Body Freedom Flutter Research Articles

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

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

Wind tunnel experiments of bending-torsion and body-freedom flutter on flying wing unmanned aerial vehicles

Wind tunnel experiments are performed on a flying wing model to investigate the effects of key design parameters and their cross-interactions on the flutter speed and frequency for bending-torsion flutter (BTF) and body-freedom flutter (BFF). These design parameters include wing sweep angle, mass of tip weights, and location of weights along the wingspan. A slider and rail setup for BFF is designed to enable rigid-body pitching and plunging degrees-of-freedom, while a custom fixed clamp is used to perform the BTF experiments. BTF and BFF experiences different dominant modes while undergoing flutter, with the former's dominant mode being torsion and the latter being the rigid-body short-period mode. For BTF, flutter speeds increase as weights are moved towards the wingtip or increasing tip weights, which increases the inertia of the system to enhance stability. The effect is opposite for BFF as the movement of weights outboard or increase of tip weights result in a rearwards shift of the centre of gravity that destabilises the system. In general, a higher sweep angle leads to increased sensitivity of flutter speeds to changes in mass of tip weights or changes to spanwise location of the weights. The findings from this study provide insights to the design of flying wing unmanned aerial vehicles for increased stability margins.

An improved linear parameter-varying modeling, model order reduction, and control design process for flexible aircraft

This paper presents an improved process for the modeling, model order reduction (MOR), and control design of a flexible flying wing unmanned aerial vehicle based on the linear parameter-varying (LPV) technology. By applying the Lagrangian formulation and doublet lattice method, the aeroservoelastic (ASE) model of the flexible aircraft is first derived and then rewritten as an airspeed-dependent LPV system, which consists of rigid-body states, structural modes, aerodynamic states, etc. This leads to a high-order LPV model, and the stability of the system varies from stable to unstable when the speed of the aircraft exceeds the critical flutter speed. To facilitate the control design, an oblique projection-based MOR method is then adopted to reduce the order of the plant. Different from previous studies, the MOR method is improved to systematically generate a reduced-order LPV model with consistent states for both the stable and unstable dynamics parts. Finally, an output-feedback LPV controller is designed to simultaneously achieve the body freedom flutter suppression and longitudinal attitude control. Numerical simulation results show the effectiveness of the improved LPV-based ASE modeling, order reduction, and control design process for the flexible aircraft.

Aircraft Flutter and Aerodynamic Work

This paper is about an application of an energy approach to computational aeroelasticity. A frequency-domain calculation of aerodynamic work is presented in a form that has not been previously discussed. In large aeroelastic systems such as aircraft flutter models, the obtained expression allows us to quantify the roles played in flutter by the generalized coordinates, the phases between them, and the generalized aerodynamic forces. This is exemplified in a body-freedom flutter analysis of a flying-wing aircraft: the X-56A. Another interesting feature that is proposed is a diagram of the aerodynamic work as a function of airspeed. Such functions allow an observance of an evolution with the airspeed of the terms that are most reflective of the aeroelastic stability changes: for example, a phase between the two dominant modes. These diagrams can complement typical flutter trends in analysis documentation and aid in flutter suppression. The approach also permits a perspective on flutter as an interaction of aircraft surfaces rather than vibrational modes. Once a sensitivity of an aeroelastic eigenvalue to a surface area is measured with the presented approach, it can be used in the aircraft design to mitigate flutter and other undesirable aeroelastic responses associated with lightly damped eigenvalues. An illustration of this idea is provided. Finally, energy-based computations allow posing energy-efficient active flutter suppression problems. This has been presented before in the literature. Examples of this aspect are made here with aircraft models (for the first time, as far as the author knows).

The Development of a Flight Test Platform to Study the Body Freedom Flutter of BWB Flying Wings

A flight test platform is designed to conduct an experimental study on the body freedom flutter of a BWB flying wing, and a flight test is performed by using the proposed platform. A finite element model of structural dynamics is built, and unsteady aerodynamics and aeroelastic characteristics of the flying wing are analyzed by the doublet lattice method and g-method, respectively. Based on the foregoing analyses, a low-cost and low-risk flying-wing test platform is designed and manufactured. Then, the ground vibration test is implemented, and according to its results, the structural dynamics model is updated. The flight test campaign shows that the body freedom flutter occurs at low flight speed, which is consistent with the updated analytical result. Finally, an active flutter suppression controller is designed using a genetic algorithm for the developed flying wing for future tests, considering the gains and sensor location as design parameters. The open- and closed-loop analyses in time- and frequency-domain analyses demonstrate that the designed controller can improve the instability boundary of the closed-loop system effectively.

Verification of a Body Freedom Flutter Numerical Simulation Method Based on Main Influence Parameters

The body freedom flutter characteristics of an airfoil and a fly wing aircraft model were calculated based on a CFD method for the Navier–Stokes equations. Firstly, a rigid elastic coupling dynamic model of a two-dimensional airfoil with a free–free boundary condition was derived in an inertial frame and decoupled by rigid body mode and elastic mode. In the fluid–solid coupling method, the rigid body was trimmed by subtracting the generalized steady aerodynamic force from the structural dynamic equation. The flutter characteristics were predicted by the variable stiffness method at a fixed Mach number and flight altitude. Finally, validation of the predicted body freedom flutter characteristics was performed through a comparison of theoretical solutions based on a Theodorsen unsteady aerodynamic model for airfoil and experimental results for a fly wing aircraft model. The mechanism of the influence of the bending mode stiffness and the position of the center of gravity on the body freedom flutter characteristics were briefly analyzed.

Body-Freedom Flutter Suppression for a Flexible Flying-Wing Drone via Time-Delayed Control

This paper describes a novel time-delayed control scheme for suppressing the body-freedom flutter of a flexible flying-wing drone and verifies its robustness. The simple formulation and strong robustness of the proposed control scheme are of particular interest. The procedure of designing the proposed delayed controller includes the following three steps. First, the displacement and velocity signals from the wingtip are taken as the input signals to delayed feedback, and the ailerons are used as the control inputs. The proportional gain, derivative gain, and specific value of a time delay are taken as control parameters. Second, the proportional and derivative gains are determined by checking the stable region for various time delays. Finally, a single time delay is determined according to both the critical stability condition and the stability margins. The stability and robustness of the closed-loop system are analyzed in time domain and frequency domain. The numerical results demonstrate that the flutter boundary of the flexible flying-wing drone can be expanded by up to 35% while retaining strong robustness via the proposed delayed controller.

Sloshing reduced-order models for aeroelastic analyses of innovative aircraft configurations

The present paper introduces the sloshing effects on aeroelastic stability and response of flying wing configurations. Using reduced order model based on data provided by computational fluid dynamics data, the description of the slosh dynamics is introduced into an integrated modelling that accounts for both rigid and elastic behaviour of flexible aircraft. The fully unsteady aerodynamics, modelled in the frequency domain via doublet lattice method, is recast in time-domain state-space form through the rational function approximation. The reference aircraft is the Body Freedom Flutter equipped with a single tank of cylindrical geometry, partially filled with water, and located underneath the center of mass. The results of the stability and response analyses are compared with the frozen fluid case with the final aim of showing how the fluid movement affects the complete aircraft behaviour.

Robust active suppression for body-freedom flutter of a flying-wing unmanned aerial vehicle

Flying-wing unmanned aerial vehicles have received extensive attention over the past decade because of their excellent aerodynamic and stealth performance. However, the aeroelastic interaction problems among unsteady aerodynamics, flight dynamics, and structural dynamics, such as the body-freedom flutter, are still open. This paper presents the study of a robust control scheme for active body-freedom flutter suppression of a flexible flying-wing unmanned aerial vehicle. The control objective is to expand the boundary of body-freedom flutter and to enhance the control robustness to external unknown disturbance simultaneously. The paper begins with the modeling procedure of a parameter-varying aeroservoelastic plant for the design of control law. Then, it presents how to synthesize a robust controller so as to suppress the flutter instability for a wide flight range of dynamic pressures. Afterwards, the paper shows how to analyze the flutter stability of the closed-loop system and the robustness of the controller, respectively. The numerical results demonstrate that the proposed robust controller can not only expand the flutter boundary of the unmanned aerial vehicle by 30%, but also exhibit the strong robustness to external disturbance.

Investigation of Sloshing Effects on Flexible Aircraft Stability and Response

The present paper provides an investigation of the effects of linear slosh dynamics on aeroelastic stability and response of flying wing configuration. The proposal of this work is to use reduced order model based on the theory of the equivalent mechanical models for the description of the sloshing dynamics. This model is then introduced into an integrated modeling that accounts for both rigid and elastic behavior of flexible aircraft. The formulation also provides for fully unsteady aerodynamics modeled in the frequency domain via doublet lattice method and recast in time-domain state-space form by means of a rational function approximation. The case study consists of the so-called body freedom flutter research model equipped with a single tank, partially filled with water, located underneath the center of mass of the aircraft. The results spotlight that neglecting such sloshing effects considering the liquid as a frozen mass may overshadow possible instabilities, especially for mainly rigid-body dynamics.

LPV modeling and controller design for body freedom flutter suppression subject to actuator saturation

In recent years, the Active Flutter Suppression (AFS) employing Linear Parameter-Varying (LPV) framework has become a hot spot in the research field. Nevertheless, the flutter suppression technique is facing two severe challenges. On the one hand, due to the fatal risk of flight test near critical airspeed, it is hard to obtain the accurate mathematical model of the aeroelastic system from the testing data. On the other hand, saturation of the actuator may degrade the closed-loop performance, which was often neglected in the past work. To tackle these two problems, a new active controller design procedure is proposed to suppress flutter in this paper. Firstly, with the aid of LPV model order reduction method and State-space Model Interpolation of Local Estimates (SMILE) technique, a set of high-fidelity Linear Time-Invariant (LTI) models which are usually derived from flight tests at different subcritical airspeeds are reduced and interpolated to construct an LPV model of an aeroelastic system. And then, the unstable aeroelastic dynamics beyond critical airspeed are ‘predicted’ by extrapolating the resulting LPV model. Secondly, based on the control-oriented LPV model, an AFS controller in LPV framework which is composed of a nominal LPV controller and an LPV anti-windup compensator is designed to suppress the aeroelastic vibration and overcome the performance degradation caused by actuator saturation. Although the nominal LPV controller may have superior performance in linear simulation in which the saturation effect is ignored, the results of the numerical simulations show that the nominal LPV controller fails to suppress the Body Freedom Flutter (BFF) when encountering the actuator saturation. However, the LPV anti-windup compensator not only enhances the nominal controller’s performance but also helps the nominal controller to stabilize the unstable aeroelastic system when encountering serious actuator saturation.

Full-Span Flying Wing Wind Tunnel Test: A Body Freedom Flutter Study

Aiming at the experimental test of the body freedom flutter for modern high aspect ratio flexible flying wing, this paper conducts a body freedom flutter wind tunnel test on a full-span flying wing flutter model. The research content is summarized as follows: (1) The full-span finite element model and aeroelastic model of an unmanned aerial vehicle for body freedom flutter wind tunnel test are established, and the structural dynamics and flutter characteristics of this vehicle are obtained through theoretical analysis. (2) Based on the preliminary theoretical analysis results, the design and manufacturing of this vehicle are completed, and the structural dynamic characteristics of the vehicle are identified through ground vibration test. Finally, the theoretical analysis model is updated and the corresponding flutter characteristics are obtained. (3) A novel quasi-free flying suspension system capable of releasing pitch, plunge and yaw degrees of freedom is designed and implemented in the wind tunnel flutter test. The influence of the nose mass balance on the flutter results is explored. The study shows that: (1) The test vehicle can exhibit body freedom flutter at low airspeeds, and the obtained flutter speed and damping characteristics are favorable for conducting the body freedom flutter wind tunnel test. (2) The designed suspension system can effectively release the degrees of freedom of pitch, plunge, and yaw. The flutter speed measured in the wind tunnel test is 9.72 m/s, and the flutter frequency is 2.18 Hz, which agree well with the theoretical results (with flutter speed of 9.49 m/s and flutter frequency of 2.03 Hz). (3) With the increasing of the mass balance at the nose, critical speed of body freedom flutter rises up and the flutter frequency gradually decreases, which also agree well with corresponding theoretical results.

Modeling, Design, and Flight Testing of Three Flutter Controllers for a Flying-Wing Drone

Three flutter-suppression designs for a flexible flying-wing research drone are discussed, along with the modeling and flight-test results. The drone, with wing span of 10 feet, aspect ratio of almost 9, and control surfaces along the entire wing trailing edges, was developed for flight research into the modeling and control of highly elastic aircraft. The low-speed vehicle was designed to exhibit body-freedom flutter in its flight envelope. The all-important dynamic modeling of the vehicle, used for analysis and control design, is based on a mean-axis formulation and quasi-steady aerodynamics, with the nondimensional aerodynamic/aeroelastic coefficients updated from flight tests. Flutter-modeling results were found to agree with those from NASTRAN and flight tests. The three different flutter-suppression approaches include both fairly classical and multivariable methods, all fixed gains but with different architectures. The primary control-design objective was to augment the damping of the eventual flutter mode at a design condition below the open-loop flutter speed, for safety of flight, and to achieve a closed-loop flutter speed at least as high as the open-loop flutter speed. Analysis and flight tests revealed that all three designs achieved these design goals. In addition, two of these designs actually expanded the flutter boundary. The theoretical stability robustness of all three controllers at the design flight condition is quite good, but there are differences in controller complexity. Research is currently underway to further expand the flutter boundary using all three design approaches.

Research on the Influences of Inertial Properties on Body Freedom Flutter for an Airfoil

For some flying-wing aircraft with large aspect ratio, the pitching inertia is small, which makes the longitudinal short-period modal frequency higher. Structural flexibility makes the 1st bending mode frequency lower. This makes the pitching mode of rigid body easily coupled with the elastic mode, resulting in aeroelastic instability, which is called body freedom flutter. There are many factors affecting the body freedom flutter characteristics. The rigid body inertia and structural characteristics of the fuselage and wing all have an impact on it. Taking the flutter of an airfoil as an example, the structural dynamics model of the system is established. The flutter characteristics of the airfoil were solved by analytical method. The effects of pitching inertia and fuselage mass on the flutter speed, flutter frequency and flutter mode shape were studied.

Bilevel Programming Weight Minimization of Composite Flying-Wing Aircraft with Curvilinear Spars and Ribs

This paper studies weight minimization of a composite flying-wing aircraft using bioinspired arbitrarily shaped spars and ribs, known as SpaRibs, for the internal structural layout design. A generalized mathematical model is developed to parameterize the shape of SpaRibs using a four-node nonuniform rational basis spline curve. Additionally, for reducing weight, composite structures and lift redistribution using multiple control surfaces are considered. A stacking sequence table is used to parameterize the wing laminate configuration with ply drops for flexible wing design. For the optimization problem including topology as well as discrete and size design variables, a bilevel programming optimization is employed by using a previously developed parallel particle swarm optimization and a gradient-based optimization, respectively, for the upper- and lower-level optimization problems. The upper-level optimization problem is employed to satisfy such design requirements as the flutter constraints for achieving a specific body freedom flutter mode. The lower-level optimization is used to optimize the control surface rotations to minimize the wing root bending moment, which is considered to be a surrogate for wing weight. Different internal structural layouts and flutter constraints are studied for comparison. Optimization studies show that using SpaRibs for aircraft wing box internal structural layout design can reduce the wing weight by 21.8% as compared to the base model and by 7.3% as compared to the wing box with traditional straight spars and ribs. The additional specific flutter result constraints lead to a 4.2% increase in the wing weight for aircraft design with SpaRibs as compared to the one obtained only with the lower bound on the flutter speed.

Assessment of body-freedom flutter for an unmanned aerial vehicle

The flutter characteristic of a highly swept flying wing unmanned aerial vehicle (UAV) is studied for the DLR-F19 concept. The compact geometry, which is based on the SACCON configuration, raises the question whether a coupling between rigid body and elastic modes, known as “body-freedom flutter”, is relevant for this configuration to be a critical flutter phenomenon. The important modes contributing to the various flutter mechanisms are identified by means of the average power of the modal unsteady aerodynamics. Furthermore, aerodynamic methods based on linear potential flow theory (MSC.Nastran DLM and ZAERO ZONA6) and the Euler equations are used to assess the accuracy of fast aerodynamic methods for flutter point prediction of this particular configuration at a low transonic Mach number of 0.8. The BFF phenomenon is further examined by modifying the mass and stiffness distributions of the configuration.

Constructal Design of Aircraft: Flow of Stresses and Aeroelastic Stability

Body-freedom flutter characteristics of flying wing aircraft vary with engine placement. Here, we show why a certain design parameter (engine placement) influences the aeroelastic flight envelope of the aircraft. The approach is based on the constructal law and the principle that a design that avoids stress strangulations provides better access to the flows that inhabit the system. This is in sharp contrast with trial-and-error techniques such as optimization, which means to opt from among different choices, cases, and designs. Under the same flight condition, the flow of stresses through the aircraft wings is investigated for several configurations including those with maximum and minimum flutter speeds. The results reveal that when the stresses flow smoothly in the wings the stability of the aircraft improves. On the other hand, in the cases in which the engine location causes stress strangulation, the flutter speed decreases considerably. The most severe stress strangulation corresponds to the aircraft configuration with minimum flutter speed (i.e., engine placement at 20% span behind the reference line). The smoothest flow of stresses happens in the configuration with maximum flutter speed (i.e., engine placement at 80% span forward of the reference line).

Variations of flutter mechanism of a span-morphing wing involving rigid-body motions

The present paper aims to reveal the significance of rigid-body motions for the flutter mechanism of a span-morphing wing model. The inclusion of rigid-body motions into aeroelastic formulation and flutter analysis is presented. A state-space aeroelastic equation combining the dynamics of stepped Euler-Bernoulli beam with unsteady strip aerodynamic theory is developed by quasi-static modeling. Using a numerical example, variations of flutter mechanism from the bending-torsional flutter to the body-freedom flutter are observed as the span increases. In addition, effects of some dimensionless parameters on the variations of flutter mechanism are investigated. The investigated parameters belonging to the fuselage have limited influences on the bending-torsional flutter but a significant impact on the body-freedom flutter.

Study of Flexible Aircraft Body Freedom Flutter with Robustness Tools

Body freedom flutter is a dynamic instability featuring strong coupling between rigid-body and elastic modes of the aircraft. Flexible configurations with adverse structural and geometric properties have been found susceptible to this phenomenon. Features that complicate its study are the presence of multiple modal instabilities and the different influence that system parameters have on each of them. The robust analysis framework based on linear fractional transformation modeling and structured singular value analysis is used in this work to study the body freedom flutter problem in a systematic way. The analyses performed showcase the potential of these methods, not only in supplying a characterization of the system in terms of its robustness but also in gaining further understanding of the body freedom flutter problem and reconciling the results with physical features. It is also shown that the robust modeling analysis framework complements the conventional, state-of-practice methods while allowing the study of highly coupled systems (of which the flexible aircraft is an example) to be addressed in an incremental and methodological manner. For this study, a simplified wing model is augmented including the short-period approximation aircraft model and the rigid–elastic coupling terms. The proposed model captures properties and trends of both restrained wing flutter and body freedom flutter instabilities.

Gust response and body freedom flutter of a flying-wing aircraft with a passive gust alleviation device

The effectiveness of a passive gust alleviation device (PGAD) mounted at the wingtip of aircraft in conventional and flying-wing configurations have been studied in previous research. However the PGAD influence on the aeroelastic stability in particular the body freedom flutter (BFF) of a flying-wing aircraft remains as a concern. This present investigation is focused on evaluating the beneficial effect of PGAD on both gust load alleviation and BFF of a small flying-wing aircraft of high aspect ratio wing made of composite. A small range of (1-cos) type of gust load has been considered to select a representative critical gust load case for the study. A parametric study indicates that there is a narrow band of optimal key parameters for the PGAD design. Subsequently a set of optimal parameters is selected to further the analysis of the PGAD mechanism. The case study results show that the PGAD can make the bending moment at the wing root due to gust reduced by 16%. In addition, the BFF speed of the flying-wing aircraft is increased by 4.2%. The investigation reveals that the PGAD mode and its interaction with the wing bending mode and short period oscillation of the aircraft can have beneficial aeroelastic effect on both gust alleviation and flutter suppression.