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An evaluation of the commercial transport aircraft developed over the past decades evidences an increasing trend toward the use of high aspect-ratio wings. This trend is justified by the well-known effect of slender wings in reducing fuel consumption, leading to lower operational costs and a milder environmental impact. There are many studies about the effects of geometric nonlinearities on aeroelastic behavior of very flexible wings in symmetrical maneuvers. However, geometric nonlinearities may also significantly affect the aeroelastic behavior of the wing under non-symmetrical conditions, especially when ailerons are deflected. Within this context, this work presents a static fluid–structure interaction approach to evaluate the rolling characteristics of very flexible wings. First, a modified version of the very flexible Pazy Wing from Aeroelastic Prediction Workshop (AEPW-3) is proposed, now equipped with ailerons. Next, a fluid–structure interaction tool that couples a full potential aerodynamic solver with an implicit nonlinear structural solver is presented to allow simulations of wings with deflected ailerons. The presented method is applied to the modified Pazy wing considering multiple linear and nonlinear structural analyses, for different aileron deflection angles. The results show that when geometric nonlinearity effects are considered, the aileron effectiveness tends to decrease as the structural flexibility increases. On the other hand, if geometric nonlinearities are neglected, the aileron effectiveness falsely enhances as the wing flexibility rises.

Flexible wings, serving as the key components of tailless flapping wing micro air vehicles (FWMAVs), simultaneously generate lift, thrust, and control torques. Due to the complex unsteady fluid-structure interactions involved in their flapping, accurately predicting their aerodynamic performance, such as mean lift and lift-to-power efficiency, becomes challenging. There is also a lack of widely accepted and rational design methods for flexible wings. To address these, we propose an experimental optimization design method based on response surfaces methodology and investigate the impact of four design parameters—aspect ratio ( A ), slack angle ( θ ), taper ratio ( λ ), and flapping frequency ( f )—on the aerodynamic performance of flexible wings. The results show that the models accurately predict the aerodynamic performance of flexible wings, with an error margin of less than 10% compared to experimental measurements. Utilizing these models, an optimal flexible wing for a tailless FWMAV with a mass of 15 g was designed and manufactured, which can generate 15.24 gf of lift while maintaining a lift-to-power efficiency of 6.07 gf/W. Additionally, the models indicate that the four parameters are nearly equally important for the aerodynamic performance of flexible wings, and the coupling between these parameters also significantly affects the aerodynamic performance. Specifically, A & λ , A & f , θ & f , and λ & f affect mean lift, while A & λ , θ & λ , and θ & f affect lift-to-power efficiency. These coupling effects help explain the contradictions found in previous studies regarding the influence of different parameters. Our research provides clear guidance and practical methods for designing flexible wings in tailless FWMAVs.

This paper addresses the robust output regulation and even output constraints of a flexible wing system, where an exosystem is supposed to generate the unknown time-varying output constraints, output disturbances, distributed disturbances, boundary disturbances and references. Besides the signals of displacements and velocities, high-order boundary signals are used to guarantee the exponential convergence of the tracking errors. At first, two exosystem observers are designed based on the PDE observer of the wing system in order to give the approximation of the unknown references and output constraints. Then, two observer based output feedback controls are proposed based on state feedback controls and the PDE-ODE coupled observer. For the closed-loop system, the tracking errors are proved to be convergent toward zero, and further regulated to be restrained by two unknown time-varying and positive trajectories. Numerical simulation shows the effectiveness of the proposed robust controls.

Flapping wing micro aerial vehicles (FWMAVs) with flexible wings offer unique advantages across multiple scenarios due to their high energy efficiency and precision capabilities. This study explores the fluid-structure interaction (FSI) mechanisms and aerodynamic performance differences among three flexible wing motion patterns – passive twisting (PT), chordwise active twisting (CAT), and ‘Figure-8’ active twisting (FAT) – using a bidirectional FSI numerical simulation platform. A bionic wing model (aspect ratio AR = 3.86) and a Multiphysics-coupled framework were developed to evaluate the effects of dynamic wing torsion on lift and energy recovery. Results show that PT enhances aerodynamic performance by delaying flow separation and stabilising leading-edge vortices (LEVs). At 4 m/s, the average lift of flexible wings (FW) with PT is 6.31 times higher than that of rigid wings (RW). Active twisting strategies further improve efficiency: CAT increases average lift by 143% compared to PT at θmax  = 40°, while FAT achieves 14.9% energy recovery rate through wake capture and elastic potential energy release, with an elastic energy release rate 2.79 times higher than CAT. Vortex dynamics analysis reveals that active twisting optimises lift by enhancing LEV circulation and proximity to the wing surface. CAT strengthens LEV attachment near the wing root, while FAT stabilises vortices at the wingtip. This research provides insights into energy efficiency optimisation and active control strategies for FWMAVs, highlighting the benefits of flexible deformation and intelligent motion regulation in improving aerodynamic performance and energy management.

Flight and swimming in nature can inspire the design of highly adaptive robots capable of working in complex environments. In this letter, we reviewed our work on robotic propulsion in the air and water, with a specific focus on the crucial functions of elastic components involved in the driving mechanism and flapping wings. Elasticity in the driving mechanism inspired by birds and insects can enhance both the aerodynamic efficiency of flapping wings and robustness against disturbances with appropriate design. A flapping wing surface with a stiffness distribution inspired by hummingbirds was fabricated by combining tapered spars and ribs with a thin film. The biomimetic flexible wing could generate more lift than the nontapered wing with a similar amount of power consumption. Underwater flapping-wing propulsion inspired by penguins was investigated by combining the 3-degree-of-freedom (DoF) flapping mechanism and hydrodynamic calculation, which indicates that wing bending increases the propulsion efficiency. This work demonstrates the importance of passive deformation of both wing surfaces and driving mechanisms for improving the fluid dynamic efficiency and robustness in flight and swimming, as well as providing biological insight from an engineering perspective.

The trailing edge deformable wing is one of the main development directions of future aircraft design. The technology of active camber of wing trailing edge can significantly improve the aerodynamic performance of aircraft. In this paper, the motor drives the parabolic crankshaft and the distributed crankshaft drives the flexible skin of the trailing edge of the wing, which can realize the deflection of the trailing edge of the wing at a large angle of 0~30 degrees. At the same time, the surface of the wing is continuous and smooth. Moreover, the aerodynamic simulation results of the deformed wing show that the trailing edge deflection is beneficial to increase the lift. It can increase the maximum lift coefficient by 2 times and the maximum lift drag ratio by 18%. Adaptive flexible wing technology is applied to rocket sleds with side wings. This technology can increase the downward pressure of the side wing of the rocket block and improve the operation safety.

Insects have various wing morphologies and flapping systems to achieve a highly maneuverable performance at low speed. Among unsteady aerodynamic mechanisms in flapping flights, a leading-edge vortex is a significant key to generating lift stably in insect flights. The leading-edge vortex behavior is correlated with an overall vortical system around flapping wings. In addition, the insects have flexible wing structures that are deformable while flapping their wings. The wing deformations can be easily affected by wing morphologies and kinematic motions, leading to different vortical structures around the flexible wings. Thus, lift enhancement in flapping flexible wings depends on the wing shape and structural deformation in diverse species of insects. Here, by measuring and comparing time-varying force/torque and flow structures of two different flexible wings, rectangular (non-curved, at Re =  ~ 6044) and hawkmoth-like (curved, at Re =  ~ 5309) shapes, it was found that a wingtip curve is a meaningful factor in studying flapping flexible wings. In a flexible case, the hawkmoth-like model had a widened leading-edge vortex region and strengthened circulations around the inner wing, thereby producing more lift (12.7% increase) and achieving better aerodynamic performance (4.8% increase of lift-power ratios). However, despite both flexible models having similar flexural stiffnesses, these features were not observed in the rectangular model, even generating more aerodynamic force even generating more aerodynamic force than the hawkmoth-like model in the rigid case (8.12%, 1.52%, and 16.99% greater in lift, drag, and power, respectively). These were caused by different wingtip motions between two flexible wings during wing reversal, leading to different downwash and corresponding leading-edge vortex structures. These findings demonstrate that the wingtip curve effect might be improved when combined with wing flexibility. They, thus, inspire future research on flapping motions, wing shapes, and structures.

The long-range migration of monarch butterflies, extended over 4000 km, is not well understood. Monarchs experience varying density conditions during migration, ranging as high as 3000 m, where the air density is much lower than at sea level. In this study, we test the hypothesis that the aerodynamic performance of monarchs improves at reduced density conditions by considering the fluid–structure interaction of chordwise flexible wings. A well-validated, fully coupled Navier–Stokes/structural dynamics solver was used to illustrate the interplay between wing motion, aerodynamics, and structural flexibility in forward flight. The wing density and elastic modulus were measured from real monarch wings and prescribed as inputs to the aeroelastic framework. Our results show that sufficient lift is generated to offset the butterfly weight at higher altitudes, aided by the wake-capture mechanism, which is a nonlinear wing–wake interaction mechanism, commonly seen for hovering animals. The mean total power, defined as the sum of the aerodynamic and inertial power, decreased by 36% from the sea level to the condition at 3000 m. Decreasing power with altitude, while maintaining the same equilibrium lift, suggests that the butterflies generate lift more efficiently at higher altitudes.

This paper proposes a hybrid rigid–flexible wing design that enables large-area folding and reconfiguration. Based on elasticity theory and fabric constitutive equations, a surface-outward mechanical model incorporating mesoscale weave structures was developed for plain-woven wing membranes. To address the degradation of the model under low-prestress conditions, a more accurate second-order nonlinear model for the out-of-plane mechanics of wing membranes was further developed. This paper developed a dual-axis tensile fixture and, through conducting load-bearing performance experiments on wing membrane elements, verified that the improved theoretical model possesses a certain degree of predictive accuracy. A dual-axis tensile fixture was designed, and load-bearing tests on membrane elements were conducted to verify that the improved theoretical model provides reasonable predictive accuracy. To investigate how pre-tensioning regulates membrane stiffness, the variation in out-of-plane stiffness under symmetric and asymmetric prestress conditions was analysed. A prestressing strategy prioritising the principal-modulus direction is proposed, providing theoretical guidance for prestress application in wing membranes. Based on these findings, a prototype rigid–flexible composite wing with a “membrane-scaffold” structure was fabricated and tested.

Beam-like flexible structures are of interest in many fields of engineering, particularly aeronautics, where wings are frequently modelled and represented as such. Experimental modal analysis is commonly used to characterise the wing’s dynamical response. However, unlike other flexible structure applications, no benchmark problems involving high-aspect-ratio flexible wings have appeared in the open literature. To address this, this paper reports on ground vibration testing results for a flexible wing and its sub-assembly and parts. The experimental data can be used as a benchmark and are available to the aeronautical and structural dynamics community. Furthermore, non-linearities in the structure, where present, were detected. Tests were performed on the whole wing as well as parts and sub-assembly, providing four specimens. These were excited with random vibration at three different amplitudes from a shaker table. The modal properties of a very flexible high-aspect-ratio wing model, its sub-assembly and parts, were extracted, non-linear behaviour was detected and the experimental data are shared in an open repository.