In the past few decades, substantial work has been directed towards the design of aircraft structures that maximise fuel efficiency, improve performance and curtail emissions. Aeroelastic optimisation offers an effective way to devise lightweight and fuel efficient structures, with structural stability constraints often driving the design. To date, the aeroelastic optimisation community has relied mostly on linear buckling predictions for the evaluation of structural stability constraints, mainly because of their conservativeness, computational efficiency and simplicity of implementation. This approach typically leads to overly conservative buckling margins, and this over-conservativeness places a glass ceiling over the load carrying capacity of wing structures, consequently restricting the exploration of regions within the design space where considerable weight savings could be achieved. By contrast to previous works that predominantly rely on linear buckling constraints, the present paper introduces a method to incorporate nonlinear structural stability analysis into aeroelastic optimisations of wingbox-like structures. The method relies on the evaluation of the positive-definiteness of the tangent stiffness matrix, which is an indicator of structural stability. The sign of the stiffness eigenvalues is monitored while tracing the load-displacement equilibrium paths by means of the arc-length method, thus pinpointing the onset of instability. The proposed constraint is tested in a proof of concept structural optimisation of an idealised version of the CRM wingbox. This optimisation shows a $10.9{\rm{\% }} $ reduction in mass with respect to a baseline design that is optimal with a linear buckling approach, promising great potential for application to more realistic aeroelastic optimisations.

Highly flexible wings can experience complex aerodynamic phenomena, such as dynamic stall, which induce nonlinear forces and lead to instabilities or limit-cycle oscillations that are challenging to predict and mitigate. A low-order accurate and efficient numerical model is in demand to give near real-time on-site nonlinear aeroelastic prediction during the wind tunnel testing, to help ensure that suitable tests are safely conducted. For this purpose, reducing the states of either the aerodynamic or structural model is extremely important in lowering the computation cost for numerical continuation. This paper explores a low-order modeling approach to analyze dynamic stall and bifurcation behavior in highly flexible wings, with applications in the design and control of next-generation highly efficient air transport. In this paper, the low-order unsteady aerodynamic model is derived by reducing the order of the attached flow portion of the original Beddoes-Leishman model (BLM). The reduced set of governing equations is tailored to retain significant aerodynamic and structural couplings while minimizing computational overhead; the nonlinear beam shape (NBS) formulation is used to model the flexible wing structure. Numerical comparisons for a NACA 0012 airfoil show that the modified BLM with six states is close to matching the original BLM with twelve states when prescribed periodic motion is given. The caveat is that the model is useful in a relatively low-frequency range; however, this is considered to be enough to cover the frequency range of aerodynamic phenomena associated with limit cycle oscillations (LCOs) related to highly flexible wings. The numerical model is expected to quickly identify and predict parameter regimes where stable, unstable, and oscillatory behaviors emerge, enabling a deeper understanding of aerodynamic load variations and structural deformation patterns. To further validate the low-order aerodynamic model, the final version of the paper will incorporate open-sourced experimental data to assess the model's accuracy and evaluate the capability of the developed numerical tool to predict the nonlinear aeroelastic behavior of the high-aspect-ratio wing. This includes key features such as dynamic stall characteristics and post-stall behavior.

The ongoing quest for more efficient aircraft operations has led to several high aspect ratio wing concepts that may take flight in the next decade. A wing tends to become more flexible as the aspect ratio is increased, which results in the interaction between the wing structural response and aircraft flight dynamics, with an increased likelihood of nonlinear response of the wing structure and aerodynamics as well as an increase in the complexity of the aircraft systems that must be designed in the nonlinear domain. In this context, developing nonlinear numerical tools is crucial to predict the behaviour of this new generation of aircraft. This paper discusses the numerical and experimental work on a 2.4 m very flexible high aspect ratio wing, where the results of these tests can be used to validate nonlinear aeroelastic software. The wing was designed to exhibit specific nonlinear dynamic behaviour and does not represent any wing that would be used on an aircraft. Following a brief description of the experimental test model, three different numerical models are presented: two low-order aeroelastic models, one based on the multibody toolbox Simscape, one based on a low-order geometrical exact beam formulation and one model based on the industrial standard MSC Nastran software. The low-order models were used to carry out numerical continuation and bifurcation analysis to predict the unstable nonlinear behaviour of the wing and the onset of limit cycle oscillations. Ground Vibration Tests and static tests were carried out to update the numerical models. The wing model was tested in the Airbus' low-speed wind tunnel in Filton (UK). Experimental data were processed with the eigensystem realisation algorithm, and the Zimmerman flutter-margin criterion was applied to predict the flutter onset boundary. Results showed that the driving mode for the flutter onset is the first in-plane mode. The comparison between experimental and numerical data shows the ability of low-order models to capture the nonlinear effects and predict the reduction in the flutter onset speed as the angle of attack of the model is increased.

The paper summarizes the research activities and the results obtained in the framework of CS2 U-HARWARD EU project, focused on the high aspect ratio wing technologies.The project started May 2020 and finished October 31, 2023.Comprehensive numerical analysis was performed to explore the optimum design for three high aspect ratio wing aircraft configurations: cantilever wing, strut braced wing (SBW) and folding wingtips (FWT).Whereas the increased wingspan causes significant aircraft weight penalties, resulting in a compromised overall aircraft performance, the studies show that there is a "sweet spot" of an optimal AR where the performance (fuel burn or Breguet Range) is maximized and this point is greater than current designs.Further benefits can be achieved through the use of Gust Load Alleviation and Manouevre Load Alleviation.The U-HARWARD project also included four main experimental wind tunnel campaigns：i.An aero-acoustic model to investigate the combination of the strut and wing wakes in the generation of the airframe noise, ii.An aeroelastic model composed of a wing plus strut to investigate static aeroelastic and flutter characteristics, iii.An aerodynamic model of the complete SBW configuration to identify the low speed aerodynamic characteristics and related stability derivatives, and iv. a large aeroelastic half model with a wing equipped with a folding wingtip mechanism to explore the gust load alleviation characteristics.A summary of the results, as well as the most relevant lessons learned, are included.

Experimental data are presented for a cantilevered vertically vibrating beam supporting a tank partially filled with liquid, inside a vacuum chamber where the air pressure can be reduced. Results are presented with and without the tank and contained liquid, as well as under two different gas pressures (atmospheric and vacuum). When the liquid is absent from the tank, aerodynamic damping and added mass effects are quantified. When the tank is partially filled with liquid, the damping versus tank amplitude curves indicate differences that are mainly due to aerodynamic effects, with more noticeable effects in the 50% fill case. The results support the observation that at the density ratios presented here, two-phase liquid/ gas modelling may not be needed for the evaluation of net damping due to violent sloshing flows.

There has been a growing interest in utilizing flared folding wingtips as an in-flight load alleviation device to enable increased wing spans that meet airport gate limits but with little increase in wing weight. The semi-aeroelastic hinge (SAH) concept is implemented in high-aspect-ratio wings to enable wingtips to be released during severe load cases such as maneuvers and gusts to alleviate the bending moments while maintaining optimum aerodynamic shape for the rest of the flight. In this paper, scaling methods for wings incorporating the SAH are explored, allowing for the development of equivalent scaled unmanned aerial vehicles or wind tunnel models with similar aeroelastic behavior as full-size aircraft. Three scaling approaches are considered in this study, namely, Iso-Froude, Iso-Frequency, and Iso-Strain, where a set of governing nondimensional quantities and scaling factors are determined. Despite the significant nonlinearities resulting from large wingtip fold angles, it is shown that a linear scaling approach can be appropriate for such a wing configuration. Furthermore, the aeroelastic properties of each scaled model are compared to those of the full-scale model, where the best match was obtained from the Iso-Strain model, although it is challenging to meet the required operational conditions.

In this paper, the potential effectiveness of a nonlinear energy sink (NES) to absorb the energy from a wing that is vibrating as a result of flying in a gusty environment is investigated. The structural dynamics of the wing is simulated using a rigid airfoil mounted on two linear/nonlinear springs to represent the bending and torsional stiffness of the wing. The wing is subjected to a combination of gust and aerodynamic loads. The unsteady aerodynamic lift and moment are modelled using Wagner's theory. Furthermore, the gust loads are obtained by assuming two different gust profiles, e.g. sharp-edged and 1-cosine gust profiles. A nonlinear energy sink, which comprises of a concentrated mass, damper and a nonlinear spring, is attached to the wing, and its effectiveness to absorb the gust energy is investigated. The coupled nonlinear aeroelastic equations are integrated numerically to determine the response of the wing. To verify the developed aeroelastic model, the obtained results are compared with the available results in the literature and an excellent agreement is observed. The results highlight that adding the NES to the wing is capable of reducing the gust oscillation amplitude of the wing significantly when the NES parameters are chosen accordingly.

Smoothed particle hydrodynamics using artificial compressibility (ACSPH) is developed, with the inclusion of pressure smoothing terms. Theoretical links between pressure/velocity correction incompressible SPH and artificial compressibility are explored, illustrating that ACSPH may be considered an extension of, or closely related to, the δ-SPH method. An implicit dual-time integration procedure is used to enforce an incompressible solution at every time-step, removing acoustic effects arising from the common assumption of weak compressibility. An established weakly-compressible quasi-Lagrangian δ-SPH method is used for comparison against ACSPH, and a series of test cases show that ACSPH provides a similar solution cost to δ-SPH. However, the residual acoustic effects in δ-SPH are removed entirely in ACSPH, providing improved pressure prediction capabilities across all test cases, including intense fluid impacts. Improved modelling of fluid–structure-interaction cases and coupled energy dissipation are also recorded as a result of correctly capturing incompressible flow.

High aspect ratio wings promise greater aerodynamic efficiency with subsequent savings for airlines. However, these types of designs could be prone to unstable aeroelastic responses within the standard flight envelope, which may result from the reduction in the natural frequencies. This paper proposes a fully nonlinear low order aeroelastic framework able to predict the onset of any potential subcritical and supercritical limit cycle oscillations in very flexible wings, a critical tool required for the design of modern wings. Numerical continuation is used to detect unstable aeroelastic oscillations triggered by nonlinear geometrical effects, nonlinear aerodynamics or both. For this work, a 2-state aerodynamic model is used to predict the unsteady aerodynamic response of the model. Numerical results are verified and validated against wind tunnel data. The comparison shows a close match of the wing static response and the prediction of the flutter speed. The subject of this work is a very flexible wind tunnel model of 2.4 m span tested in 2018 in the 12 x 10 ft subsonic Airbus wind tunnel in Filton, which was part of the Agile Wing Integration (AWI) project. The model was specifically designed for the purposes of numerical code validation with certain dynamic characteristics and does not resemble any wing that would be used on an aircraft. It was equipped with accelerometers, strain gauges, pressure sensors and markers for video tracking to provide a complete picture of the onset of aeroelastic instabilities. The bifurcation analysis presents the equilibrium branches for the wing model in different configurations for different angles of attack and structural damping. Results show that the Hopf bifurcation velocity (flutter) strongly depends on the structural damping for the clean wing configuration, which also presents pitchfork-like behaviour at zero incidence due to the asymmetry in the inertia of the model.

This work proposes a deterministic updating of a scaled research wing demonstrator, implemented inside the study of Airbus-led Sloshing Wing Dynamics (SLOWD). Before updating, a variance-based global sensitivity analysis is carried out to identify the relevant parameter to update. The sensitivity method is then applied to the parameters selected in the first step to converge the model outputs on the experimental data. The results show that the dynamics of the system are mainly influenced by local stiffness inside the numerical model (joints), and the updated system showed a good agreement with the experimental data.

The variability in ground manoeuvre occurrences for aircraft landing gear is intrinsically linked to the airport geometries served by aircraft in-service and consequently, the cyclic loads that landing gear carry are driven by the route network and characteristics of aircraft operators. Currently, assumptions must be made when deriving fatigue load spectra for aircraft landing gear, which may fail to capture the operator characteristics, potentially leading to design conservatism. This paper presents the enhanced characterisation of ground turning manoeuvres within the Automatic Dependent Surveillance-Broadcast (ADS-B) trajectories for six narrow-body aircraft across a full-service carrier (FSC) and a low-cost carrier (LCC) fleet. The methodology presented within this paper employs ADS-B latitude and longitude information to overcome limitations of previous approaches, increasing the rate of correct manoeuvre identification within ADS-B trajectories to 77% of flights from the 50% rate achieved previously. When characterising the ground manoeuvres across 3,000 flights, significant differences in manoeuvre occurrences were observed between individual aircraft within the LCC fleet and between the FSC and LCC fleets. The occurrence of tight and pivot turns were shown to vary across the six aircraft with six and eight fatigue-critical turns being performed by the FSC and LCC fleet for every 10 flights performed. In addition, it was observed that the direction of fatigue critical turns is biased in specific directions, suggesting that individual main landing gear assemblies will accumulate fatigue damage at an increased rate, leading to greater justification for operator-specific spectra and structural health monitoring of aircraft landing gear.

Recent studies have shown that semi-aeroelastic hinge devices can enable larger aircraft wingspans. Such a device would be folded on the ground to meet airport width restrictions, locked during cruise for optimal aerodynamic performance, and released during maneuvers to alleviate flight loads. In contrast, this paper uses a wind tunnel experiment to study the aeroelastic behavior of floating wingtip fuel tanks. This device consists of a freely floating wingtip with an additional mass attached in the form of a liquid-filled fuel tank. The static aeroelastic results show that altering the fuel tank's filling level and position allows the wingtip to float at an optimal angle for aerodynamic efficiency across various angles of attack and fuel masses. Additionally, this paper shows that, with careful selection of the mass distribution of the wingtip, dynamic load alleviation comparable to the semi-aeroelastic hinge concept can be achieved during turbulence and one-minus-cosine encounters. Furthermore, the effect of fluid motion is shown to reduce incremental loads during random turbulence encounters by up to 10%; however, it has a negligible impact on the response to one-minus-cosine encounters. Such results are also confirmed by a numerical model incorporating a simple reduced-order fluid sloshing model.

In this paper, the effect of thrust vectoring of propulsors on the aeroelastic stability of an electric aircraft wing powered up with electric propulsors is investigated. The electric aircraft is composed of six high-lift and one cruise propulsors. The developed model resembles the NASA X-57 electric aircraft. It is assumed that the rotor disc of propulsors is able to be tilted in two directions (e.g. pitch and yaw) to change the thrust vector. Three aeroelastic models are developed and compared to verify the aeroelastic results. In the first method, the wing has been modelled using a linear beam combined with an unsteady compressible source and doublet panel method. In the second method, a linear beam and the 2D unsteady incompressible Theoderson theory are combined. While the third method is based on coupling a geometrically exact beam formulation with the 2D incompressible unsteady Peters' aerodynamic model. The comparison between these three methods results in a fairly good agreement with the unsteady source and doublet panel method predicting a slightly higher flutter speed than the other two methods. This could be due to the effects of tips that have not been included in the other two methods. Furthermore, the propulsors are modelled using a follower force that acts directly on the centre of gravity of it. It is highlighted that by vectoring the thrust it is possible to enhance the aeroelastic stability of the wing. But the amount of change is dependent on the pitch or yaw angle of thrust vector, thrust value and mass of the propulsors. Also, it is obtained that yawing the thrust has more effect on the stability of the wing than pitching the vector. Finally, the effect of wing bending to torsion stiffness ratio on the effectiveness of the proposed concept is investigated. It is observed that the thrust vectoring mechanism is more effective for higher stiffness ratios.

Flared folding wingtip (FFWT) devices have been shown to enable higher aspect ratios in future aircraft designs while meeting airport width restrictions and reducing the loads experienced by an airframe during gust encounters and manoeuvres. Studies have highlighted that including an additional control surface on the wingtip can augment the performance of such devices. This paper aims to explore the effect of freeplay on this additional control surface and, in particular, will explore how freeplay affects the stability of this nonlinear system. As such, this study presents the results of an experimental study with a semi-span wing incorporating an FFWT with an additional control surface. The results show that freeplay leads to the onset of small limit cycle oscillations (LCOs) well below the linear flutter speed of the original system. The introduction of freeplay is also shown to re-stabilise the model at higher velocities, and these effects are similar across a wide range of freeplay region sizes and flare angles.

This paper presents low Reynolds number experimental wind tunnel investigations of flexible high aspect ratio aircraft models with body pitch degree-of-freedom. The aim is to assess nonlinear dynamic interactions of highly flexible wings with aircraft dynamics. Two sets of wings, one designed to be highly flexible and the other to be near-rigid, were considered for comparison. The first test category involves the aircraft being trimmed for three lift cases of 20, 25, and 30N within a wind speed range of 18 to 30 m/s. The second category involves a trimmed pitch sweep ranging from -3.5 to 10.7 degrees at a single wind speed of 25 m/s. The aircraft mode frequencies and damping were identified experimentally using the Eigensystem Realization Algorithm on autocorrelated responses to random excitation of the model using gust vanes. Highly nonlinear trends in the short-period mode frequency and damping with respect to wind speed and pitch angle were observed, as well as differences between the wing design cases. A low-order geometrically-exact structural model was employed for numerical comparisons. Three aerodynamic models were considered: steady Vortex Lattice Method (VLM), steady 2-state Leishman, and unsteady 2-state Leishman aerodynamics. It was found that wing-to-tail influence captured by VLM aerodynamics is vital to accurately simulate the short-period mode and for its frequency magnitude to match with experiments. However, the local nonlinearity observed experimentally is not captured by any of the aerodynamic models considered. Introducing aerodynamic unsteadiness significantly reduces the damping of the short-period mode and has very minor impact on the wing-bending dominant mode. The trends in wing-bending mode were captured well by all aerodynamic models, with minor differences between them. In general, the short-period mode frequency increases with wind speed and decreases with pitch angle (for wings-up deflections). An increase in the magnitude of wing deflection results in an increase in wing-bending mode frequency and a decrease in damping. A reduction in wing stiffness or increase in flexibility reduces the frequency of the short-period mode. Increasing the magnitude of wing deflection also reduces the short-period mode frequency, which was observed to be more significant in experiments than in numerical results.

Recent studies have considered the use of wings incorporating flared folding wingtips (FFWTs) to enable higher aspect ratios (reducing overall induced drag) while also reducing gust loading and meeting airport operational requirements. This paper presents the first experimental research into the nonlinear dynamic behavior of a wing incorporating an FFWT. Wind-tunnel tests were conducted at a range of velocities below and beyond the linear flutter boundary. The experimental findings are compared with results obtained from continuation and bifurcation analyses on a representative low-fidelity numerical model. The results show that beyond the linear flutter boundary, stable limit cycle oscillations form, which is dependent on the flare angle, are bounded by either geometric or aerodynamic nonlinearities. Also presented is the effect of a wingtip trim tab on the stability boundary of a wing incorporating FFWTs. It is found that the tab angle can significantly alter the stability boundary of the system, indicating that the choice of camber is an important parameter when considering the stability boundary of FFWTs and that a moveable control surface on an FFWT could be used “in flight” to extend the stability boundary of an aircraft.

Aircraft like the Boeing 777-X use on-ground folding wingtips to meet the airport gate size restriction while increasing the aspect ratio during flight to reduce induced drag. A recent concept of aircraft design is to utilise in-flight floating wingtips as a means of load alleviation, which is known as semi-aeroelastic hinge (SAH). This device allows wingtips to be released during manoeuvre and severe gusts to alleviate wing loads, while locking the wingtips during cruise to maintain an optimum aerodynamic shape. This paper develops a flight mechanics model incorporating flexible wings to study the influence of the SAH device on multiple aspects of aircraft flight dynamics. The dynamic responses of the aircraft to gusts and control surface inputs are computed and compared for various hinge and wingtip configurations and release times. It was found that the gust load measured from the wing with free hinge configuration was approximately 40% lower compared to that of the fixed hinge case. It is also shown that when the SAH is released, it can significantly reduce an aircraft's roll damping and the frequency of the short-period mode, leading to higher roll and pitch rates. Furthermore, it shows that the transient responses following the wingtip release will exacerbate the responses induced by gusts, and greater load alleviation can be achieved by manipulating the hinge release time for each gust length. Finally, a step input of the elevator during the hinge release was found to be beneficial for enhancing the gust load alleviation.

Fuel sloshing inside aircraft wing tanks is not currently considered as a means of passive loads alleviation due to the lack of maturity of modelling tools and overall understanding of vertical sloshing. In this work, a scaled research wing demonstrator is presented, designed for the study of fuel sloshing inside an aircraft wing-representative model. An experimental campaign was conducted to examine the impact of fuel sloshing on the vertical dynamics of a scaled aircraft wing demonstrator, investigating the influence of excitation amplitude, filling level, baffle geometry, spanwise liquid position, and dihedral angle. It was found that the sloshing of the liquid in the fuel tank causes significant energy dissipation following step release excitation, maximized in the 40-60% filling range depending on the dihedral angle. The sloshing-induced damping also varies with the amplitude of excitation, with maximum added damping ratio of 0.038 achieved earlier in the motion at larger excitation amplitudes. The spanwise distribution of the liquid was found to have the strongest effect on the sloshing-induced damping, with the baffles' main impact being through the compartmentalization of the tank. Solid baffles that maintain favorable liquid distribution can increase the damping effect, while perforated baffles are not as effective. This work indicates that by considering the fuel dynamics rather than the fuel equivalent dry mass during the aircraft wing design, the net damping may be increased, leading to lighter wing structure designs.