Critical Flutter Speed Research Articles

Research on the flutter characteristics of folding wings with variable swept angles of the outer wing

The critical flutter speed, along with the associated stability and safety of a folding-wing aircraft, has been evaluated for variable wing configurations based on traditional designs. Through theoretical analysis and numerical simulation validation, the contributions of parameters such as the hinge stiffness, sweep angle, and folding angle on the flutter and stability of the folding wing are investigated in detail. It is observed that under a specified safe hinge stiffness, the proposed variable-sweep folding-wing configuration can enhance the critical flutter speed at a dangerous folding angle. Through the joint manipulation of the folding and sweep angles, the aerodynamic drag of the folding wing was reduced, thereby enhancing its flight speed and flutter boundaries. This paper aims to provide novel insights into the design and stability analysis of variable-wing configurations.

Aerodynamic and flutter performance of the bridge deck with various countermeasures using computational fluid dynamics

Aerodynamic layouts of bridge decks considerably affect aerostatic torsional divergence and flutter for bridges. The crucial operation is choosing the optimal bridge deck shape considering the aerodynamic effect. The present study intends to provide a better solution for the flutter control scheme by changing five aspect ratios and four passive aerodynamic countermeasures. The countermeasures are an eccentric wing, inspection rail, down vertical central stabilizer and wind barrier, which have been used for three deck shapes: streamlined, semi-streamline and bluff body sections with large angles of attack. Nowadays, wind barriers are frequently installed on bridges to shield vehicles from the harmful effects of crosswinds, which can influence the flutter characteristics of the bridge. Therefore, the present study contemplates reducing the flutter effect with countermeasures. These countermeasures adversely affect the deck’s dynamic stability, mainly manifested in the different divergence forms of the structure. Finally, the eccentric wing, which runs parallel to the bridge deck, increases the critical flutter speed. However, the flow that passes through the eccentric wing extracts considerable energy from the flow field of the countermeasure. Therefore, the framework and solution of the present investigation are sustainable and safe for bridge design.

Simulasi Numerik Aeroelastik Model Seksional 2D Jembatan Bentang Panjang untuk Mengetahui Karakteristik Ketidakstabilan Flutter

Flutter is an aerodynamic instability on a long span bridge that can cause damage to the entire bridge deck structure. The interaction between wind and structure in long span bridges can be investigated by numerical simulation. In this study, an aeroelastic simulation was performed on a 2 DoFs sectional model of a long-span bridge deck with free vibration techniques to analyze flutter speed and determine the effect of deck shape on flutter instability characteristics using ANSYS software. The simulation result data was then extracted using the Modified Ibrahim Time-Domain Method (MITD) identification method to obtain the damping ratio and flutter derivatives coefficients. The damping ratio value is used to determine the critical flutter speed, whereas the coefficient flutter derivatives is used to determine the characteristics of flutter instability and the flutter mechanism that occurs in the bridge. The results showed that the rectangular shape (bluff body) is more susceptible to flutter instability than the streamlined shape, and has a lower flutter speed value than the other shapes. The flutter mechanism that occurs is torsional flutter, whereas in the streamline body is coupling flutter.

Modelling and analysis of two-dimensional static and dynamic aeroelasticity of Fish Bone Active Camber morphing aerofoils

As a continuous and smooth morphing concept for aerofoils, the Fish Bone Active Camber (FishBAC) concept has demonstrated significant aerodynamic efficiency improvements over traditional hinged flaps. In this paper, to investigate the static and dynamic aeroelasticity of FishBAC aerofoils, an unsteady two dimensional coupled fluid-structure interaction model is developed, which includes the structural response of the FishBAC spine, skin, stringers, tendons and actuator, coupled to an unsteady aerodynamics model. The structural dynamic model is Timoshenko beam-theory-based, while the aerodynamic model is based on Peters’ unsteady model. The static and dynamic aeroelasticity is studied after the model is validated. Results show that the increase in pulley rotational angle reduces the zero-lift angle of attack, while keeping the slope between the lift coefficient and angle of attack the same. A shorter morphing region closer to the trailing edge is beneficial for generating larger lift coefficient with the same tendon moment and angle of attack. Flutter occurs with the increase of the air speed. When the morphing end position is fixed at 0.9 chord, increasing the morphing length reduces the critical flutter speed significantly, with the second bending mode tending to drive instability. With the same morphing length, moving the morphing region closer to the leading edge increases the critical flutter speed, and the unstable mode changes from the second mode into the first mode.

Wind tunnel bench test of a pitch-and-plunge aeroelastic model undergoing nonlinear post-flutter oscillations

The nonlinear post-flutter aeroelastic behavior of a classical pitch-and-plunge airfoil model in low-speed wind tunnel bench tests is reported in this study for a range of airflow speeds where stable oscillations are observed. An experimental airfoil prototype is designed, characterized and evaluated. Time domain data of the airfoil motion as well as other pertinent frequency and bifurcation characteristics are presented for different values of airflow speed, starting at the critical linear flutter speed of the airfoil model and increasing up to the sudden manifestation of violent unstable oscillations (when the test is interrupted for the safety of the structural apparatus). Stable post-flutter nonlinear oscillations, mainly attributed to the dynamic stall phenomenon and in a lesser degree to hardening structural effects, are observed for a range of airflow speeds starting at the neutral stability boundary of the aeroelastic system. The amplitudes of oscillation increase with increasing airflow speed and settle onto a limit-cycle. The coupled frequency of oscillation is dominated by the plunge degree-of-freedom and also increases with increasing airflow speed. The observed critical airfoil cut-in speed of limit-cycle onset is about 8.1 m/s (reduced speed of 5.1), and the observed cut-out speed of unstable response is about 9.5 m/s (reduced speed of 6.0). This work contributes with the literature of Aeroelasticity by presenting the realization, evaluation, and wind tunnel test data of a pitch-and-plunge airfoil model undergoing nonlinear post-flutter oscillations that may be useful to support other studies for verification purposes of eventual numerical simulations of similar aeroelastic systems.

Experimental studies of the influence of elastic-dissipative parameters of engine mounting units on the dynamic characteristics of the “wing model – elastic pylon – engine” system

A feature of modern heavy transport aircraft is their layout with engines on elastic pylons under the wing, with the fuel tanks located in the wing consoles. In this case, the main elastic tones of the aircraft’s own oscillations, which determine its dynamic response to external disturbing influences, include the so-called motor tones (vertical and horizontal (lateral) oscillations of engines on elastic pylons). A new type of flutter has appeared – pylon, which for some aircraft determines the critical flutter speed of the aircraft as a whole. The main reason for this phenomenon is the low oscillation damping of the engine on the pylon under the wing. Therefore, research aimed at modernizing the engine mounting points on the pylon in order to reduce the level of elastic oscillations during aircraft operation seems relevant. One of the possible ways to solve this problem is to use the concept of a freed engine, when the engine attachment points to the pylon are modernized, providing more effective damping of engine oscillations. In order to confirm the possibility of practical implementation of these solutions, corresponding experimental studies were carried out on an experimental setup developed by the authors. A design of engine mounting units has been developed that allows specified displacements of the engine relative to the pylon during forced elastic oscillations of the system, which includes a hinged suspension, installation of additional elastic elements and hydraulic dampers.The article presents the results of studies of the influence of elastic-dissipative parameters (partial frequency of natural oscillations and partial decrement of oscillations) of an engine mount on an elastic pylon on the dynamic characteristics of the dynamic system “wing model – elastic pylon – engine”. It is shown that by introducing specially designed engine suspension units on pylons, it is possible to significantly change the dynamic characteristics (frequencies and amplitudes of natural oscillations) of the elastic system as a whole. Thus, the amplitudes of oscillations of the engine’s center of mass in the region of motor tones decrease by 3...7 times during forced harmonic oscillations.

Development of a low-cost flutter test bed with an EPS foam model for preliminary wing design

This paper discusses a novel, low-cost approach for the design and testing of a flutter test article made out of expanded polystyrene (EPS) foam. The low mass of this test article makes it especially suitable for serving as a test bed for similar low structure-to-fluid mass ratio wing configurations, though it could just as easily be used as the first step in the flutter testing of any structure with complex shape and mechanical properties. The material properties of EPS foam were tested using two different approaches: a 3-point bending test based on ASTM Standards for cellular materials and a new finite element model updating approach that used experimental data collected from simple ground vibration tests (GVT). It was found that the second approach provided material properties that were the most representative of the behavior of the specimen under flutter loads. That information was then used in a computational aeroelastic flutter model of the EPS foam wing. Wind tunnel flutter tests were performed for the EPS foam model. The computational frequency domain decomposition (CFDD) method was used to identify modal parameters and the damping trend extrapolating method was used to predict the critical flutter speed from pre-flutter experimental data. The flutter results from the aeroelastic model were in good agreement with the test data.

Bistable dual cantilever flutter for potential wind energy harvesting applications

This paper examines the potential of bistable dual cantilever flutter (DCF) for wind energy harvesting applications. Two cantilever beams were placed side by side and perpendicular to the direction of the wind flow to create a unique phenomenon known as the DCF. Similar pole magnets were then attached to the free end of each beam to establish a bistable condition. A theoretical model was presented and was shown to agree well with the experimental measurement. The mass of the magnets caused the frequency of the beams to drop by approximately 4.5 times compared to the monostable DCF. When the two beams were placed 21.0 mm apart, the bistable beams achieved a stable state at a critical flutter speed of 5.3 ms−1 and displayed significantly large, anti-phase oscillations that is approximately three times larger than the monostable DCF. Further increase in this distance showed a decreasing trend with the critical flutter speed, which opposes the expected trend of the monostable DCF. Due to the bistable effect, significant flutter amplitudes were also obtained during a backward sweep when the wind speeds were incrementally reduced from high to low, recording a 73.2 % increase in bandwidth for one of the tested cases. This suggests the possibility of an ultra-wide bandwidth energy harvester. Finally, it was shown that the piezoelectric conversion method is more favourable for the bistable DCF whereas electromagnetic induction is preferred for the monostable DCF.

Нелинейный флаттер переходного процесса наследственно-деформируемых систем при сверхзвуковом режиме полета

In this paper, the problem of nonlinear flutter of a transient process of a hereditarily deformable wing of an aircraft moving at supersonic speed is considered. The aim of the work is to study the flutter problem for plate elements of aircraft in a gas flow under loads caused by atmospheric turbulence. Aerodynamic effects are specified according to the linearized piston theory. Nonlinear wing oscillations are described by a system of nonlinear integro-differential equations. They are solved numerically by the method proposed by F. Badalov, which is based on the Bubnov–Galerkin method, finite difference method, and power series. Free vibration is analyzed under conditions of ideal elasticity with account for a hereditarily deformable thin wing. The displacements of characteristic points of the wing under flutter conditions are comparatively assessed. It is established that aerodynamic nonlinearity has little impact on the critical speed, but with an increase in the Mach number, this impact increases. The mechanical effect of a significant dependence of the critical flutter speed on the relaxation kernel amplitude and Poisson's ratio is revealed.

Parametric optimisation of a dual cantilever flutter for electromagnetic wind energy harvesting

This paper investigates the parametric optimisation of dual cantilever flutter (DCF) beams for electromagnetic wind energy harvesting application. When two cantilever beams are placed side by side facing the direction of the wind flow, both beams would oscillate in an anti-phase motion once the critical flutter speed has been achieved. This arrangement is known as the DCF and it represents an ideal situation for energy harvesting through electromagnetic induction due to its anti-phase motion. Experimental results showed that the optimum load resistance value for the device is equivalent to a single-degree-of-freedom vibration energy harvester for low electromagnetic coupling case, despite the difference in the type of oscillations. Further analysis showed that there among the two possible arrangements for the magnets one arrangement results in a 51.5% larger magnetic flux density. It was seen that reducing the length of the electromagnetic DCF by 41.2% can increase the power output of the device by approximately six times, although the critical flutter speed also increased by 125.0%. Finally, some suggestions were provided on how to further improve the device.

An improved linear parameter-varying modeling, model order reduction, and control design process for flexible aircraft

This paper presents an improved process for the modeling, model order reduction (MOR), and control design of a flexible flying wing unmanned aerial vehicle based on the linear parameter-varying (LPV) technology. By applying the Lagrangian formulation and doublet lattice method, the aeroservoelastic (ASE) model of the flexible aircraft is first derived and then rewritten as an airspeed-dependent LPV system, which consists of rigid-body states, structural modes, aerodynamic states, etc. This leads to a high-order LPV model, and the stability of the system varies from stable to unstable when the speed of the aircraft exceeds the critical flutter speed. To facilitate the control design, an oblique projection-based MOR method is then adopted to reduce the order of the plant. Different from previous studies, the MOR method is improved to systematically generate a reduced-order LPV model with consistent states for both the stable and unstable dynamics parts. Finally, an output-feedback LPV controller is designed to simultaneously achieve the body freedom flutter suppression and longitudinal attitude control. Numerical simulation results show the effectiveness of the improved LPV-based ASE modeling, order reduction, and control design process for the flexible aircraft.

Stochastic flutter analysis of a three-degree-of-freedom airfoil under vertical turbulence disturbance

This paper investigates the nonlinear stochastic dynamic response of a three-degree-of-freedom(3-DOF) airfoil with high substructural nonlinearity under vertical turbulent disturbances. Considering a two-dimensional flow field, the Dryden turbulence model is used to describe the vertical turbulent disturbance, and a nonlinear stochastic aerodynamic model based on the Theodorsen theory is established for the stochastic flutter problem of the wing. An analysis is conducted to reduce the dimensionality of the airfoil system and solve the critical flutter velocity of the system. The Monte-Carlo method is applied to analyze the stochastic P-bifurcation problem of the system, and the effects of parameters such as the incoming velocity, turbulence scale and intensity on the stochastic dynamics behavior of the system are clarified. It is shown that the amplitude of the steady-state oscillation of the system increases with the incoming velocity and turbulence intensity, whereas the critical flutter speed decreases with increases in these parameters.

Prediction and suppression of chaos following flutter in wind turbines

Chaotic motion in a fluttering wind turbine blade is investigated by the development of an efficient analytical predictive model that is then used to suppress the phenomenon. Flutter is a dynamic instability of an elastic structure in a fluid, such as an airfoil section of a wind turbine blade. It is presently modelled using generalised two degree of freedom coupled modes of a blade airfoil section (pitch and plunge) combined with local unsteady aerodynamics, based on flutter derivatives and a continuous bilinear lift curve under damping. The mode coupling causes instability and limit cycle flutter due to a Hopf bifurcation. Following the critical flutter speed, the response can transition to chaos through successive other bifurcations like period doubling. New closed-form conservative analytical conditions for chaos following blade flutter are identified and discussed for the wind turbine section taking into account the blade geometry and optimal design of the wind turbine. These predictions are numerically verified for a range of conditions including stall slope and damping. The results confirm that chaos following blade flutter can occur due to nonlinearities in the aerodynamics, i.e. due to a bilinear lift law. This phenomenon is then suppressed to unrealistically high wind speeds and/or eliminated by quantified variation of system parameters using the predictive model. The results show that small changes in tip speed ratio (−15%), and stall slope factor (−17%) can eliminate or suppress chaos following flutter, while, in general, larger magnitude changes in dynamic parameters (i.e. mass, inertia > 81%, stiffness > 97%, damping > 100%) are required to achieve the same, by detuning the coupled plunge and pitch natural frequencies or damping out overlapping parametric resonances. These results also highlight that the analytical predictions can remarkably be generalized to any parameter set and provide almost instantaneous calculations representing many thousands of numerical simulations from many bifurcation diagrams (computational acceleration factor of 107 times). General insight is also provided into the occurrence and suppression of airfoil chaos following flutter in aeroelastic structures like wind turbines.

Partial Feedback Linearized RISE Controller for Active Flutter Suppression

In this paper, Robust Integral of Sign of Error (RISE) based partial feedback linearized controller for active flutter suppression (AFS) of a two dimensional aerofoil is proposed. The aeroelastic system has two degrees of freedom i.e. pitch and plunge. To design the controller, linearized pitch dynamics of the aerofoil is considered. A significant feature of the proposed controller is that it does not need an accurate model of the plant as well as any knowledge of external disturbance or parametric uncertainty. Zero dynamics stability and closed loop stability of the overall system have been established. Simulations prove the robustness and efficacy of the designed controller against variation in free stream velocity, parametric uncertainty and external disturbances as compared to existing designs. Results prove that the designed controller has increased the flutter boundary by 48% more than critical flutter speed.

Supersonic flutter characteristics of dielectric rectangular plate: The effects of magneto-aero-hydrodynamic interactions

This paper offers the authors’ views on critical magneto-aeroelastic behavior for dielectric rectangular isotropic plates. Magneto-aeroelastic stability and dynamic models are used to determine the total perturbed pressure caused by the incident flow of a perfectly conducting supersonic gas and a magnetic field as well as the critical flutter speed of flowing stream. The analytical description presented here is a generalization of the well-known pressure’s formula obtained on the basis of the “piston theory” of the classical theory of gas dynamics in the case of a magneto-hydrodynamic flow of elastic plates. Along with the analytical solutions, parametric studies are supplied to inform the reader about the influence of magnetic field on the flutter boundary.

A cost-effective algorithm for the co-simulation of unsteady and non-linear aeroelastic phenomena

Increasingly flexible structures force engineers and scientists to improve simulation capabilities incorporating an adequate description of non-linear phenomena. Furthermore, many critical operating conditions of aeronautical and civil structures are associated with unsteady phenomena, which makes it necessary to tackle this kind of problems. A critical aspect to be analyzed is the stability of the system: the determination of, not only the critical flutter speed, but also the post-critical behavior, is fundamental to guarantee the safety of designs and determine mitigation strategies. In this work, a numerical technique that allows simulating the non-linear and unsteady behavior of highly flexible structures immersed in a fluid at high Reynolds numbers is presented. This problem is addressed using a co-simulation approach, coupling the Unsteady Vortex Lattice Method (as the aerodynamic model) with the Finite Element Method using non-linear beams and rigid bodies (as the structural dynamics model). The coupling is achieved through a weak interaction algorithm. The resulting method has a very good compromise between versatility and computational cost, and is not restricted to periodic motions or linear equations of motion. Nonlinearity is included through the possibility to represent large displacements and rotations of the structure, a visco-elastic material behavior, and a nonlinear relation between the aerodynamic loads and the incidence of the incoming flow. The domains considered in the submodels and the temporal and spatial discretizations used for each one are essentially different; the interaction process must take into account these aspects. The computational implementation is carried out by combining a general-purpose structural dynamics code with an aerodynamic tool oriented to the analysis of three-bladed horizontal axis wind turbines. Examples to validate the code and show the potential of the proposed method are presented in the Results section.

The impact of the wind attack angle on a typical bridge deck’s flutter behavior by the distributed aerodynamic characteristics method

To investigate the influence of the wind attack on a bridge deck’s flutter performance, the concept of “pressure flutter derivatives” was introduced as a part of the “distributed aerodynamic characteristics” method, which can be used to visualize the dominant fluctuations of the pressure field. The distributions of the aerodynamic damping and stiffness under different wind attack angles were visualized, instead of using an overall force perspective. The analysis was carried out through two-dimensional computational fluid dynamics simulations based on a typical box deck section. Necessary data were obtained through the forced vibrations of the deck. The dominant pressure fluctuations were demonstrated, around which the wind attack angles’ impact on the Scanlan flutter derivatives was discussed. For the deck section used in this study, the wind attack angle was found to most affect the windward parts of the deck. When wind attack angle ranged from − 1.5 ° to 3 ° , two regions contributed the most: one located behind the windward faring vertex and the other located behind the first vertex of the upper slab. When the wind attack angle decreased to − 3 ° , a new dominant region appeared behind the first vertex of the lower slab, which caused a sudden reduction of the flutter critical speed.

Structurally Nonlinear Fluttering of a Three-Degree-Freedom Wing with Random Disturbances

The differential equations of motion are established for a three-degree-freedom wing dynamic model subjected to unsteady aerodynamic loads and random perturbations. The system is dimensionally reduced by the improved average method to obtain the standard equations. Flutter problems of the deterministic wing system with high-order structural nonlinearity are studied using Hopf bifurcation theory and numerical simulation, the critical flutter speed is obtained and the effectiveness of the improved average method in the process of dimensionality reduction is verified. The stochastic P-bifurcation behaviors of the system are analyzed considering the effects of random perturbations of the longitudinal airflow by examining the qualitative variations of the probability density function curves. The results show that the deterministic wing system has a secondary bifurcation, a bistable phenomenon in which the equilibrium and the limit cycle oscillations coexist. The random disturbances significantly increases the critical flutter speed of the wing system, and the amplitude of limit cycle oscillations increases after including random perturbations for the same incoming flow speed.

Aeroelastic tailoring of composite rudder skin considering variable angle tow laminates by a hybrid backtracking search-JAYA-Sine Cosine Algorithm

Flutter is a typical dynamic instability phenomenon of the wing or rudder structure. Besides, the phenomenon of aerodynamic heating will be quite significant and temperature can rise rapidly with the increase of the flight speed, thermal flutter characteristics should be taken into consideration for the rudder structure of supersonic vehicle. To improve the thermal flutter characteristics of the rudder structure and meet the design requirements of a lightweight structure, this article optimizes the variable stiffness laminates of the skin on the premise of keeping the thickness of the skin unchanged, so as to improve the critical flutter speed of the rudder. A novel intelligent optimization algorithm named BJASCA, which is a hybrid algorithm coupling of Backtracking Search Algorithm, Sine Cosine Algorithm, and JAYA Algorithms is proposed in this article to improve the efficiency of structural optimization and this algorithm shows obvious advantages in searching global optima compared with several other algorithms. The finite element model and aerodynamic model of the rudder are established to calculate the critical flutter speed. The results represent that the rudder structure optimized by the BJASCA algorithm shows better flutter characteristics and the critical flutter speed can be increased by 76.4% compared with the un-optimized structure.

Stall flutter prediction based on multi-layer GRU neural network

The modeling of dynamic stall aerodynamics is essential to stall flutter, due to the flow separation in a large-amplitude pitching oscillation process. A newly neural network based Reduced Order Model (ROM) framework for predicting the aerodynamic forces of an airfoil undergoing large-amplitude pitching oscillation at various velocities is presented in this work. First, the dynamic stall aerodynamics is calculated by solving RANS equations and the transitional SST-γ model. Afterwards, the stall flutter bifurcation behavior is calculated by the above CFD solver coupled with structural dynamic equation. The critical flutter speed and limit-cycle oscillation amplitudes are consistent with those obtained by experiments. A newly multi-layer Gated Recurrent Unit (GRU) neural network based ROM is constructed to accelerate the calculation of aerodynamic forces. The training and validation process are carried out upon the unsteady aerodynamic data obtained by the proposed CFD method. The well-trained ROM is then coupled with the structure equation at a specific velocity, the Limit-Cycle Oscillation (LCO) of stall flutter under this flow condition is predicted precisely and more quickly. In order to predict both the critical flutter velocity and LCO amplitudes after bifurcation at different velocities, a new ROM with GRU neural network considering the variation of flow velocities is developed. The stall flutter results predicted by ROM agree well with the CFD ones at different velocities. Finally, a brief sensitivity analysis of two structural parameters of ROM is carried out. It infers the potential of the presented modeling method to depict the nonlinearity of dynamic stall and stall flutter phenomenon.