Nonlinear metamaterial enabled aeroelastic vibration reduction of a supersonic cantilever wing plate

The violent vibration of supersonic wings threatens aircraft safety.This paper proposes the strongly nonlinear acoustic metamaterial(NAM)method to mitigate aeroelastic vibration in supersonic wing plates.We employ the cantilever plate to simulate the practical behavior of a wing.An aeroelastic vibration model of the NAM cantilever plate is established based on the mode superposition method and a modified third-order piston theory.The aerodynamic properties are systematically studied using both the timedomain integration and frequency-domain harmonic balance methods.While presenting the flutter and post-flutter behaviors of the NAM wing,we emphasize more on the preflutter broadband vibration that is prevalent in aircraft.The results show that the NAM method can reduce the low-frequency and broadband pre-flutter steady vibration by 50%-90%,while the post-flutter vibration is reduced by over 95%,and the critical flutter velocity is also slightly delayed.As clarified,the significant reduction arises from the bandgap,chaotic band,and nonlinear resonances of the NAM plate.The reduction effect is robust across a broad range of parameters,with optimal performance achieved with only 10%attached mass.This work offers a novel approach for reducing aeroelastic vibration in aircraft,and it expands the study of nonlinear acoustic/elastic metamaterials.

A New Approach for Aeroelastic Robust Stability Analysis

Air vehicles undergo variations in structural mass and stiffness because of fuel consumption and the failure of structural components, which might lead to serious influences on the aeroelastic characteristics. An approach for aeroelastic robust stability analysis taking into account the perturbations of structural mass and stiffness is developed. Applying the perturbation method and harmonic unsteady aerodynamic forces, the frequency-domain linear fractal transformation （LFT） representation of perturbed aeroelastic system is modeled. Then, the robust stability is analyzed by using the structured singular value ,u-method. The numerical results of a bi-spar wing show its effectiveness and low computational time in dealing with the robust problems with mass and stiffness perturbations. In engineering analysis for solving aeroelastic problems, the robust approach can be applied to flutter analysis for airplane with the fuel load variation and taking the damage conditions into consideration.

MULTI-BODY AEROELASTIC STABILITY ANALYSIS OF TILTROTOR AIRCRAFT IN HELICOPTER MODE

The muhi-body analysis of the aeroelastic stability of the tiltrotor aircraft is presented. Muhi-body dynamic differential equations are combined with the equations of the unsteady dynamic inflow model to establish the complete unsteadily aeroelastic coupling analytical model of the tiltrotor. The stability of the tiltrotor in the helicopter mode is analyzed aiming at a semi span soft-inplane tihrotor model with an elastic wing. Parametric effects of the lag stiffness of blades and the flight speed are analyzed. Numerical simulations demonstrate that the multibody analytical model can analyze the aeroelastic stability of the tiltrotor aircraft in the helicopter mode.

Analysis and Flexible Structural Modeling for Oscillating Wing Utilizing Aeroelasticity

Making use of modal characteristics of the natural vibration of flexible structure to design the oscillating wing aircraft is proposed. A series of equations concerning the oscillating wing of flexible structures are derived. The kinetic equation for aerodynamic force coupled with elastic movement is set up, and relevant formulae are derived. The unsteady aerodynamic one in that formulae is revised. The design principle, design process and range of application of such oscillating wing analytical method are elaborated. A flexible structural oscillating wing model is set up, and relevant time response analysis and frequency response analysis are conducted. The analytical results indicate that adopting the new-type driving way for the oscillating wing will not have flutter problems and will be able to produce propulsive force. Furthermore, it will consume much less power than the fixed wing for generating the same lift.

Structural Modeling and Aeroelastic Analysis of High-Aspect-Ratio Composite Wings

A unified structural model for high-aspect-ratio composite wing with arbitrary cross-section is developed. Two types of lay-ups of the composite wing, namely, circumferentially uniform stiffness （CUS） configuration and circumferentially asymmetric stiffness （CAS） configuration, are investigated. The present structural modeling method is validated through ANSYS FEM software for the case of a composite box beam. Then, the case of a single-cell composite wing with NACA0012 airfoil shape is considered. To investigate the aeroelastic problem of high-aspect-ratio composite wings, the linear ONERA aerodynamic model is used to model the unsteady aerodynamic loads under the case of small angle of attack. Finally, flutter speeds of the high-aspect-ratio wing with various composite ply angles are determined by using U-g method.

Performance enhancement of wing-based piezoaeroelastic energy harvesting through freeplay nonlinearity

We investigate experimentally how controlled freeplay nonlinearity affects harvesting energy from a wing-based piezoaeroelastic energy harvesting system. This system consisits of a rigid airfoil which is supported by a nonlinear torsional spring （freeplay） in the pitch degree of freedom and a linear fiexural spring in the plunge degree of freedom. By attaching a piezoelectric material （PSI-5A4E） to the plunge degree of freedom, we can convert aeroelastic vibrations to electrical energy. The focus of this study is placed on the effects of the freeplay nonlinearity gap on the behavior of the harvester in terms of cut-in speed and level of harvested power. Although the freeplay nonlinearity may result in subcritical Hopf bifurcations （catastrophic for real aircrafts）, harvesting energy at low wind speeds is beneficial for designing piezoaeroelastic systems. It is demonstrated that increasing the freeplay nonlinearity gap can decrease the cut-in speed through a subcritical instability and gives the possibility to harvest energy at low wind speeds. The results also demonstrate that an optimum value of the load resistance exists, at which the level of the harvested power is maximized.

Composite Rotor Blade Design Optimization for Vibration Reduction with Aeroelastic Constraints

The paper presents an analytical study of the helicopter rotor vibratory loadreduction design optimization with aeroelastic stability constraints. The composite rotor blade ismodeled by beam type finite elements, and warping deformation is taken into consideration for2-dimension analysis, while the one-dimension nonlinear differential equations of blade motion areformulated via Hamilton's principle. The rotor hub vibratory loads is chosen as the objectivefunction, while rotor blade section construction parameter, composite material ply structure andblade tip swept angle as the design variables, and au-torotation inertia, natural frequency andaeroelastic stability as the constraints. A 3-bladed rotor is designed, as an example, based on thevibratory hub load reduction optimization process with swept tip angle and composite material. Thecalculating results show a 24. 9 percent-33 percent reduction of 3/rev hub loads in comparison withthe base-line rotor.

APPLICATION OF HYBRID GENETIC ALGORITHM IN AEROELASTIC MULTIDISCIPLINARY DESIGN OPTIMIZATION OF LARGE AIRCRAFT

The genetic/gradient-based hybrid algorithm is introduced and used in the design studies of aeroelastic optimization of large aircraft wings to attain skin distribution,stiffness distribution and design sensitivity.The program of genetic algorithm is developed by the authors while the gradient-based algorithm borrows from the modified method for feasible direction in MSC/NASTRAN software.In the hybrid algorithm,the genetic algorithm is used to perform global search to avoid to fall into local optima,and then the excellent individuals of every generation optimized by the genetic algorithm are further fine-tuned by the modified method for feasible direction to attain the local optima and hence to get global optima.Moreover,the application effects of hybrid genetic algorithm in aeroelastic multidisciplinary design optimization of large aircraft wing are discussed,which satisfy multiple constraints of strength,displacement,aileron efficiency,and flutter speed.The application results show that the genetic/gradient-based hybrid algorithm is available for aeroelastic optimization of large aircraft wings in initial design phase as well as detailed design phase,and the optimization results are very consistent.Therefore,the design modifications can be decreased using the genetic/gradient-based hybrid algorithm.

Stiffness Distribution and Aeroelastic Performance Optimization of High-Aspect-Ratio Wings

The relationship between stiffness distribution and aeroelastic performance for a beam-frame model and a3-D model is investigated based on aeroelastic optimization of global stiffness design for high-aspect-ratio wings.The sensitivity information of wing spanwise stiffness distribution with respect to the twist angle at wing tip,the vertical displacement at wing tip,and the flutter speed are obtained using a sensitivity method for both models.Then the relationship between stiffness distribution and aeroelastic performance is summarized to guide the design procedure.By using the genetic/sensitivity-based hybrid algorithm,an optimal solution satisfying the strength,aeroelastic and manufacturing constraints is obtained.It is found that the summarized guidance is well consistent with the optimal solution,thus providing a valuable design advice with efficiency.The study also shows that the aeroelastic-optimization-based global stiffness design procedure can obtain the optimal solution under multiple constraints with high efficiency and precision,thereby having a strong application value in engineering.

Aeroelastic modeling of wind loading on a cable-net supported glass wall

Wind loading study on a cable-net supported glass wall is conducted by means of wind tunnel tests. An equiva- lent aeroelastic model is designed and constructed. Response of displacements of the wall is measured and analyzed. In order to design a glass wall under wind loading, the ＂wind- vibration factor＂ is estimated and discussed. In fact, the mech- anism of wind acting on the wall is commonly known not only as positive pressure, but also as negative pressure caused by the flow separation on the corners of the building. Due to the diffidence in the mechanism of wind acting, two typi- cal response cases are classified. The results show that the dynamic response of the structure caused by the negative pressure is stronger than that of the positive pressure case. To determine the aerodynamic wind loading on a flexible part of structure on a building, wind tunnel study may be useful and play an important role.

A modified airfoil-based piezoaeroelastic energy harvester with double plunge degrees of freedom

In this letter, a piezoaeroelastic energy harvester based on an airfoil with double plunge degrees of freedom is proposed to additionally take advantage of the vibrational energy of the airfoil pitch motion. An analytical model of the proposed energy harvesting system is built and compared with an equivalent model using the well-explored pitch-plunge configuration. The dynamic response and average power output of the harvester are numerically studied as the flow velocity exceeds the cut-in speed （flutter speed）. It is found that the harvester with double-plunge configuration generates 4%-10% more power with varying flow velocities while reducing 670 of the cut-in speed than its counterpart.

The Effect of Composite Flexures on Aeroelastic Stability of a Hingeless Rotor Blade

The effects of ply orientation angle of composite flexures on stability of hingeless rotor blade system are studied.The composite hingeless rotor blade system is simplified as a hub,a flap flexure and a lag flexure.pitch bearing and main blade.The kinematics formulations are inferred by employing the moderate deflection beam theory.The shear deformation and warping related to torsion are considered.The quasi-steady strip theory with dynamic inflow effects is applied to obtain the aerodynamic loads acting on the blade.Based on these.the set of finite element formulations of a hingeless rotor blade system is worked out.The numerical results show that the ply angle of the composite flexures has great effects on the aeroelastic stability of rotor blade.

Semi-analytical method for calculating aeroelastic effect of profiled rod flying at high velocity

The key technique of a kinetic energy rod(KER) warhead is to control the flight attitude of rods. The rods are usually designed to different shapes. A new conceptual KER named profiled rod which has large L/D ratio is described in this paper. The elastic dynamic equations of this profiled rod flying at high velocity after detonation are set up on the basis of Euler-Bernoulli beam, and the aeroelastic deformation of profiled rod is calculated by semi-analytical method for calculating the vibration characteristics of variable cross-section beam. In addition, the aeroelastic deformation of the undeformed profiled rod and the aeroelastic deformation of deformed profiled rod which is caused by the detonation of explosive are simulated by computational fluid dynamic and finite element method(CFD/FEM), respectively. A satisfactory agreement of these two methods is obtained by the comparison of two methods. The results show that the semi-analytical method for calculating the vibration characteristics of variable cross-section beam is applied to analyze the aeroelastic deformation of profiled rod flying at high velocity.

AEROELASTIC TAILORING OF AERONAUTICAL COMPOSITE WING STRUCTURES

This paper deals with the aeroelastic tailoring of aeronautical composite wing surfaces. The objective function is structural weight. Multi constraints, such as displacements, flutter speed and gauge requirements, are taken into consideration. Finite element method is used to the static analysis. Natural vibration modes are obtained by the spectral transformation Lanczos method. Subsonic doublet lattice method is used to obtain the unsteady aerodynamics.The critical flutter speed is generated by V-g method.The optimal problem is solved by the feasible direction method.The thickness of the composite wing skin is simulated by bicubic polynomials, whose coefficients combined with the cross-sectional areas or thicknesses of other finite elements are the design variables. The scale of the problem is reduced by variable linkage. Derivative analysis is performed analytically.Two composite wing boxes and a swept-back composite wing are optimized at the end of the paper.

Electroaeroelastic Modeling and Analysis for Flow Energy Piezoelectric Harvester

An electroaeroelastic model for wind energy harvesting using piezoelectric generators is presented.The flow field is mapped in detail.The force which the fluid flow exerts on the generator is formulated.The output voltage levels generated from the mechanical strain within the piezoelectric elements are determined.An analytical model is developed with consideration of the interactions between the fluid,solid and electric.Various analytical results are obtained,such as flow velocity contour and pressure contour for the flow,moving trajectories,stress contour and output voltage of the harvester.A prototype is fabricated and tested.The simulation result is close to the experimental result.The model developed in this paper can predict the performance and behavior of different energy harvesters.And it also can be used as a design tool for optimizing the performance of the harvester.

Optimal Control of Aeroelastic StochasticVibration of Aerocraft

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Control-Oriented Modeling and Simulation on Rigid-Aeroelasticity Coupling for Hypersonic Vehicle

Since the subsystems of aerodynamics,propulsion,structure and so on in hypersonic vehicles involve characteristics of nonlinearity,strong coupling and uncertainty,and typical hypersonic vehicles adopt slender-body and wave-rider layout with widely-used lightweight materials,the accuracy of the modeling with a conventional rigid-body assumption is challenged.Therefore,a nonlinear mathematical longitudinal model of a hypersonic vehicle is established with its geometry provided to estimate aerodynamic force and thrust using hypersonic aerodynamics and quasi-one-dimensional flow with heat added and capture vehicle aeroelasticity using a single free-free Bernoulli-Euler beam model.Then the static and dynamic properties of the rigid and rigid-aeroelasticity coupling model are compared via theoretical analysis and numerical simulation under the given flight condition.Finally,a LQR controller for rigid model is designed and the comparable results are obtained to explain the aerolasticity influence on the control effect.The simulation results show that the aeroelasticity mode of slender-body hypersonic vehicles affects short period mode significantly and it cannot be simply neglected.

Aeroelastic Responses for Wind Turbine Blade Considering Bend-Twist Coupled Effect

The Euler-Bernoulli beam model coupled with the sectional properties obtained by the variational asymptotic beam sectional analysis(VABS)method is used to construct the blade structure model.Combined the aerodynamic loads calculated by unsteady blade element momentum model with a dynamic inflow and the dynamic stall correction,the dynamics equations of blade are built.The Newmark implicit algorithm is used to solve the dynamics equations.Results of the sectional properties and blade structure model are compared with the multi-cell beam method and the ANSYS using shell elements.It is proved that the method is effective with high precision.Moreover,the effects on the aeroelastic response caused by bend-twist coupling are analyzed.Torsional direction is deflected toward the upwind direction as a result of coupling effects.The aerodynamic loads and the displacement are reduced.

Effects of static aeroelasticity on composite wing characteristics under different flight attitudes

Composite wing static aeroelasticity was analyzed through a loosely coupled method and the effects on composite wing characteristics under different flight attitudes were presented. Structural analysis and aerodynamic analysis were carried out through finite element method (FEM) software NASTRAN and computational fluid dynamics (CFD) software FLUENT, respectively. Correlative data transfer and mesh regenerate procedure were applied to couple the results of computational structure dynamics (CSD) and CFD. After static aeroelasticity analysis under different flight attitudes, it can be seen that lift increases with the increase of flight speed and the incremental value enlarges gradually in both rigid and elastic wings. Lift presents a linear increment relationship with the increase of attack angle when the flight speed is 0.4Ma or 0.6Ma, but nonlinear increment in elastic wing when flight speed is 0.8Ma. On the effect of aeroelasticity, the maximum of deformation increases with the increase of flight speed and attack angle, and the incremental value decreases with the increase of flight speed while uniform with different attack angles. The results provide a reference for engineering applications.

Nonlinear aeroelastic coupled trim and stability analysis of rotor-fuselage

Based on the Hamilton principle and the moderate deflection beam theory, discretizing the helicopter blade into a number of beam elements with 15 degrees of freedora, and using a quasi-steady aero-model, a nonlinear coupled rotor/fuselage equation is established. A periodic solution of blades and fuselage is obtained through aeroelastic coupled trim using the temporal finite element method （TEM）. The Peters dynamic inflow model is used for vehicle stability. A program for computation is developed, which produces the blade responses, hub loads, and rotor pitch controls. The correlation between the analytical results and related literature is good. The converged solution simultaneously satisfies the blade and the vehicle equilibrium equations.