Wing Stiffness Research Articles

Metaheuristic Approaches to Solve a Complex Aircraft Performance Optimization Problem

The increasing demands for travelling comfort and reduction of carbon dioxide emissions have been considered substantially in the stage of conceptual aircraft design. However, the design of a modern aircraft is a multidisciplinary process, which requires the coordination of information from several specific disciplines, such as structures, aerodynamics, control, etc. To address this problem with adequate accuracy, the multidisciplinary analysis and optimization (MAO) method is usually applied as a systematic and robust approach to solve such complex design issues arising from industries. Since MAO method is tedious and computationally expensive, genetic programming (GP)-based metamodeling techniques incorporating MAO are proposed as an effective approach to minimize the wing stiffness of a large aircraft subject to aerodynamic, aeroelastic and stability constraints in the conceptual design phase. Based on the linear small-disturbance theory, the state-space equation is employed for stability analysis. In the process of multidisciplinary analysis, aeroelastic response simulations are performed using Nastran. To construct metamodels representing the responses of the interests with high accuracy as well as less computational burden, optimal Latin hypercube design of experiments (DoE) is applied to determine the optimized distribution of sampling points. Following that, parametric optimization is carried out on metamodels to obtain the optimal wing geometry shape, elastic axis positions and stiffness distribution, and then the solution is verified by finite element simulations. Finally, the superiority of the GP-based metamodel technique over genetic algorithm is demonstrated by multidisciplinary design optimization of a representative beam-frame wing structure in terms of accuracy and efficiency. The results also show that GP metamodel-based strategy for solving MAO problems can provide valuable insights to tailoring parameters for the effective design of a large aircraft in the conceptual phase.

Gust Response at High Angles of Attack

The responses of a NACA0012 airfoil and a large-aspect-ratio wing, subjected to gust excitation about high mean angles of attack, close to stall, are presented here. Reynolds-averaged Navier–Stokes turbulent simulations were employed to compare the gust responses at high and low mean angles of attack. It was observed that, for a rigid configuration at incipient stall conditions, the peak aerodynamic loads due to short gust lengths are higher than their counterparts at low angles of attack. However, they decrease asymptotically with increasing gust length. A convolution-based gust analysis methodology that can predict accurate gust loads at incipient stall conditions is also presented. The convolution-based method was employed to perform tuned-gust analysis with varying wing stiffness. The results show that the changes in peak modal displacements with wing flexibility at incipient stall are significantly different from their low-angle-of-attack counterparts, resulting in significantly different critical gust lengths, and 40% lower peak bending moment for a moderately flexible wing. This shows that high-fidelity gust analysis is imperative at incipient stall conditions, and the convolution-based method provides a computationally efficient yet accurate approach to achieve this.

Local deformation and stiffness distribution in fly wings

ABSTRACTMechanical properties of insect wings are essential for insect flight aerodynamics. During wing flapping, wings may undergo tremendous deformations, depending on the wings’ spatial stiffness distribution. We here show an experimental evaluation of wing stiffness in three species of flies using a micro-force probe and an imaging method for wing surface reconstruction. Vertical deflection in response to point loads at 11 characteristic points on the wing surface reveals that average spring stiffness of bending lines between wing hinge and point loads varies ∼77-fold in small fruit flies and up to ∼28-fold in large blowflies. The latter result suggests that local wing deformation depends to a considerable degree on how inertial and aerodynamic forces are distributed on the wing surface during wing flapping. Stiffness increases with an increasing body mass, amounting to ∼0.6 Nm−1 in fruit flies, ∼0.7 Nm−1 in house flies and ∼2.6 Nm−1 in blowflies for bending lines, running from the wing base to areas near the center of aerodynamic pressure. Wings of house flies have a ∼1.4-fold anisotropy in mean stiffness for ventral versus dorsal loading, while anisotropy is absent in fruit flies and blowflies. We present two numerical methods for calculation of local surface deformation based on surface symmetry and wing curvature. These data demonstrate spatial deformation patterns under load and highlight how veins subdivide wings into functional areas. Our results on wings of living animals differ from previous experiments on detached, desiccated wings and help to construct more realistic mechanical models for testing the aerodynamic consequences of specific wing deformations.

Repetitive firing and wing stiffness in the locomotory musculature of the pteropod Clione limacina

AbstractThe locomotory musculature of the pteropod Clione limacina includes slow‐twitch, fatigue‐resistant muscle fibers and fast‐twitch fatigable fibers. Dorsal musculature produces a dorsal bend of the wing, while ventral musculature produces a ventral bend. During the change to fast swimming, ~10% of the slow‐twitch fibers, including both dorsal and ventral fibers, exhibit fast repetitive firing that greatly exceeds the in‐phase excitation of the appropriate wing musculature. The normal wing‐beat frequency for fast swimming is 2–4 Hz, while repetitive firing occurs at 11 Hz. A component of fast‐swimming control is excitation of Pd‐SW neurons of the pedal ganglion. These cells are serotonin immunoreactive, and they innervate the slow‐twitch musculature of the wing. Induced excitation of a Pd‐SW neuron was capable of triggering repetitive firing in some slow‐twitch muscle cells. Repetitive firing in a subset of muscle fibers of the swim musculature could represent a contribution to wing stiffening, which has been documented to occur during the change to fast swimming.

Slender-Wing Beam Reduction Method for Gradient-Based Aeroelastic Design Optimization

The efficiency and scope of aeroelastic wing optimization strategies can be increased using analysis-specific structural idealizations, such as high-fidelity models for detailed stress analyses and low-fidelity models for aeroelastic analyses. In this work, a numerical method is presented that enables the efficient and accurate reduction of a high-fidelity finite element model to a Timoshenko beam-based model with lumped masses. The result is a representation based on 13 independent physical beam stiffness parameters per element. The method also yields analytical beam sensitivities with respect to changes in the high-fidelity model. Using these, an approach is suggested for integrating the beam reduction method into a gradient-based multidisciplinary-design-optimization architecture. The reduction technique is demonstrated on a simplified wing box and on the University of Bristol Ultra-Green aircraft configuration wing. The effects of unbalanced skin composite laminates, rotated internal ribs, varying wing taper and sweep, and wing boundary constraints on the wing stiffness are shown to be captured with sufficient accuracy for static and dynamic aeroelastic analysis purposes. The accuracy of the analytically calculated gradients is demonstrated by comparison with complex-step and finite difference derivative approximations.

Influence of hydrodynamic pressure and vein strength on the super-elasticity of honeybee wings

The wings of honeybees (Apis mellifera L.) usually produce bending and torsional deformations during flapping wing movement. These deformations endow honeybees with perfect aerodynamic control to escape predators and exploit scattered resources. However, the mechanisms by which honeybee wings recover from large deformations are unclear. This study demonstrates that honeybee wings are super-elastic that they can recover rapidly from one extreme contorted state to their original position. A comparative experiment is conducted to evaluate the difference in super-elastic recovery between attached and detached wings. Results show that the structural stiffness of wings is affected by the reticulate vein and the haemolymph pressure generated by the blood circulation. Further analysis indicates that the haemolymph pressure can increase the stiffness of honeybee wings, especially that of the subcostal veins. This phenomenon shortens the recovery time of wing deflection behaviour.

Effects of flexibility and aspect ratio on the aerodynamic performance of flapping wings

In the current study, we experimentally investigated the flexibility effects on the aerodynamic performance of flapping wings and the correlation with aspect ratio at angle of attack α = 45°. The Reynolds number based on the chord length and the wing tip velocity is maintained at Re = 5.3 × 103. Our result for compliant wings with an aspect ratio of 4 shows that wing flexibility can offer improved aerodynamic performance compared to that of a rigid wing. Flexible wings are found to offer higher lift-to-drag ratios; in particular, there is significant reduction in drag with little compromise in lift. The mechanism of the flexibility effects on the aerodynamic performance is addressed by quantifying the aerodynamic lift and drag forces, the transverse displacement on the wings and the flow field around the wings. The regime of the effective stiffness that offers improved aerodynamic performance is quantified in a range of about 0.5–10 and it matches the stiffness of insect wings with similar aspect ratios. Furthermore, we find that the aspect ratio of the wing is the predominant parameter determining the flexibility effects of compliant wings. Compliant wings with an aspect ratio of two do not demonstrate improved performance compared to their rigid counterparts throughout the entire stiffness regime investigated. The correlation between wing flexibility effects and the aspect ratio is supported by the stiffness of real insect wings.

Ecological and phylogenetic perspectives on wing stiffness in nine Theclini species (Lepidoptera: Lycaenidae)

AbstractWe studied the relationship between wing stiffness and butterfly ecology and phylogeny. Nine species belonging to the tribe Theclini of the family Lycaenidae were selected and examined for the wing stiffness of dried specimens by a three‐point bending test. It was found in Japonica lutea that the wing stiffness was not affected by the humidity to which it had been exposed, but was strongly affected by wing size and sex. Comparisons of sexual differences in four species indicated that females of patrolling species had stiffer wings than conspecific males, but that males of territorial species had stiffer wings than conspecific females. Finally, the wing stiffness was compared among males of nine species that use different mate‐locating tactics, and the results revealed a tendency that males of territorial species have stiffer wings than males of patrolling species. These results, though including a few exceptional cases, are discussed from the perspective of ecological requirements and phylogenetic constraints on the species.

Aeroelastic Tailoring and Active Aeroelastic Wing Impact on a Lambda Wing Configuration

Two aeroelastic design approaches are applied to a supersonic lambda wing configuration with the goal of improving the wing’s aeroelastic performance. Aeroelastic tailoring and active aeroelastic wing technologies are investigated in a sequential manner to quantify their benefits. Industry-standard tools are used to perform these design studies. First, a finite element model of a lambda wing is developed. Second, eight structural variants of the finite element model are created to study variations in wing stiffness. Finally, two sizing optimization processes are applied. The first is an aeroelastic sizing approach standard to MSC NASTRAN, and the second is an active aeroelastic wing design process, which is presented in this paper. The latter process integrates control and structural sizing design variables together. Both of these processes are used to size all eight structural variants. The optimized variants are compared based on weight and control surface effectiveness. Additionally, the optimal variations in percent ply utilization over the wing for the lightest weight concept are explored. It is found that applying aeroelastic tailoring simultaneously with active aeroelastic wing has the potential to reduce the aircraft gross takeoff weight by 7% in lambda wing configurations.

Effect of Wing Deformation on the Aerodynamic Performance of Flapping Wings: Fluid-Structure Interaction Approach

Wing stiffness is very crucial in augmenting aerodynamic forces in flapping wing flyers. In this work, the effect of wing deformation was studied using three-dimensional numerical analysis (two-way fluid structure interaction), coupling the flow solver (FLUENT) and the structural (ABAQUS) solver via the MpCCI platform. Three different degrees of bending stiffness corresponding to rigid, flexible, and highly flexible case wings were investigated. Moreover, the wings were tested for both low Reynolds number (R=9,000) and high Reynolds number (R=40,000), at a flapping frequency of 9 Hz corresponding to an angle of attack (AoA) ranging from α=0 to 50°. The results of mean aerodynamic lift and drag coefficients showed good agreement between numerical and experimental findings. Also, the time-averaged lift-to-drag ratio reveals that the highly flexible wing exhibited the best overall aerodynamic performance when compared to the rigid and flexible wing.

Effect of Inertial and Constitutive Properties on Body-Freedom Flutter for Flying Wings

The class of high-altitude long-endurance aircraft often has very slender wings with minimal structure. This leads to large trim deflections and coupling between the vehicle flight dynamics and wing vibrations. When this coupled behavior becomes unstable, it is referred to as body-freedom flutter. Body-freedom flutter behavior is dependent on the inertial and constitutive properties of the wing, as well as the fuselage. This relationship is explored for an aircraft representative of the Horten IV flying wing, using an efficient yet rigorous analysis that relies on geometrically exact, fully intrinsic beam equations and a finite-state induced flow model, which is implemented in the computer code NATASHA (which stands for nonlinear aeroelastic trim and stability of high-altitude long-endurance aircraft). The wing inertial and stiffness properties were calculated using a realistic representative section using the section analysis tool called variational asymptotic beam section analysis. Trade studies on the body-freedom flutter behavior were performed by varying the fuselage properties and the internal wing structure, as well as examining the effects on the flutter speed, flutter frequency, and flutter mode shape.

Instantaneous wing kinematics tracking and force control of a high-frequency flapping wing insect MAV

The superior maneuverability of insect flight is enabled by rapid and significant changes in aerodynamic forces, a result of subtle and precise change of wing kinematics. The high sensitivity of aerodynamic force to wing kinematic change demands precise and instantaneous feedback control of the wing motion trajectory, especially in the presence of various parameter uncertainties and environmental disturbances. Current work on flapping wing robots was limited to open-loop averaged wing kinematics control. Here we present instantaneous closed-loop wing trajectory tracking of a DC motor direct driven wing-thorax system under resonant flapping. A dynamic model with parameter uncertainties and disturbances was developed and validated through system identification. For wing trajectory generation, we designed a Hopf oscillator based central pattern generator with smooth convergence. Using the linearized model while treating the nonlinearity as disturbance, we designed a proportional-integral-derivative (PID) controller and a linear quadratic regulator (LQR) for instantaneous wing trajectory tracking at 24 Hz; Using the original nonlinear model, we designed a nonlinear controller to achieve robust performance at over 30 Hz. The control algorithms were implemented and compared experimentally on a 7.5 g Flapping Wing Micro Air Vehicle (MAV). The experiments showed that the PID and nonlinear controls resulted in precise trajectory tracking; while LQR controller tracked with less precision but with smaller input effort. In addition, the nonlinear control algorithm achieved better tracking of wing trajectories with varying amplitude, bias, frequency, and split-cycles while adapting to the variations on wing morphological parameters such as wing geometry and stiffness. Furthermore, the lift force measurements of the nonlinear control results were compared with those of open-loop average wing kinematics control commonly adopted in current designs.

Measurement of Vibrational Stiffness and Air Damping of Damselfly Wings

A simple cantilever beam vibration test method made of biomorph and insect wing, were used to measure the vibrational stiffness and the air damping of insect wings. Vibration tests were performed in vacuum pressures to atmosphere and the wing stiffness and air damping factor were measured. The test method was found to be a viable method for measuring wing stiffness, natural frequencies and mode shapes. The vibrational deformation of the insect wings was found to be combination of bending and torsion because of unsymmetrical geometry of wing. The measured stiffness (K) of damselfly wings varied from 0.18 to 0.31 N/m and the air damping ratio ranged from 0.72 to 0.79. The undamped natural frequency (fn) at 13 kPa varied from 249 to 299 Hz and at atmosphere it varied from 168 to 198 Hz.

Organization of the dorsoventral musculature in the wings of the pteropod mollusc Clione limacina

AbstractThe wings of the pteropod mollusc Clione limacina provide forward propulsive force through flapping movements in which the wings bend throughout their length in both dorsal and ventral directions. The musculature of the wings includes oblique, striated muscle bundles that generate the swimming movements of the wings, longitudinal and transverse (smooth) muscle bundles that collapse the wings and pull them into the body during a wing withdrawal response, and dorsoventral muscles that control the thickness of the wings. All muscles act against a hydrostatic skeleton that forms a central hemocoelic space within the wings. Of these muscle types, all have been thoroughly described and studied except the dorsoventral muscles. The fortuitous discovery that the dorsoventral musculature can be intensely labeled with an antibody against the vertebrate hyperpolarization‐activated cation channel (HCN2) provided the opportunity to describe the organization of the dorsoventral musculature in detail. In addition, electrical recordings and microelectrode dye injections supported the immunohistochemical data, and provided preliminary data on the activity of the muscle fibers. The organization and activity of the dorsoventral musculature suggests it may be involved in regulation of wing stiffness during the change from slow to fast swimming.

Torsional spring is the optimal flexibility arrangement for thrust production of a flapping wing

While it is understood that flexibility can improve the propulsive performance of flapping wings and fins, the flexibility distribution leading to optimal performance has not been explored. Using 2D small-amplitude theory and a fast Chebyshev method, we examine how thrust depends on the chord-wise distribution of wing stiffness. Through numerical optimization, we find that focusing flexibility at the wing’s front, e.g., through a torsional spring, maximizes thrust. A wing with an optimally chosen spring constant typically generates 36% more thrust than a wing of optimal uniform stiffness. These results may relate to material distributions found in nature, such as insect wings, and may apply to the design of biomimetic swimmers and flyers, such as ornithopters.

Aerodynamic performance of two-dimensional, chordwise flexible flapping wings at fruit fly scale in hover flight

Fruit flies have flexible wings that deform during flight. To explore the fluid-structure interaction of flexible flapping wings at fruit fly scale, we use a well-validated Navier–Stokes equation solver, fully-coupled with a structural dynamics solver. Effects of chordwise flexibility on a two dimensional hovering wing is studied. Resulting wing rotation is purely passive, due to the dynamic balance between aerodynamic loading, elastic restoring force, and inertial force of the wing. Hover flight is considered at a Reynolds number of Re = 100, equivalent to that of fruit flies. The thickness and density of the wing also corresponds to a fruit fly wing. The wing stiffness and motion amplitude are varied to assess their influences on the resulting aerodynamic performance and structural response. Highest lift coefficient of 3.3 was obtained at the lowest-amplitude, highest-frequency motion (reduced frequency of 3.0) at the lowest stiffness (frequency ratio of 0.7) wing within the range of the current study, although the corresponding power required was also the highest. Optimal efficiency was achieved for a lower reduced frequency of 0.3 and frequency ratio 0.35. Compared to the water tunnel scale with water as the surrounding fluid instead of air, the resulting vortex dynamics and aerodynamic performance remained similar for the optimal efficiency motion, while the structural response varied significantly. Despite these differences, the time-averaged lift scaled with the dimensionless shape deformation parameter γ. Moreover, the wing kinematics that resulted in the optimal efficiency motion was closely aligned to the fruit fly measurements, suggesting that fruit fly flight aims to conserve energy, rather than to generate large forces.

Body Freedom Flutter of a Blended Wing Body Model Coupled with Flight Control System

Aeroservoelastic model is developed for a blended wing body aircraft coupled with flight control system. Body freedom flutter of such aeroservoelastic system is analyzed and trend studies considering varied loop gain value, center of gravity of the balanced weight and wing stiffness are delivered to determine their influence on body freedom flutter characteristics of this aeroservoelastic system. It is found that the closed loop flutter speed decreases dramatically compared to that of the open loop case. The loop gain value and the wing stiffness have strong influence on the closed loop flutter characteristics. It is noted that the static unstable unaugmented blended wing body aircraft can be stabilized by proper designed flight control system, however, the closed loop body freedom flutter speed is still quite low which needs further consideration in flight control system synthesis.

Optimization of Flexible Flapping-Wing Kinematics in Hover

Hover-capable flapping-wing micro air vehicles are well suited for missions in confined spaces. The best design practices for flapping wings and their kinematics are largely unknown, especially for flexible wings. To address this issue, numerical optimization is applied to the design of the kinematics and structural sizing of a flapping wing using a surrogate-based approach. The surrogates are generated using kriging interpolation of the time-averaged thrust generated and power required by the wings. The thrust and power data are computed using a nonlinear approximate aeroelastic model developed in previous studies by the authors. A numerical optimization algorithm is used to identify designs that produce the desired combination of thrust and power. The design variables consist of parameters describing the flap–pitch kinematics and the stiffness of the flexible wings. A trend study of thrust and power indicate that the phase angle between flap and pitch motions significantly affects the wing performance when the stroke amplitudes and the frequency are fixed. Smaller amounts of pitch actuation produced peak thrust in flexible wings when compared to the rigid wings. Several flexible configurations produce higher thrust when compared to the best thrust-producing rigid configuration. However, rigid wings have higher propulsive efficiency when compared to flexible wings for the same amount of generated thrust. Thus, the actual design of a flapping wing will depend on the relative importance given to thrust production and propulsive efficiency.

Membrane muscle function in the compliant wings of bats

Unlike flapping birds and insects, bats possess membrane wings that are more similar to many gliding mammals. The vast majority of the wing is composed of a thin compliant skin membrane stretched between the limbs, hand, and body. Membrane wings are of particular interest because they may offer many advantages to micro air vehicles. One critical feature of membrane wings is that they camber passively in response to aerodynamic load, potentially allowing for simplified wing control. However, for maximum membrane wing performance, tuning of the membrane structure to aerodynamic conditions is necessary. Bats possess an array of muscles, the plagiopatagiales proprii, embedded within the wing membrane that could serve to tune membrane stiffness, or may have alternative functions. We recorded the electromyogram from the plagiopatagiales proprii muscles of Artibeus jamaicensis, the Jamaican fruit bat, in flight at two different speeds and found that these muscles were active during downstroke. For both low- and high-speed flight, muscle activity increased between late upstroke and early downstroke and decreased at late downstroke. Thus, the array of plagiopatagiales may provide a mechanism for bats to increase wing stiffness and thereby reduce passive membrane deformation. These muscles also activate in synchrony, presumably as a means to maximize force generation, because each muscle is small and, by estimation, weak. Small differences in activation timing were observed when comparing low- and high-speed flight, which may indicate that bats modulate membrane stiffness differently depending on flight speed.

Fluid–structure interaction in compliant insect wings

Insect wings deform significantly during flight. As a result, wings act as aeroelastic structures wherein both the driving motion of the structure and the aerodynamic loading of the surrounding fluid potentially interact to modify wing shape. We explore two key issues associated with the design of compliant wings: over a range of driving frequencies and phases of pitch-heave actuation, how does wing stiffness influence (1) the lift and thrust generated and (2) the relative importance of fluid loading on the shape of the wing? In order to examine a wide range of parameters relevant to insect flight, we develop a computationally efficient, two-dimensional model that couples point vortex methods for fluid force computations with structural finite element methods to model the fluid–structure interaction of a wing in air. We vary the actuation frequency, phase of actuation, and flexural stiffness over a range that encompasses values measured for a number of insect taxa (10–90 Hz; 0-π rad; 10−7–10−5 N m2). We show that the coefficients of lift and thrust are maximized at the first and second structural resonant frequencies of the system. We also show that even in regions of structural resonance, fluid loading never contributes more than 20% to the development of flight forces.