的非线性静气动弹性分析十分必要.      

Aeroelastic dynamic response and control of an airfoil section with control surface nonlinearities

Nonlinearities in aircraft mechanisms are inevitable, especially in the control system. It is necessary to investigate the effects of them on the dynamic response and control performance of aeroelastic system. In this paper, based on the state-dependent Riccati equation method, a state feedback suboptimal control law is derived for aeroelastic response and flutter suppression of a three degree-of-freedom typical airfoil section. With the control law designed, nonlinear effects of freeplay in the control surface and time delay between the control input and actuator are investigated by numerical approach. A cubic nonlinearity in pitch degree is adopted to prevent the aeroelastic responses from divergence when the flow velocity exceeds the critical flutter speed. For the system with a freeplay, the responses of both open- and closed-loop systems are determined with Runge-Kutta algorithm in conjunction with Henon’s method. This method is used to locate the switching points accurately and efficiently as the system moves from one subdomain into another. The simulation results show that the freeplay leads to a forward phase response and a slight increase of flutter speed of the closed-loop system. The effect of freeplay on the aeroelastic response decreases as the flow velocity increases. The time delay between the control input and actuator may impair control performance and cause high-frequency motion and quasi-periodic vibration.     

风力机翼型气弹响应的风洞模拟实验研究

非定常气弹设计是叶片大型化设计的瓶颈技术,开展叶片气弹响应实验研究具有重要的科学意义和较高的挑战性.本文提出一种气弹相似准则,搭建了模拟三维叶片弯扭耦合气弹响应的翼型俯仰沉浮二自由度风洞气弹实验平台,分析了安攻角和结构刚度对气弹稳定性和振荡形态的影响规律.研究发现了4类不同的气弹响应类型,增大刚度和安装角可以在一定程度...     

Stochastic nonlinear aeroelastic analysis of a supersonic lifting surface using an adaptive spectral method

An adaptive stochastic spectral projection method is deployed for the uncertainty quantification in limit-cycle oscillations of an elastically mounted two-dimensional lifting surface in a supersonic flow field. Variabilities in the structural parameters are propagated in the aeroelastic system which accounts for nonlinear restoring force and moment by means of hardening cubic springs. The physical nonlinearities promote sharp and sudden flutter onset for small change of the reduced velocity. In a stochastic context, this behavior translates to steep solution gradients developing in the parametric space. A remedy is to expand the stochastic response of the airfoil on a piecewise generalized polynomial chaos basis. Accurate approximation andaffordable computational costs are obtained using sensitivity-based adaptivity for various types of supersonic stochastic responses depending on the selected values of the Mach number on the bifurcation map. Sensitivity analysis via Sobol' indices shows how the probability density function of the peak pitch amplitude responds to combined uncertainties: e.g. the elastic axis location, torsional stiffness and flap angle. We believe that this work demonstrates the capability and flexibility of the approach for more reliable predictions of realistic aeroelastic systems subject to a moderate number of uncertainties.     

Moiré interferometric fringe patterns about crack tips: Experimental observations and numerical simulation

The local deformation about fatigue cracks has been investigated by the coherent optics method of moiré interferometry. The complexity of the interference fringe patterns motivated the parallel development of companion numerical models for simulating moiré interferometric response for known boundary conditions. Experimental patterns are here examined in the light of computer-generated fringe systems for a stationary crack in elastic as well as elastic-plastic solids. Various effects due to material plasticity, specimen-dependent non-singular stress, and mixed mode loading are identified in the fringe patterns.     

Numerical study on the correlation of transonic single-degree-of-freedom flutter and buffet

Transonic single-degree-of-freedom(SDOF) flutter and transonic buffet are the typical and complex aeroelastic phenomena in the transonic flow. In this study, transonic aeroelastic issues of an elastic airfoil are investigated using Unsteady Reynolds-Averaged Navier-Stokes(URANS) equations. The airfoil is free to vibrate in SDOF of pitching. It is found that, the coupling system may be unstable and SDOF self-excited pitching oscillations occur in pre-buffet flow condition, where the free-stream angle of attack(AOA) is lower than the buffet onset of a stationary airfoil. In the theory of classical aeroelasticity, this unstable phenomenon is defined as flutter. However, this transonic SDOF flutter is closely related to transonic buffet(unstable aerodynamic models) due to the following reasons. Firstly, the SDOF flutter occurs only when the free-stream AOA of the spring suspended airfoil is slightly lower than that of buffet onset, and the ratio of the structural characteristic frequency to the buffet frequency is within a limited range. Secondly, the response characteristics show a high correlation between the SDOF flutter and buffet. A similar "lock-in" phenomenon exists, when the coupling frequency follows the structural characteristic frequency. Finally, there is no sudden change of the response characteristics in the vicinity of buffet onset, that is, the curve of response amplitude with the free-stream AOA is nearly smooth. Therefore, transonic SDOF flutter is often interwoven with transonic buffet and shows some complex characteristics of response, which is different from the traditional flutter.     

声门下共鸣的谱规整用于非特定人的语音识别

提出在参数的提取过程中用不同的感知规整因子对不同人的参数归一化,从而实现在非特定人语音识别中对不同人的归一化处理。感知规整因子是基于声门上和声门下之间耦合作用产生声门下共鸣频率来估算的,与采用声道第三共振峰作为基准频率的方法比较,它能较多的滤除语义信息的影响,更好地体现说话人的个性特征。本文提取抗噪性能优于Mel倒谱参数的感知最小方差无失真参数作为识别特征,语音模型用经典的隐马尔可夫模型(HMM)。实验证明,本文方法与传统的语音识别参数和用声道第三共振峰进行谱规整的方法相比,在干净语音中单词错误识别率分别下降了4%和3%,在噪声环境下分别下降了9%和5%,有效地改善了非特定人语音识别系统的性能。      

Chaos and chaotic transients in an aeroelastic system

Chaotic motions of a two dimensional airfoil with coupled structural nonlinearities, both in pitch as well as plunge degrees of freedom, are investigated via a numerical integration method. The original system of coupled integro-differential equations governing the motion of the present aeroelastic model is transformed into a simple system of six ordinary differential equations (ODEs), rather than the previously frequently used eight ODEs. Complex dynamical behaviors are revealed and identified through the means of bifurcation diagrams, the phase portraits, the amplitude spectra and the Poincare maps. Besides, a more quantitative method, namely that of observing the evolution of the largest Lyapunov exponent (LLE) is also applied to diagnose the motions. Two peculiar phenomena, namely, long (perhaps super-persistent) chaotic transients, and fluctuating Lyapunov exponents, are observed; in the two such cases the LLE method fails to work. In addition, the effects of various system parameters, namely, the position of the elastic axis, the frequency ratio, the airfoil/air mass ratio, the viscous damping ratios, and the location of the center of mass, on the response of the aeroelastic system, are investigated.     

基于CFD/CSD的舵面控制气动弹性数值模拟方法

在动态网格上通过耦合求解流动控制方程和结构动力学方程, 发展了一种舵面控制下飞行器运动响应过程中气动弹性数值模拟研究方法.流动控制方程采用N-S方程, 结构动力学采用线性模态叠加方法, 其中流动控制方程空间离散采用基于非结构网格的有限体积方法, 对流通量采用计算HLLC格式, 非定常时间离散采用基于LU-SGS的双时间步长方法.模拟中, 气动运动和结构变形在双时间步长方法推进过程中采用改进松耦合方法, 气动网格与结构网格之间信息交换采用无限平板样条法实现, 飞行器的运动和变形采用基于重叠网格和Delaunay图映射变形网格相结合的方法进行处理.采用多个考核算例对发展的数值方法进行考核验证, 结果表明该方法可以高效精确模拟舵面开环控制下飞行器运动响应过程中的气动弹性特性.      

Uncertainty analysis near bifurcation of an aeroelastic system

Variations in structural and aerodynamic nonlinearities on the dynamic behavior of an aeroelastic system are investigated. The aeroelastic system consists of a rigid airfoil that is supported by nonlinear springs in the pitch and plunge directions and subjected to nonlinear aerodynamic loads. We follow two approaches to determine the effects of variations in the linear and nonlinear plunge and pitch stiffness coefficients of this aeroelastic system on its stability near the bifurcation. The first approach is based on implementation of intrusive polynomial chaos expansion (PCE) on the governing equations, yielding a set of nonlinear coupled ordinary differential equations that are numerically solved. The results show that this approach is capable of determining sensitivity of the flutter speed to variations in the linear pitch stiffness coefficient. On the other hand, it fails to predict changes in the type of the instability associated with randomness in the cubic stiffness coefficient. In the second approach, the normal form is used to investigate the flutter (Hopf bifurcation) boundary that occurs as the freestream velocity is increased and to analytically predict the amplitude and frequency of the ensuing LCO. The results show that this mathematical approach provides detailed aspects of the effects of the different system nonlinearities on its dynamic behavior. Furthermore, this approach could be effectively used to perform sensitivity analysis of the system's response to variations in its parameters.     

A COUPLED FLUID-STRUCTURE ANALYSIS FOR 3-D INVISCID FLUTTER OF IV STANDARD CONFIGURATION

A three-dimensional non-linear time-marching method and numerical analysis for aeroelastic behaviour of an oscillating blade row is presented. The approach is based on the solution of the coupled fluid-structure problem in which the aerodynamic and structural equations are integrated simultaneously in time. In this formulation of a coupled problem, the interblade phase angle at which a stability (or instability) would occur is a part of the solution. The ideal gas flow through multiple interblade passage (with periodicity on the whole annulus) is described by the unsteady Euler equations in the form of conservative laws, which are integrated by use of the explicit monotonic second order accurate Godunov-Kolgan volume scheme and a moving hybrid H-H (or H-O) grid. The structure analysis uses the modal approach and 3-D finite element model of the blade. The blade motion is assumed to be a linear combination of modes shapes with the modal coefficients depending on time. The influence of the natural frequencies on the aerodynamic coefficient and aeroelastic coupled oscillations for the Fourth Standard Configuration is shown. The stability (instability) areas for the modes are obtained. It has been shown that interaction between modes plays an important role in the aeroelastic blade response. This interaction has an essentially non-linear character and leads to blade limit cycle oscillations.     

NON-LINEAR AEROELASTIC ANALYSIS USING THE POINT TRANSFORMATION METHOD, PART 2: HYSTERESIS MODEL

This paper investigates the dynamic response of a two-dimensional aeroelastic system with structural non-linearity represented by hysteresis. The formulations of the point transformation method developed in Part 1 of this study for the aeroelastic system with a freeplay model is extended for a hysteresis model. These formulations can be applied not only to predict the amplitude and frequency of limit cycle oscillations, but also to detect complex aeroelastic responses such as periodic motion with harmonics, period doubling, chaotic motion and the coexistence of stable limit cycles. It is shown that the point transformation technique is the most suitable to analyze the aeroelastic response of systems containing piecewise continuous restoring forces.     

Analysis of CCD moiré pattern for micro-range measurements using the wavelet transform

A new approach based on the moiré theory and wavelet transform (WT) is proposed for measuring the micro-range distance between a charge-couple-device (CCD) camera and a two-dimensional reference grating. The micro-range distance is determined by measuring the pitch of the moiré pattern image, which is digitized by a CCD camera. A one-dimensional WT algorithm is applied to estimate the pitch of the moiré pattern. Experimental results prove that this technique is very efficient and highly accurate. The moiré range finder is an economic technique for measuring a micro-range distance.     

Transverse galloping of two-dimensional bodies having a rhombic cross-section

Transverse galloping is a type of aeroelastic instability characterized by oscillations perpendicular to wind direction, large amplitude and low frequency, which appears in some elastic two-dimensional bluff bodies when they are subjected to an incident flow, provided that the flow velocity exceeds a threshold critical value. Understanding the galloping phenomenon of different cross-sectional geometries is important in a number of engineering applications: for energy harvesting applications the interest relies on strongly unstable configurations but in other cases the purpose is to avoid this type of aeroelastic phenomenon. In this paper the aim is to analyze the transverse galloping behavior of rhombic bodies to understand, on the one hand, the dependence of the instability with a geometrical parameter such as the relative thickness and, on the other hand, why this cross-section shape, that is generally unstable, shows a small range of relative thickness values where it is stable. Particularly, the non-galloping rhombus-shaped prism’s behavior is revised through wind tunnel experiments. The bodies are allowed to freely move perpendicularly to the incoming flow and the amplitude of movement and pressure distributions on the surfaces is measured.     

Variations on the warped deformed conifold

The warped deformed conifold background of type IIB theory is dual to the cascading SU(M(p+1))×SU(Mp) gauge theory. We show that this background realizes the (super-)Goldstone mechanism where the U(1) baryon number symmetry is broken by expectation values of baryonic operators. The resulting massless pseudo-scalar and scalar glueballs are identified in the supergravity spectrum. A D-string is then dual to a global string in the gauge theory. Upon compactification, the Goldstone mechanism turns into the Higgs mechanism, and the global strings turn into ANO strings. To cite this article: S.S. Gubser et al., C. R. Physique 5 (2004).

Résumé

La configuration de fond pour la théorie de type IIB donnée par le conifold voilé déformé est duale à la cascade de théorie de jauge SU(M(p+1))×SU(Mp). Nous montrons que cette configuration donne une réalisation du mécanisme de (super-)Goldstone où la symètrie baryonique U(1) est brisée par la valeur moyenne dans le vide des opérateurs baryoniques. Les boules de glue pseudo-scalaires et scalaires de masse nulle résultantes sont identifiées dans le spectre de supegravité. Une D-corde est alors duale à une corde globale dans la théorie de jauge. Après compactification, le mécanisme de Goldstone devient un mécanisme de Higgs, et une corde globale devient une corde ANO. Pour citer cet article : S.S. Gubser et al., C. R. Physique 5 (2004).     

气动弹性能量采集系统空气动力建模研究综述

气动弹性能量采集旨在将结构气动弹性振动机械能转化为可利用的电能, 近年来引起了国内外学者的关注.在气动弹性能量采集系统理论建模的过程中, 空气动力建模至关重要, 显著影响系统的动力学响应和能量输出分析结果.文章针对当前各类气动弹性能量采集系统的气动建模,对其研究现状进行了综述.首先介绍气动弹性能量采集的研究背景; 随后, 分别针对基于翼段非流线体平板和机翼结构气动弹性振动的能量采集系统, 对相关气动模型进行了总结和讨论; 最后, 结合现有气动建模的待完善之处,给出了未来可能的发展方向.      

Passive control of aeroelastic instability in a long span bridge model prone to coupled flutter using targeted energy transfer

In this paper we study a problem of passive nonlinear targeted energy transfer between a two degrees of freedom long span bridge model prone to coupled flutter and a single degree of freedom nonlinear energy sink (NES). This study is mainly analytical and use complexification methods, multiple scales expansions and exploits also the concept of limiting phase trajectories (LPTs). The system is studied under 1:1:1 nonlinear resonance involved in targeted energy transfer mechanisms. Several behaviors that suppress aeroelastic instability are identified. We show that analytical calculations permit to design a NES able to efficiently control the aeroelastic instability of the bridge. Numerical simulations are performed and good agreement with analytical predictions is observed. It results that the concept of limiting phase trajectories (LPT) allows formulating adequately the problem of intensive energy transfer from a bridge to a nonlinear energy sink.     

AN INVESTIGATION OF STABILITY IN THE LARGE BEHAVIOUR OF A CONTROL SURFACE WITH STRUCTURAL NON-LINEARITIES IN SUPERSONIC FLOW

It is well known that the presence of non-linearities may significantly affect the aeroelastic response of an aerospace vehicle structure. In this paper, the aeroelastic behaviour at high Mach numbers of an all-moving control surface with a non-linearity in the root support is investigated. Very often, a stable equilibrium point, corresponding to zero displacement of the structure, together with an unstable limit cycle arising from a sub-critical Hopf bifurcation results from the presence of the non-linearity. The stable equilibrium point will then possess a domain of attraction. In this paper, this situation is investigated by first applying the averaging method to obtain a new set of aeroelastic equations in which the limit cycle is replaced by an unstable equilibrium point. A fourth order power series approximation to the stable manifold in the neighbourhood of this equilibrium point is then determined. From the stable manifold, predictions of the domain of attraction of the stable equilibrium point may then be made. The method is applied to two examples in which the non-linearity in the root support was due to either a cubic hardening restoring moment or the presence of freeplay. The approximation to the stable manifold was sufficient to enable significant information about the domain of attraction of the stable equilibrium point of the control surface to be obtained; agreement with predictions from numerical integration of the aeroelastic equations in the time domain was shown to be generally good in the cases considered, though outside the region of validity of the stable manifold expansion, discrepancies will occur. The averaging method was shown to be sufficiently accurate for this analysis even when the non-linearities could not be considered as weak.