Analysis and Flexible Structural Modeling for Oscillating Wing Utilizing Aeroelasticity

Making use of modal characteristics of the natural vibration of flexible structure to design the oscillating wing aircraft is proposed. A series of equations concerning the oscillating wing of flexible structures are derived. The kinetic equation for aerodynamic force coupled with elastic movement is set up, and relevant formulae are derived. The unsteady aerodynamic one in that formulae is revised. The design principle, design process and range of application of such oscillating wing analytical method are elaborated. A flexible structural oscillating wing model is set up, and relevant time response analysis and frequency response analysis are conducted. The analytical results indicate that adopting the new-type driving way for the oscillating wing will not have flutter problems and will be able to produce propulsive force. Furthermore, it will consume much less power than the fixed wing for generating the same lift.

Control-Oriented Modeling and Simulation on Rigid-Aeroelasticity Coupling for Hypersonic Vehicle

Since the subsystems of aerodynamics,propulsion,structure and so on in hypersonic vehicles involve characteristics of nonlinearity,strong coupling and uncertainty,and typical hypersonic vehicles adopt slender-body and wave-rider layout with widely-used lightweight materials,the accuracy of the modeling with a conventional rigid-body assumption is challenged.Therefore,a nonlinear mathematical longitudinal model of a hypersonic vehicle is established with its geometry provided to estimate aerodynamic force and thrust using hypersonic aerodynamics and quasi-one-dimensional flow with heat added and capture vehicle aeroelasticity using a single free-free Bernoulli-Euler beam model.Then the static and dynamic properties of the rigid and rigid-aeroelasticity coupling model are compared via theoretical analysis and numerical simulation under the given flight condition.Finally,a LQR controller for rigid model is designed and the comparable results are obtained to explain the aerolasticity influence on the control effect.The simulation results show that the aeroelasticity mode of slender-body hypersonic vehicles affects short period mode significantly and it cannot be simply neglected.

Effects of static aeroelasticity on composite wing characteristics under different flight attitudes

Composite wing static aeroelasticity was analyzed through a loosely coupled method and the effects on composite wing characteristics under different flight attitudes were presented. Structural analysis and aerodynamic analysis were carried out through finite element method (FEM) software NASTRAN and computational fluid dynamics (CFD) software FLUENT, respectively. Correlative data transfer and mesh regenerate procedure were applied to couple the results of computational structure dynamics (CSD) and CFD. After static aeroelasticity analysis under different flight attitudes, it can be seen that lift increases with the increase of flight speed and the incremental value enlarges gradually in both rigid and elastic wings. Lift presents a linear increment relationship with the increase of attack angle when the flight speed is 0.4Ma or 0.6Ma, but nonlinear increment in elastic wing when flight speed is 0.8Ma. On the effect of aeroelasticity, the maximum of deformation increases with the increase of flight speed and attack angle, and the incremental value decreases with the increase of flight speed while uniform with different attack angles. The results provide a reference for engineering applications.

Recent Progress on Aeroelasticity of High-Performance Morphing UAVs

The high-performance morphing aircraft has become a research focus all over the world.The morphing aircraft,unlike regular unmanned aerial vehicles(UAVs),has more complicated aerodynamic characteristics,making itmore difficultto conduct its design,model analysis,and experimentation.This paper reviews the recent process and the current status of aeroelastic issues,numerical simulations,and wind tunnel test of morphing aircrafts.The evaluation of aerodynamic characteristics,mechanism,and relevant unsteady dynamic aerodynamicmodeling throughout the morphing process are the primary technological bottlenecks formorphing aircrafts.The unstable aerodynamic forces have a significant impact on the aircraft handling characteristics,control law design,and flight safety.In the past,the structural analysis of morphing aircrafts,flight dynamics modeling,computational mesh morphing technology,and aerodynamic calculation were performed in promoting the development of next generation UAVs,with nonlinear dynamic challenges includingtransonic aeroelastic problems and high angle of attack aeroelastic problems.At present,many facets of these difficulties,together with the accompanying numerical simulation studies,remain under-explored.In addition,wind tunnel experiments face significant challenges in the dynamic morphing process.Finally,dynamic unsteady aerodynamic characteristics in the continuous morphing process still need to be verified by more related experiments.

Model Order Reduction of Complex Airframes Using Component Mode Synthesis for Dynamic Aeroelasticity Load Analysis

Airframe structural optimization at different design stages results in new mass and stiffness distributions which modify the critical design loads envelop. Determination of aircraft critical loads is an extensive analysis procedure which involves simulating the aircraft at thousands of load cases as defmed in the certification requirements. It is computationally prohibitive to use a GFEM （Global Finite Element Model） for the load analysis, hence reduced order structural models are required which closely represent the dynamic characteristics of the GFEM. This paper presents the implementation of CMS （Component Mode Synthesis） method for the generation of high fidelity ROM （Reduced Order Model） of complex airframes. Here, sub-structuring technique is used to divide the complex higher order airframe dynamical system into a set of subsystems. Each subsystem is reduced to fewer degrees of freedom using matrix projection onto a carefully chosen reduced order basis subspace. The reduced structural matrices are assembled for all the subsystems through interface coupling and the dynamic response of the total system is solved. The CMS method is employed to develop the ROM of a Bombardier Aerospace business jet which is coupled with aerodynamic model for dynamic aeroelasticity loads analysis under gust turbulence. Another set of dynamic aeroelastic loads is also generated employing a stick model of same aircraft. Stick model is the reduced order modelling methodology commonly used in the aerospace industry based on stiffness generation by unitary loading application. The extracted aeroelastic loads from both models are compared against those generated employing the GFEM. Critical loads modal participation factors and modal characteristics of the different ROMs are investigated and compared against those of the GFEM. Results obtained show that the ROM generated using Craig Bampton CMS reduction process has a superior dynamic characteristics compared to the stick model.

Review of Proper Orthogonal Decomposition Method Applied to Computational Aeroelasticity

Over the recent years there has been an increased trend in the use of Reduced Order Models （ROM） for modeling the coupled aeroelastic system. Of all the ROM models, the Proper Orthogonal Decomposition Method （POD） has been the most widely used, reason being the relative simplicity of implementation and the physical insight that it offers towards the physical problem. In this paper we begin by briefly recalling the recent work using POD for the computational aeroelasticity followed by the mathematical formulation. Mathematical formulation is important as it provides understanding of how POD method works. Implementation issues related to the POD method are presented next. Since POD is an empirical technique therefore, it is marred by the robustness issues as is the case with all the ROMs. In the end the variations of POD method, developed over the years are presented along with the most recent trend of using hybrid ROM.

Static aeroelasticity analysis of a rotor blade using a Gauss-Seidel fluid-structure interaction method

The present study introduces a Gauss-Seidel fluid-structure interaction(FSI)method including the flow solver,structural statics solver and a fast data transfer technique,for the research of structural deformation and flow field variation of rotor blades under the combined influence of steady aerodynamic and centrifugal forces.The FSI method is illustrated and validated by the static aeroelasticity analysis of a transonic compressor rotor blade,NASA Rotor 37.An improved local interpolation with data reduction(LIWDR)algorithm is introduced for fast data transfer on the fluid-solid interface of blade.The results of FSI calculation of NASA Rotor 37 show that when compared with the radial basis function(RBF)based interpolation algorithm,LIWDR meets the interpolation accuracy requirements,while the calculation cost can be greatly improved.The data transmission time is only about 1%of that of RBF.Moreover,the iteration step of steady flow computation within one single FSI has little impact on the converged aerodynamic and structural results.The aerodynamic load-caused deformation accounts for nearly 50%of the total.The effects of blade deformation on the variations of aerodynamic performance are given,demonstrating that when static aeroelasticity is taken into account,the choke mass flow rate increases and the peak adiabatic efficiency slightly decreases.The impact mechanisms on performance variations are presented in detail.

Static aeroelasticity of the propulsion system of ion propulsion unmanned aerial vehicles

“Ionic wind”generators are used as the main propulsion system in ion propulsion unmanned aerial vehicles(UAVs).Owing to the large size and poor stiffness of the electrode array in the propulsion system,the electrode array is prone to deformation under the flight load.In this work,the thrust characteristics and static aeroelastic properties of“ionic wind”propulsion systems were analyzed in detail.The simulation model for an“ionic wind”propulsion system was established by coupling a two-dimensional gas discharge model with a gas dynamics model.The influences of electrode voltage,spacing,size,and shape on the performance of the propulsion system were investigated.The fluid-solid interaction method was used to solve static aeroelastic characteristics under deformation.The aerodynamic and thrust performances of the elastic state and the rigid state were compared.It was found that the operating voltage,the distance between two electrodes,and the emitter radius had greater impacts on the thrust of the propulsion system.The propulsion system had a small contribution to the lift but a large contribution to the drag.In the elastic state,the lift coefficient accounted for 12.2%,and the drag coefficient accounted for 25.8%.Under the action of the downwash airflow from the wing,the propulsion system formed an upward moment around the center of mass,which contributed greatly to the pitching moment derivative of the whole aircraft.In the elastic state,the pitching moment derivative accounted for 29.7%.After elastic deformation,the thrust action point moved upward by 28.7 mm.Hence,the no lift pitching moment is reduced by 0.104 N$m,and the pitching moment coefficient is reduced by 0.014,causing a great impact on the longitudinal trimming of the whole aircraft.

Time-Domain Analysis of Body Freedom Flutter Based on 6DOF Equation

The reduced weight and improved efficiency of modern aeronautical structures result in a decreasing separation of frequency ranges of rigid and elastic modes.Particularly,a high-aspect-ratio flexible flying wing is prone to body freedomflutter(BFF),which is a result of coupling of the rigid body short-periodmodewith 1st wing bendingmode.Accurate prediction of the BFF characteristics is helpful to reflect the attitude changes of the vehicle intuitively and design the active flutter suppression control law.Instead of using the rigid body mode,this work simulates the rigid bodymotion of the model by using the six-degree-of-freedom(6DOF)equation.A dynamicmesh generation strategy particularly suitable for BFF simulation of free flying aircraft is developed.An accurate Computational Fluid Dynamics/Computational Structural Dynamics/six-degree-of-freedom equation(CFD/CSD/6DOF)-based BFF prediction method is proposed.Firstly,the time-domain CFD/CSD method is used to calculate the static equilibrium state of the model.Based on this state,the CFD/CSD/6DOF equation is solved in time domain to evaluate the structural response of themodel.Then combinedwith the variable stiffnessmethod,the critical flutter point of the model is obtained.This method is applied to the BFF calculation of a flyingwing model.The calculation results of the BFF characteristics of the model agree well with those fromthe modalmethod andNastran software.Finally,the method is used to analyze the influence factors of BFF.The analysis results show that the flutter speed can be improved by either releasing plunge constraint or moving the center ofmass forward or increasing the pitch inertia.

Computational methods and engineering applications of static/dynamic aeroelasticity based on CFD/CSD coupling solution

The CFD/CSD coupling method is turning into the main research direction for the static/dynamic aeroelastic analyses. If one wants to use the method for the complex engineering aeroelastic problems, he needs to investigate the relative aeroelasfic algorithms, such as the numerical computational method of unsteady aerodynamic forces, equivalent low-dimensional structural fi- nite element model and the solution method of structural dynamic equations, data transfer technique between fluid and structure, the moving grid method, etc. Besides, he also needs to improve the computational efficiency by such as massive parallel CFD algorithm, reduced-order model （ROM） of unsteady aerodynamic forces, etc. In this paper, based on the authors＇ recent investigations, the research progresses in computational aeroelastic methods and their applications to engineering problem are summarized.

Nonlinear metamaterial enabled aeroelastic vibration reduction of a supersonic cantilever wing plate

The violent vibration of supersonic wings threatens aircraft safety.This paper proposes the strongly nonlinear acoustic metamaterial(NAM)method to mitigate aeroelastic vibration in supersonic wing plates.We employ the cantilever plate to simulate the practical behavior of a wing.An aeroelastic vibration model of the NAM cantilever plate is established based on the mode superposition method and a modified third-order piston theory.The aerodynamic properties are systematically studied using both the timedomain integration and frequency-domain harmonic balance methods.While presenting the flutter and post-flutter behaviors of the NAM wing,we emphasize more on the preflutter broadband vibration that is prevalent in aircraft.The results show that the NAM method can reduce the low-frequency and broadband pre-flutter steady vibration by 50%-90%,while the post-flutter vibration is reduced by over 95%,and the critical flutter velocity is also slightly delayed.As clarified,the significant reduction arises from the bandgap,chaotic band,and nonlinear resonances of the NAM plate.The reduction effect is robust across a broad range of parameters,with optimal performance achieved with only 10%attached mass.This work offers a novel approach for reducing aeroelastic vibration in aircraft,and it expands the study of nonlinear acoustic/elastic metamaterials.

CONCERNING A BASIC ASSUMPTION FOR AEROELASTICITY IN TURBOMACHINERY

One of the basic assumptions for aeroelasticity in turbomachinery that the interbladephase angle along a blade row is constant has been proved to be invalid by the fact that nei-ther dynamic stresses nor interblade phase angles are constant along a blade row when thestall flutter occurs. With this assumption abandoned, a new model and the correspondingnumerical method have been developed. Comparisons between calculations and measurementsshowed that the main cause which makes blade dynamic stresses unequal along a blade rowin the unstable aeroelastic process is inequable interblade phase angle distribution along theblade row.

Wing aeroelasticity analysis based on an integral boundary-layer method coupled with Euler solver

An interactive boundary-layer method, which solves the unsteady flow, is developed for aeroelastic computation in the time domain. The coupled method combines the Euler solver with the integral boundary-layer solver （Euler/BL） in a ＂semi-inverse＂ manner to compute flows with the inviscid and viscous interaction. Unsteady boundary conditions on moving surfaces are taken into account by utilizing the approximate small-perturbation method without moving the computational grids. The steady and unsteady flow calculations for the LANN wing are presented. The wing tip displacement of high Reynolds number aero-structural dynamics （HIRENASD） Project is simulated under different angles of attack. The flutter-boundary predictions for the AGARD 445.6 wing are provided. The results of the interactive boundary-layer method are compared with those of the Euler method and experimental data. The study shows that viscous effects are significant for these cases and the further data analysis confirms the validity and practicability of the coupled method.

Theoretic analysis and experiment on aeroelasticity of very flexible wing

A high-altitude long-endurance aircraft with high-aspect-ratio wing usually generates large deformation,which brings the geometric nonlinear aeroelastic problems.In recent decades,it has become a key focus of the international researchers of aeroelasticity.But some critical technologies are not developed systematically,such as aerodynamic calculation methods of the curved wing with deformation,moreover,there are few experimental validations of these technologies.In this paper,we established the steady aerodynamic calculating method of the curved wing with quite large deformation based on the extended lifting line method,and calculated the unsteady aerodynamics using the strip theory considering curved surface effects.Combining the structure geometrical nonlinear finite element method,we constructed a systematic analytic approach for the static aeroelasticity and flutter of very flexible wing,and further designed the ground vibration and wind tunnel test to verify this approach.Through the test and the theoretic results comparison,we concluded that the extended lifting line method has adaptable precision for the static aeroealsticity and the strip theory considering curved surface effects for flutter analysis can give exact critical speed and flutter mode when the dynamic stall does not happen.The work in this paper shows that the geometric nonlinear aeroelastic analytic approach for very flexible wing has very high efficiency and adaptable precision.It can be used in the engineering applications,especially the iterated design in preliminary stage.

Pressure-induced instability and its coupled aeroelasticity of inflated pillow

A floating air weapon system(such as airborne floating mines)plays an important role in modern air defense operations.This paper focuses on aeroelastic characteristics of airborne floating mine named inflated pillow.Firstly,the dynamic deployable process of the pillow and characteristics of the local instability of the edge are studied,and the evolution mechanism of wrinkles and kinks is analyzed.Secondly,in the cruising stage,the fluid-structural-thermal coupling analysis is performed on the pillow,and the aeroelastic characteristics are studied.Thirdly,the shapepreserving effect of the inflated pillow during the“negative pressure”slow landing stage is evaluated.It is found that when the wind velocity is higher,the pillow has a collapsed instability(surface extrusion and contact),and when the wind velocity is lower,snap-through instability occurs.Finally,for the collapsed instability,a carbon fiber skeleton is added to discrete the large global collapsed fold into small local folds,thus achieving shape-preserving effect of pillow.For snapthrough instability,the critical internal pressure and different shape evolution under different wind velocity are evaluated.Through the analysis of the mechanical mechanism and control of the structural morphological evolution,it provides theoretical guidance for the application of the curved shell structure in floating air weapon system.

Geometrically Nonlinear Flutter Analysis Based on CFD/CSD Methods and Wind Tunnel Experimental Verification

This study presents a high-speed geometrically nonlinear flutter analysis calculation method based on the highprecision computational fluid dynamics/computational structural dynamics methods.In the proposed method,the aerodynamic simulation was conducted based on computational fluid dynamics,and the structural model was established using the nonlinear finite element model and tangential stiffness matrix.First,the equilibrium position was obtained using the nonlinear static aeroelastic iteration.Second,the structural modal under a steady aerodynamic load was extracted.Finally,the generalized displacement time curve was obtained by coupling the unsteady aerodynamics and linearized structure motion equations.Moreover,if the flutter is not at a critical state,the incoming flow dynamic pressure needs to be changed,and the above steps must be repeated until the vibration amplitude are equal.Furthermore,the high-speed geometrically nonlinear flutter of the wing-body assemblymodel with a high-aspect ratio was investigated,and the correctness of the method was verified using high-speed wind tunnel experiments.The results showed that the geometric nonlinearity of the large deformation of the wing caused in-plane bending to become a key factor in flutter characteristics and significantly decreased the dynamic pressure and frequency of the nonlinear flutter compared to those of the linear flutter.

A New Approach for Aeroelastic Robust Stability Analysis

Air vehicles undergo variations in structural mass and stiffness because of fuel consumption and the failure of structural components, which might lead to serious influences on the aeroelastic characteristics. An approach for aeroelastic robust stability analysis taking into account the perturbations of structural mass and stiffness is developed. Applying the perturbation method and harmonic unsteady aerodynamic forces, the frequency-domain linear fractal transformation （LFT） representation of perturbed aeroelastic system is modeled. Then, the robust stability is analyzed by using the structured singular value ,u-method. The numerical results of a bi-spar wing show its effectiveness and low computational time in dealing with the robust problems with mass and stiffness perturbations. In engineering analysis for solving aeroelastic problems, the robust approach can be applied to flutter analysis for airplane with the fuel load variation and taking the damage conditions into consideration.

IMPROVED ALGORITHM FOR CFD/CSD COUPLED SYSTEM DESIGN AND CALCULATION

The data information transfer and time marching strategies between computational fluid dynamics （CFD） and computational structural dynamics （CSD） play crucial roles on the aeroelastic analysis in a time domain. An improved CFD/CSD coupled system is designed, including an interpolation method and an improved loosely coupled algorithm. The interpolation method based on boundary element method （BEM） is developed to transfer aerodynamic loads and structural displacements between CFD and CSD grid systems, it can be universally used in fluid structural interaction solution by keeping energy conservation. The improved loosely coupled algo-rithm is designed, thus it improves the computational accuracy and efficiency. The new interface is performed on the two-dimensional （2-D） extrapolation and the aeroelastie response of AGARD445.6 wing. Results show that the improved interface has a superior accuracy.

MULTI-BODY AEROELASTIC STABILITY ANALYSIS OF TILTROTOR AIRCRAFT IN HELICOPTER MODE

The muhi-body analysis of the aeroelastic stability of the tiltrotor aircraft is presented. Muhi-body dynamic differential equations are combined with the equations of the unsteady dynamic inflow model to establish the complete unsteadily aeroelastic coupling analytical model of the tiltrotor. The stability of the tiltrotor in the helicopter mode is analyzed aiming at a semi span soft-inplane tihrotor model with an elastic wing. Parametric effects of the lag stiffness of blades and the flight speed are analyzed. Numerical simulations demonstrate that the multibody analytical model can analyze the aeroelastic stability of the tiltrotor aircraft in the helicopter mode.

Flight Loads and Dynamics of Flexible Air Vehicles

Based on the equations of motion of flexible air vehicles includingrigid-body modes and elastic structural modes, and applying influence coefficients of linearaerodynamics, a set of equations are derived and a method is presented for analysis of flight loadsand dynamic characteristics. The problems in the fields of flight mechanics and aeroelasticity suchas static aeroelastic divergence, trim and deformation, aerodynamic loads distribution, flutter andflight dynamics can be solved by the procedure. An airplane with high aspect ratio wings isanalyzed, and the results show that the coupling between rigid -body modes and elastic modes isdistinct and should not be overlooked.