Wing Stiffness Research Articles

Subtle frequency matching reveals resonant phenomenon in the flight of Odonata.

In this work, we investigate the connection between the flight flapping frequency and the intrinsic wing properties in Odonata (dragonflies and damselflies). For such large flying insect species, it has been noted that the wingbeat frequency is significantly lower than the structural resonance of the wing itself. However, the structural resonance mechanism is often evoked in the literature for flying and swimming animals as a means to increase locomotion performance. Here, we show that the flight of Odonata is based on a nonlinear mechanism that strongly depends on the wingbeat amplitude. For large flapping amplitudes (as observed in natural flight), the resonant frequency of the wings decreases with respect to its value at low amplitudes to eventually match the wingbeat frequency used in flight. By means of this nonlinear resonance, Odonata keep a strong wing stiffness while benefiting from a passive energy-saving mechanism based on the dynamic softening of the wing.

Correlation of High-Speed Tiltrotor Stability Predictions with Test Data and Parametric Study

High-speed stability of tiltrotor was studied. The University of Maryland’s Maryland Tiltrotor Rig (MTR) was chosen for the analysis due to availability of properties and test data, and its interesting high-stability behavior observed in the Glenn L. Martin wind tunnel in August 2022. A Rotorcraft Comprehensive Analysis System (RCAS) model of the MTR gimbaled hub was built in addition to the University of Maryland Advanced Rotorcraft Code-II (UMARC-II) model from previous work. The objective is threefold: i) validate RCAS tiltrotor stability predictions, ii) shed light on the high-stability behavior of the MTR, and iii) find ways to lower the instability speed of the MTR for future wind tunnel tests. Trim collective for freewheeling and stability predictions were compared with wind tunnel test data up to 200 knots. RCAS and UMARC-II predictions showed good agreement with each other and the test data. Predictions show that MTR is stable up to 215 knots (490-knots full-scale flight) although the wing is only 18% thick (current technology is 23%). A parametric study was carried out. The impact of wing stiffness, pitch-flap coupling (δ3 angle), lag stiffness, blade chord, number of blades, pylon mass, pylon center of gravity (c.g.), pylon location, and rotor speed was studied. MTR’s pylon c.g. is unconventionally behind the wing elastic axis. It was found that this significantly improved stability. This behavior is not specific to MTR; full-scale aircraft stability can also be improved by moving the pylon c.g. backward if wing beam is the least stable mode. A combination of forward pylon c.g., reduced rotor speed, and increased blade chord reduced the instability speed by more than 55 knots to near 160 knots, helping researchers obtain high-quality test data in the upcoming Glenn L. Martin wind tunnel tests.

Fluid-structure analysis of flapping-wing rotorcraft considering stiffness influence

As a novel aerial vehicle, flapping-wing rotorcrafts (FWRs) leverage both aerodynamic advantages of flapping and rotary wings, which can enhance the lift by using the passive rotational effect generated by the flexible deformation of their center symmetrical flapping wings. Due to FWRs’ unique wing kinematics, considering the aeroelastic deformation of wings is essential for the aerodynamic optimization of FWRs. In this paper, we propose a computational method of fluid-structure interaction for FWRs based on a simplified structural model. Such a method guarantees accurate results and works with high computational efficiency. To experimentally validate the proposed computational method, motion capture testing is constructed to simultaneously measure FWR wing deformation and aerodynamic forces during flapping. By comparing the experimental and computational results, the proposed method is capable of predicting the flapping lift effectively. Moreover, it can interpret the wing rotation and twist of the tested FWR. The computational efficiency in this paper is extremely close to that of the CFD calculation without considering the fluid-structure interaction. Based on this proposed computational method, the lift force of the test FWR platform is increased by 36.2 % by changing wing stiffness.

Effect of Wing Stiffness and Folding Wingtip Release Threshold on Gust Loads

This study presents an aeroelastic wind-tunnel experiment to identify the influence of the wing stiffness and hinge release threshold on the gust load alleviation performance of a folding wingtip design. Five models with different stiffness and tailoring properties are tested, and the wing root bending moment at different conditions is compared to the response with the locked-hinge condition to assess the impact on the gust load alleviation capabilities of the folding wingtip. The results show that the structural properties do not have an important impact on the peak load alleviation but the hinge release threshold and timing do. Releasing with the correct timing can reduce significantly the peak loads. However, the dynamics of the system are affected by this release; the flutter speed is decreased, and, although the performance can improve, load oscillations increase, which can be considered detrimental for reasons such as fatigue or passenger comfort.

The Wing Structure of an F3J/F5J Competition Sailplane: Topological Optimisation with Simplex Method and Additive Manufacturing

This research concerns the optimization study of the wing of an ultralight competition sailplane, category F5J/F3J. Fundamental for this category is the characteristic of lightness associated with good wing stiffness (bending/torsional). All the elements composing the wing of the sailplane were modelled in 3D by using the Autodesk Inventor parametric solid modeler. They were assembled in the FEM environment and were suitably constrained and studied from a structural point of view. The structural characteristics of the wing and its components were analysed in detail after assigning the materials currently used and adopting appropriate materials to make the same with the Additive Manufacturing (AM) technic. A topological optimization, performed by using the Simplex Method (SIMP), was conducted on the internal structure of the wing in order to lighten the ribs with the same performance. The experimental investigations implemented in the laboratory allowed the ’Oralight’ material used for the wing surface coating to be characterized. It is an extremely thin and light material, whose elasticity and strength were accurately assessed in this study. The data obtained, considered along with the elasticity and the resistance values of the other materials constituting the wing structure, taken from the literature, were inserted into the finite element simulations with the aim of evaluating the torsional and bending stiffness of the wing. Finally, the rib was redesigned using a FDM material which makes construction particularly simple.

Efficient Fluid–Structure Interaction Model for Twistable Flapping Rotary Wings

Wing flexibility is critical to flapping rotary wings (FRWs), and in that the deformation is bilaterally coupled with aerodynamic forces and thus determines the performance. Conventional solutions to this fluid–structure interaction (FSI) topic require considerable computational resources. In this paper, an efficient FSI model is proposed to calculate the aerodynamic force and passive twisting of FRWs. The passive pitching is regulated by a torsional spring, and the twisting is simplified as a quadratic distribution. A well-verified quasi-steady model is employed to estimate the aerodynamic forces. Our results show that the performance of rigid FRWs is superior to twistable FRWs within an upper limit of the wing-root stiffness , which is around . At higher values, the twistable FRWs generate comparable lift to rigid FRWs at a higher efficiency. An increase in flapping frequency can remarkably reduce the efficiency of twistable FRWs despite the lift enhancement, while a concomitant reduction of flapping amplitude can moderate the loss of efficiency at higher flapping frequencies. Our model provides an efficient tool for the quick estimation of the aeroelastic performance of twistable FRWs and can thus contribute to the wing stiffness design.

Design and Analysis of a Deployment Mechanism with Clearance Compensation for High Stiffness Missile Wings

The deployment performance of the unfolded wing determines whether the winged missiles can fly normally after being launched, infecting the attack performance of the winged missiles. The paper proposes a new deployment mechanism with clearance eliminator. Based on the slider-crank principle, the proposed deployment mechanism achieves fast and low-impact deployment of the wings. The proposed clearance eliminator with shape memory alloy (SMA) effectively eliminates the clearance of the sliding pair and improves the support stiffness and stability of the deployed wing. The collision characteristics and the clearance elimination are studied for the deployment mechanism. The influence of the collision force on the motion state of the wing during the deployment is analyzed. The static stiffness of the wing under the clearance state and the deformation is analyzed. The dynamic stiffness under the catapult clearance elimination state is modeled based on the fractal geometry and contact stress theory. The relationship between the locking force and the support stiffness is revealed. The kinetic simulation is used to analyze the motion response during the action of the deployment mechanism. Modal analysis, harmonic response analysis, and random vibration analysis were conducted for the whole wings. A prototype was developed to verify the ejection performance of the wing according to the input load characteristics. The dynamic stiffness of the unfolded wings is tested by the fundamental frequency experiments to verify the performance of the clearance elimination assembly. The experimental results show that the designed deployment mechanism with clearance compensation achieves fast ejection and high stiffness retention of the missile wing.

An experimental data-driven mass-spring model of flexible Calliphora wings

Insect wings can undergo significant deformation during flapping motion owing to inertial, elastic and aerodynamic forces. Changes in shape then alter aerodynamic forces, resulting in a fully coupled fluid–structure interaction (FSI) problem. Here, we present detailed three-dimensional FSI simulations of deformable blowfly (Calliphora vomitoria) wings in flapping flight. A wing model is proposed using a multi-parameter mass-spring approach, chosen for its implementation simplicity and computational efficiency. We train the model to reproduce static elasticity measurements by optimizing its parameters using a genetic algorithm with covariance matrix adaptation (CMA-ES). Wing models trained with experimental data are then coupled to a high-performance flow solver run on massively parallel supercomputers. Different features of the modeling approach and the intra-species variability of elastic properties are discussed. We found that individuals with different wing stiffness exhibit similar aerodynamic properties characterized by dimensionless forces and power at the same Reynolds number. We further study the influence of wing flexibility by comparing between the flexible wings and their rigid counterparts. Under equal prescribed kinematic conditions for rigid and flexible wings, wing flexibility improves lift-to-drag ratio as well as lift-to-power ratio and reduces peak force observed during wing rotation.

Measurement of flexural and torsional stiffnesses in penguin wings

Penguins are propelled through the water by flapping their wings. During swimming, wing flapping causes bending deformation of the wings. The cross section of the wing forms a thick wing shape, and the wing skeleton consists of a humerus, a forearm, a manus, and digits. Previous anatomical studies have shown that penguin wings are mobile in the wing plane at each joint. However, the range of motion and stiffness of bending outside the wing plane have not been investigated. Furthermore, the range of motion and stiffness with respect to torsion is unknown. In this study, we measured the static flexural and torsional stiffness of wings collected from a gentoo penguin (Pygoscelis papua) cadaver. As a result, we found asymmetries in flexural stiffness with respect to the bending direction and torsional stiffness with respect to the torsional direction. Furthermore, assuming that each joint of the penguin wing is a torsional spring and the other parts are rigid, the spring stiffness of each joint during bending and torsional deformation was measured. The results showed that the asymmetry of wing flexural stiffness was strongly influenced by the wrist joint and the asymmetry of wing torsional stiffness was strongly influenced by the elbow joint.

Coupled Aeroelastic Study of a Flexible Micro Air Vehicle-Scale Flapping Wing in Hovering Flight

Instantaneous force and structural deformation experiments were performed on a flexible, structurally characterized, low-aspect-ratio representative flapping wing. A six-component force balance was used to measure aerodynamic-force time history over a flap cycle. A VICON motion capture setup tracked the wing deformations while flapping. Measured aerodynamic forces and wing deformations were compared against coupled computational fluid dynamics/computational structural dynamics (CFD/CSD) aeroelastic analysis results. The CFD solver is an unsteady Reynolds-averaged Navier–Stokes solver. The CSD solver is a general-purpose multibody dynamics solver capable of modeling geometrically nonlinear beam and shell elements. The CFD/CSD results were able to capture the overall trend in aerodynamic forces and wing deformations. Although predicted and measured variations in lift were similar, the drag-force magnitudes tended to be underpredicted by the coupled aeroelastic solver. The coupled CFD/CSD solver was used to evaluate the influence of wing flexibility on wing performance. Results showed that, in particular instances, decreasing wing stiffness increased the time-averaged aerodynamic lift and lift-to-power ratio. Decreased wing stiffness led to reduced leading-edge vortex circulation strength. This suggests that the increased wing performance is mainly due to a redirection of the resultant force vector allowed by the increased wing compliance.

Wing structure and neural encoding jointly determine sensing strategies in insect flight.

Animals rely on sensory feedback to generate accurate, reliable movements. In many flying insects, strain-sensitive neurons on the wings provide rapid feedback that is critical for stable flight control. While the impacts of wing structure on aerodynamic performance have been widely studied, the impacts of wing structure on sensing are largely unexplored. In this paper, we show how the structural properties of the wing and encoding by mechanosensory neurons interact to jointly determine optimal sensing strategies and performance. Specifically, we examine how neural sensors can be placed effectively on a flapping wing to detect body rotation about different axes, using a computational wing model with varying flexural stiffness. A small set of mechanosensors, conveying strain information at key locations with a single action potential per wingbeat, enable accurate detection of body rotation. Optimal sensor locations are concentrated at either the wing base or the wing tip, and they transition sharply as a function of both wing stiffness and neural threshold. Moreover, the sensing strategy and performance is robust to both external disturbances and sensor loss. Typically, only five sensors are needed to achieve near-peak accuracy, with a single sensor often providing accuracy well above chance. Our results show that small-amplitude, dynamic signals can be extracted efficiently with spatially and temporally sparse sensors in the context of flight. The demonstrated interaction of wing structure and neural encoding properties points to the importance of understanding each in the context of their joint evolution.

Design and testing of aeroelastically tailored composite wing under fatigue and gust loading including effect of fatigue on aeroelastic performance

The aim of the paper is to experimentally validate a numerical design methodology for optimizing composite wings subject to gust and fatigue loading requirements and to assess the effect of fatigue on the aeroelastic performance of the wing. Traditionally, to account for fatigue in composite design, a knockdown factor on the maximum stress allowable is applied, resulting in a conservative design. In the current design methodology, an analytical fatigue model is used to reduce the conservativeness and exploit the potential of composite materials. To validate the proposed analytical model, a rectangular composite wing is designed and manufactured to be critical in strength, buckling and fatigue. An experimental campaign comprising wind tunnel and fatigue tests is performed. In the wind tunnel, both static and dynamic aeroelastic experiments are conducted to validate the numerical dynamic aeroelastic model. The fatigue test is used to validate the analytical fatigue model and to understand the effect of fatigue on aeroelastic properties of the wings. The results from experimental campaign validated both the aeroelastic predictions as well as fatigue predictions of the numerical design methodology. However the fatigue process resulted in degradation of the wing stiffness leading to change in the aeroelastic response of the wing.

The impact and sensitivity analysis of beam and stringer for stiffness center of composite wing structure

Wing stiffness center should be determined firstly for structure detail design. The present study focused on the impact analysis of beam and stringer for wing cross-section stiffness center based on thin wall structure mechanics theory. In order to discuss the impact of beam and stringer on stiffness center, the sensitivity formulas for stiffness center of wing cross-section were derived and expressed in terms of the dimension and layout of beams and stringers. The results indicated that the structural layouts of beam and stringer were important influencing factors in stiffness detail design of full composite wing structure. The research results can provide an important reference for the stiffness design and aeroelastic design of the full composite wing.

On the Preliminary Structural Design Strategy of the Wing of the Next-Generation Civil Tiltrotor Technology Demonstrator

The T-WING project is a Clean Sky 2 research project aimed at designing, manufacturing, qualifying and flight-testing the new wing of the Next-Generation Civil Tiltrotor Technology Demonstrator (NGCTR-TD), as part of the Fast Rotorcraft Innovative Aircraft Demonstrator Platforms (FRC IADP) activities. Requirements, design strategy, methodology and main steps followed to achieve the composite wing preliminary design are presented. The main driving requirements have been expressed in terms of dynamic requirements (e.g., limitations on natural frequencies), aeroelastic requirements, i.e., compliance with European Aviation Safety Agency (EASA) CS-25 and CS-29 Airworthiness Requirements), structural requirements (e.g., target wing structural mass), functional requirements (e.g., fuel tanks, accessibility, assembly and integration, etc.) and wing preliminary loads. Based on the above-mentioned requirements, the first design loop is performed by targeting an optimal wing structure able to withstand preliminary design loads, and simultaneously with stiffness and inertia distributions leading to a configuration free from flutter within the flight envelope. The outcome from the first design loop is then used to refine the model and compute more reliable flight loads and repeat aeroelastic analysis, returning further requirements to be fulfilled in terms of wing stiffness and inertia distributions. The process is iterated till the fulfillment of all the project requirements.

The aerodynamic performance of passive wing pitch in hovering flight

Insect wings can passively maintain a high angle of attack during each flapping stroke without the aid of the active pitching motion due to the torsional flexibility of the wing basal region. However, there is no clear understanding of how torsional wing flexibility should be designed for achieving optimal aerodynamic performance. In this work, a computational study was conducted to investigate the passive pitching mechanism of a fruit fly wing in hovering flight using a torsional spring model. The torsional wing stiffness was characterized by the Cauchy number, a ratio between the aerodynamic force and the structural elastic force. Different flapping patterns including zero-deviation, figure-8, and oval-shaped flapping trajectories were evaluated along a horizontal stroke plane. The aerodynamic forces and associated unsteady flow structures were simulated using an in-house immersed-boundary-method based computational fluid dynamics solver. A parametric study on the Cauchy number was performed with a Reynolds number of 300. According to the analysis of the aerodynamic performance, we found that a balance of high lift and high lift-to-power ratio can be achieved in a particular range of Cauchy numbers (0.15–0.30) for all different flapping trajectories. This range is consistent with the Cauchy number calculated based on the experimental measurements of a fruit fly in the literature. In addition, 3D wake structures generated by the passive flapping wings were analyzed in detail. The findings of this work could provide important implications for designing more efficient flapping-wing micro-air vehicles.

Wing stiffness parameterisation for surrogate models

Surrogate models are key enablers for robust, multidisciplinary design in aerospace. However, a critical question for their efficient use remains in terms of how the aircraft should be parameterised into design variables. This study investigates the parameterisation of wing stiffness for a long-range, twin-engine transport aircraft by comparing the predictions of surrogates with different input parameterisations to the outputs of a physics-based aircraft load analysis. The stiffness parameters were defined to be percent changes in wing stiffness versus a baseline aircraft applied on discrete spanwise sections of the wing box. The number of stiffness parameters was varied between 6 and 64 to see if some of the wing box sections could be grouped together by averaging the stiffness changes across the wing section to reduce the dimensionality of the problem. In addition, a sensitivity analysis using Sobol indices was performed which demonstrated which stiffness parameters contributed most to the variability in wing loads during various manoeuver and static and dynamic gust cases. It was found that geometry-based stiffness parameters show poor consistency between parameterisations and thus the stiffness changes applied over discrete sections of the wing cannot be combined into an average stiffness change without a significant sacrifice in accuracy. However, good consistency was shown in the sensitivity of load responses between different parameterisations.

Design and Experimental Study of Dragonfly-Inspired Flexible Blade to Improve Safety of Drones

A flexible blade that is easy to fabricate and repair is presented: It has a low impact load when colliding with obstacles, and can generate enough thrust for drone flight. The flexible blade has a camber structure that mimics the feature of dragonflies to increase wing stiffness. It makes the blade's deformation decline when it receives a lift force and drag force. A commercially available drone that conformed to standards was used to design, fabricate, and test the flexible blade. The flexible blade consists of a pivot column made by three-dimensional printer and a polyethylene film. The design variables were defined as values with thrust and efficiency that were determined to be similar to those of the original blade through experiments. Experiments for safety verification were conducted by comparing the impact and sharpness of the original and the flexible blades. Experimental results show that the flexible blade's impact force is approximately a tenth of the original blade's impact force, and only the original blade damaged a 100-μm film obstacle. In general terms, the suggested flexible blade is safer and more economical than a plastic blade, in addition to having performance close to that of the original blade during flight.

Energy-efficient wing design for flapping wing micro aerial vehicles

Flapping wing micro aerial vehicles (FWMAVs) have attracted more attention during the development of the robotic systems field. The size of the flapping wing plays an important role in the lift force and torque generation based on quasi-steady aerodynamic model. Therefore, it is necessary to study energy-efficient design methods for wings to provide sufficient lift force and torque with minimal energy consumption for hovering flight. In this paper, the sensitive parameters for the lift force and power consumption were first selected based on design of experiment (DOE) and the parameter of the distributed wing stiffness was determined based on experimental data. Design optimization models for three different cases were then built by considering the lift force as one constraint and the energy consumption as the objective function. The combination of subset simulation and the gradient-based optimization was finally used for solving design optimization models, and the corresponding sensitivity analysis was provided.

Experimental investigation of fluid–structure interaction in a bird-like flapping wing

Fluid–structure interaction in a bird-like flapping wing is investigated experimentally. Various materials having varied thickness (t), elastic property (E) and density (ρw) are selected as the wing for the flapping motion. Force and power measurements are performed in wind-off condition for a range of flapping frequencies. The effect of rib orientation, position of the single spanwise rib along the wing chord and multiple spanwise ribs on thrust generation is also investigated. Dynamics of the flow around different wing configurations are elucidated based on Phase-locked 2D Particle Image velocimetry (PIV) measurements. We found that the strength and size of trailing edge vortex (TEV) are closely related to the stiffness characteristics of the wing. The strength and size of TEV are found to increase with an increase in the stiffness of the wing. Based on thrust generation and TEV characteristics, we noted that the effect of rib is not identical for two different wing materials. The non-dimensional stiffness (Πe∗) for various wing without rib configurations is calculated. We found a non-linear correlation between coefficient of thrust (CT∗) and non-dimensional stiffness (Πe∗) for specific wing configurations. The major findings from this study suggest that wing stiffness cannot be the sole factor influencing the thrust generation. Apart from the wing stiffness, wing deformation especially the trailing edge (TE) deformation pattern might have a major role in thrust generation and there is a need to quantify the deformation either experimentally or computationally.

Conceptual design and simulation validation based finite element optimisation for tubercle leading edge composite wing of an unmanned aerial vehicle

A finite element model is developed to determine deformation and stresses on a composite wing of unmanned aerial vehicle (UAV) with a tubercle design at the leading edge of the wing. Tubercles, commonly known as protuberances found on the leading edge of a whale pectoral flipper, offering great performance from an aerodynamic perspective. This paper deals with a first order shear deformation theory (FSDT) approach to discover the UAV laminates composite wing model of tubercle leading edge (TLE) with rib-reinforced so that the equivalent stiffness and material properties are obtained from the simulation of finite element analysis using ANSYS. Another structural configuration of design replicating the idea of monocoque concept, whereby foam is used at the leading and trailing edges of the wing. Styrene acrylonitrile (SAN) core foam is used representing high strength-to-weight ratio with its superiority in the mechanical properties of polymeric sandwich composites. The updated static structural analysis from rib-reinforced can be applied to update the wing stiffness distribution of monocoque-foam. The optimum design is concluded from the tabulated deformation and stresses of both wings, where monocoque-foam showed better performance with a reduction in 50.72% of deformation and 35.88% of stress, compared to rib-reinforced design.