Critical Flutter Velocity Research Articles

Effects of Installation Angle on Energy Harvesting Performance of Airfoil-Based Piezoelectric Energy Harvester

This study introduces a novel optimization approach for airfoil-based flutter energy harvesters through installation angle adjustment, addressing a critical research gap in the field where previous studies have primarily focused on structural modifications. To investigate this unexplored avenue, we developed a flutter energy harvester with an adjustable installation angle mechanism, aiming to reduce critical flutter velocity, broaden operational bandwidth, and improve energy harvesting efficiency under low-speed airflow conditions. The performance characteristics of the harvester were comprehensively evaluated through both numerical simulations incorporating fluid–structure-electrical coupling and wind tunnel experiments conducted at four distinct installation angles (0°, 3°, 6°, and 9°). The experimental results demonstrated a significant correlation between installation angle and critical flutter velocity, showing a consistent reduction from 7.8 m/s at 0° to 7.2 m/s at 6°, and further decreasing to 6.3 m/s at 9°. Notably, optimal performance was achieved at a moderate installation angle of 3°, yielding a maximum output voltage of 12.0 V and power output of 0.58 mW, which substantially exceeded the baseline performance at 0° (10.9 V, 0.48 mW). However, further increasing the installation angle to 9° led to performance degradation, attributed to a premature aerodynamic stall, resulting in reduced output metrics of 7.9 V and 0.25 mW for voltage and power, respectively. These findings demonstrate a simple yet effective method for enhancing flutter energy harvesting performance in low-speed airflow conditions.

Flutter Mechanism of a Thin Plate Considering Attack Angles

It is well known that the flutter performance of a section is sensitive to the changing wind angles of attack. Exploring the thin plate’s flutter mechanism under different angles of attack is excellent, which helps understand inner flutter characteristics and ensures structural safety. This study investigated flutter derivatives of a thin plate with an aspect ratio of 40 under different wind angles of attack via the forced vibration technique. The otherness of aerodynamic damping and phase lag under different wind angles, which helps in understanding the flutter mechanism, are analyzed using the bimodal-coupled flutter method. It is shown that coupled vertical–torsional flutter dominated the flutter modality under 0° and 3° wind angles of attack. The critical flutter velocity dramatically decreased with increasing wind angles of attack which is attributed to the increasing negative aerodynamic damping induced by coupled self-excited forces and the decreasing positive aerodynamic damping induced by uncoupled self-excited forces. Moreover, the vertical motion lags behind the torsional motion under the 7° angle of attack, which was totally contrary to other angles of attack. Major works in this study reveal the aerodynamic mechanism of the weakened flutter performance of thin plates under large wind angles of attack and provide a reference for the flutter analysis of thin plates.

Active control of transonic airfoil flutter using synthetic jets through deep reinforcement learning

This paper presents a novel framework for the active control of transonic airfoil flutter using synthetic jets through deep reinforcement learning (DRL). The research, conducted in a wide range of Mach numbers and flutter velocities, involves an elastically mounted airfoil with two degrees of freedom of pitching and plunging oscillations, subjected to transonic flow conditions at varying Mach numbers. Synthetic jets with zero-mass flux are strategically placed on the airfoil's upper and lower surfaces. This fluid–structure interaction (FSI) problem is treated as the learning environment and is addressed by using the arbitrary Lagrangian–Eulerian lattice Boltzmann flux solver (ALE-LBFS) coupled with a structural solver on dynamic meshes. DRL strategies with proximal policy optimization agents are introduced and trained, based on the velocities probed around the airfoil and the dynamic responses of the structure. The results demonstrate that the pitching and plunging motions of the airfoil in the limited cycle oscillation (LCO) can be effectively alleviated across an extended range of Mach numbers and critical flutter velocities beyond the initial training conditions for control onset. Furthermore, the aerodynamic performance of the airfoil is also enhanced, with an increase in lift coefficient and a reduction in drag coefficient. Even in previously unseen environments with higher flutter velocities, the present strategy is achievable satisfactory control results, including an extended flutter boundary and a reduction in the transonic dip phenomenon. This work underscores the potential of DRL in addressing complex flow control challenges and highlights its potential to expedite the application of DRL in transonic flutter control for aeronautical applications.

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 pre-flutter 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.

Rational design of the aerodynamic rudder structure taking into account strength, rigidity and aeroelastic stability

The paper considers a design process of an aerodynamic rudder, which structure comprises the skin of constant thickness, a load-bearing structure and a trimmed nose that plays the role of an anti-flutter balancer. The aim of the work is to set and solve the design problem of a rational structural and technological solution of the rudder that meets the requirements of strength, rigidity, aeroelastic stability and minimum mass. To solve this problem, a design algorithm for the rudder, using topological and parametric optimization, is proposed. The main parameters of the design area and the trimmed nose required for topological optimization are determined. The ANSYS Workbench software package was used for the finite element analysis and topological optimization. Based on the results of optimization, post-processing was carried out. A structural and technological solution, that combines structural layouts with constant and variable width of the trimmed nose, was proposed. An analysis of the stress-strain state was carried out, and it was found that the designed structure meets the strength requirements for the given design case. A scheme for solving the parametric optimization problem of the rudder under the condition of aeroelastic stability is proposed. Within the framework of solving this problem, a flutter study was conducted, using a multi-mode model, which makes it possible to study the rudder and body-rudder flutter forms of an unmanned aerial vehicle (UAV) equipped with aerodynamic rudders. The results of the flutter study for the design mode of the UAV flight are obtained in the form of dependencies of the critical flutter velocity and frequency on the average width of the trimmed nose. The analysis of these dependencies allowed us to derive the optimal values of the trimmed nose parameters from the minimum weight condition for two rudder configurations: with a constant and variable width of the trimmed nose.

Approximate global mode method for flutter analysis of folding wings

The aircraft with folding wings benefits from the ability to transform its folding wings to adapt to various flight missions but suffers from the change of the wings’ aeroelastic characteristics as a result. To clarify the change, it is necessary to study the dynamical modeling of the folding wing and also its aeroelastic response. This paper proposes a novel approximate global mode method (AGMM) for dealing with complex boundary conditions and models a folding wing consisting of separate rectangular plates for nonlinear flutter analysis. A high-precision low-dimensional dynamical model of the folding wing is developed, which is first validated by comparing the modal results obtained from the AGMM model with those obtained from an equivalent finite element model and is also experimentally validated by a comparison of forced vibration responses. On this basis, an AGMM model of the folding wing in supersonic aerodynamic loads based on the piston theory is further developed. The critical flutter velocity at different folding angles and the aeroelastic response are comprehensively studied by simulations based on the model. The result shows that the first 7th-order modes are sufficient for obtaining a converged critical flutter velocity, which varies with geometric parameters and potentially increases by 714 %. In addition, the low-order torsional modes of the wing contribute more to the vibration than the other modes during flutter. This work provides a new way of developing advanced dynamical modeling methods of folding and combinational structures for their dynamics design, optimization, and system control.

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.

Active flutter suppression on a flexible wing via leading-edge blowing and circulation control

Flutter is a classical aeroelastic phenomenon that seriously affects the performance of flexible wings. This study investigates flutter suppression through flow control for a flexible wing. Aerodynamic force, flow field, and dynamic aeroelastic response measurements are conducted to analyze the mechanism of flutter suppression through flow control on a flexible wing modified to include leading-edge blowing (LEB) and circulation control (CC) actuators around the wing tip. Furthermore, the flutter control effects of two control strategies, i.e., steady state control and proportion–integral–differential (PID) control, are compared. The results show that steady LEB and steady CC can effectively reduce the flutter amplitude and increase the critical flutter velocity. When the mass flow coefficient CQ≥1.46×10−3, the Coanda jet has better flutter suppression effect than the leading-edge jet. Moreover, a closed-loop CC control based on the PID algorithm demonstrates that PID control can effectively improve the flutter control efficiency. Compared to steady flow control, PID control increases the critical velocity by more than 52.60% and reduces the air consumption by 90.44%.

A study on dynamic characteristics of the flutter for three-layer plates and shells flown around by a gas flow

The nonlinear flutter of viscoelastic three-layer plates and shallow shells with a structure asymmetrical in thickness, flown around by a supersonic gas flow is studied in this paper. Mathematical models of problems on the flutter of viscoelastic three-layer plates, cylindrical panels, and shells with a structure asymmetrical in thickness, flown around by a supersonic gas flow are developed. The flutter of viscoelastic three-layer plates is studied in linear and nonlinear formulations. The critical flutter velocities of elongated plates are compared with the results obtained in previously published studies, where the solutions were obtained in an elastic formulation. The flutter of viscoelastic three-layer plates, cylindrical panels with a rigid filler that resists transverse shear, flown from the outside by a supersonic flow, was studied. It is shown that an increase in the geometric parameter characterizing the flexural rigidity of the bearing layers of three-layer structures leads to an increase in the flutter velocity by 25–40%.

Suppression of panel flutter in supersonic flow based on acoustic black hole as a linear energy sink

Panel flutter is a critical challenge for supersonic aircraft, impacting their structural integrity and safety. This study introduces a new method to suppress panel flutter in supersonic flow using an add-on acoustic black hole (AABH). Numerical simulations investigate the interaction between the panel and supersonic flow, comparing the panel only, panel with AABH, and panel with equivalent mass. Results show that the AABH increases the critical flutter velocity by 33.9%, outperforming the equivalent mass configuration (18.7%). The AABH acts as a linear energy sink with high damping and rich modal characteristics, transferring and dissipating energy from the supersonic flow effectively. This capability stabilizes the panel and reduces flutter amplitude, demonstrating the AABH's potential for supersonic flutter suppression.

Flutter Qualification of a Composite Light Trainer Aircraft (Csir-Nal Hansa - 3 (Vt-Hoa))

This paper presents the aeroelastic analysis and flight flutter tests aimed at ascertaining the freedom from flutter instability in the design flight envelope of a composite light trainer aircraft. The critical flutter, divergence and control reversal velocities of the complete aircraft were computed using MSC/NASTRAN and the typical section method. The results thus obtained from the analyses have been correlated with the ground vibration and flight flutter test results. The dispersion in the damping and frequency results obtained from computations and the flight flutter tests were within acceptable limits showing a good correlation. The flutter margins and the total damping of the aircraft satisfy the JAR-VLA/ FAR 23 requirements, thus enabling the aircraft to be type certified for the required flight safety standards.

Design Sensitivity Studies on the T-Tail Flutter of a Transport Aircraft

The studies of dynamic and aeroelastic characteristics of a high T-Tail transport aircraft at component and full level using MSC/NASTRAN code and correlation with the results obtained from ground vibration tests of the aircraft have thrown light on the complexities of the T-Tail dynamics and flutter characteristics. The critical flutter velocities of the complete aircraft have been evaluated by the PK and KE methods of NASTRAN. The effects of variability of the locations and magnitude of the non-structural masses in the fuselage on the T-Tail flutter velocities have been studied by a parametric analysis. Sensitivity study of the elevator mass balancing on its dynamics and the flutter velocities have also been addressed. The flutter velocities and margins have been examined from the certification aspects. Addressing design issues of the aircraft related to fuselage flexibility and T-Tail flutter from an aeroelastic point of view has been attempted in this paper.

Intelligent Identification and Verification of Flutter Derivatives and Critical Velocity of Closed-Box Girders Using Gradient Boosting Decision Tree

Flutter derivatives (FDs) of the bridge deck are basic aerodynamic parameters by which flutter analysis determines critical flutter velocity (CFV), and they are traditionally identified by sectional model wind tunnel tests or computational fluid dynamics (CFD) numerical simulation. Based on some wind tunnel testing results and numerical simulation data, the machine learning models for identifying FDs of closed-box girders are trained and developed via a gradient boosting decision tree in this study. The models can explore the underlying input–output transfer relationship of datasets and realize rapid intelligent identification of FDs without wind tunnel tests or numerical simulation. This method also provides a convenient and feasible option for expanding datasets of FDs, and the distribution of FDs can be analyzed through the post-interpretation of trained models. Combined with FD sensitivity analysis, the models can be verified by the calculation error of CFV. In addition, the proposed method can help determine the appropriate shape of the box girder cross-section in the preliminary design stage of long-span bridges and provide the necessary reference for aerodynamic shape optimization by modifying the local geometric features of the cross-section.

Data-driven prediction of critical flutter velocity of long-span suspension bridges using a probabilistic machine learning approach

Among the consequences of wind-induced excitation on long-span cable-supported bridges, flutter instability is the most dangerous and can collapse bridge structures. Until now, the flutter velocity of long-span bridges can be computed after conducting an experimental wind tunnel test or by means of computational fluid dynamics (CFD). However, the approaches mentioned above are cost-prohibitive and time-consuming especially when there are many sampling designs to evaluate. Therefore, it is crucial to develop an alternative solution for evaluating the flutter performance of such structures while minimizing the associated cost and computation time without worsening the accuracy of the results. Scholars have proposed machine learning (ML) techniques to address this issue. Unfortunately, some ML techniques do not provide excellent generalization for small datasets and are prone to bias even when the accuracy is relatively high. Besides, conventional ML models do not consider the uncertainty in data. This study proposes a probabilistic machine learning approach to overcome the weaknesses of the conventional ML models. The dataset used to train the proposed model was generated from 73 sampling designs using a fully numerical approach that involved 2D URANS (Unsteady Reynolds-averaged Navier-Stokes) CFD simulations, quasi-steady flutter theory, finite element model, and multi-mode approach for critical flutter velocity computation. The deck cross-section's most influential parameters and the critical flutter velocity constitute the datasets used to build the proposed probabilistic machine learning model. Our finding substantiates that the probabilistic machine learning approach based on hierarchical Bayesian modeling (PML-HBM) overperformed the conventional machine learning models, including extreme gradient boosting regression (XGBR), random forest (RF), and the support vector regression(SVR). Therefore, PML-HBM can accurately predict the critical flutter velocity. This model is an interesting approach to circumvent the time and cost associated with wind tunnel tests and CFD simulations at the earlier design stage of long-span bridge aerodynamic study.

Dynamic stability of cantilevered piping system conveying slug flow

In this paper, the dynamics and stability of a cantilevered piping system conveying slug flow are examined using the stable slug flow model and hysteretic model. The truncation technique of Galerkin and eigenvalue analysis are used to discrete and solve the model equations. The Argand diagrams and stability maps are employed to investigate the effects of superficial gas and liquid velocities and structural damping on the dynamics and stability of the system. The results showed that the increase of superficial gas velocities have a negative influence on the stability under the condition that the dimensionless liquid velocity is caused by the pipe length. In the process of the increase of the superficial gas velocity, the critical flutter velocity reduced and the system underwent several phenomena such as instability-restabilization-instability and mode exchange. However, the superficial liquid velocities have a positive effect on the stability, and the critical flutter velocities increased with it, which resulted in the stability boundary moving upward. It should be pointed out that its increase made the stability of the 4th mode worse and the vibration became more complex. Additionally, the structural damping could improve the stability of the high superficial gas velocity system. This work is helpful to design operating parameters to ensure the safety of the piping system.

Bending-torsional vibrations of aircraft wing

The problems of bending-torsional flutter of an aircraft wing are considered. Using equations of motion by the Bubnov-Galerkin method, based on the polynomial approximation of deflections and angle of twist, the problem is reduced to studying a system of ordinary integro-differential equations, where the independent variable is time. The solution of integro-differential equations with singular kernels is found by a numerical method based on quadrature formulas. The influence of physical-mechanical and geometric parameters on the flutter of the aircraft wing was studied. It was established that an account for the viscoelastic properties of the material of thin-walled aircraft structures leads to a 40-60% decrease in the critical flutter velocity. It is shown that an increase in the elongation parameter of an aircraft wing leads to a decrease in the flutter velocity.

Forced vibrations of hereditary deformable shell elements of aircraft structures in gas flow under influence of atmospheric turbulence

The problem of vibrations of thin, hereditarily deformable shell elements moving in a gas under the action of atmospheric turbulence is considered. The work aims to study the flutter phenomenon of aircraft elements in a gas flow under the action of loads caused by atmospheric turbulence. Assuming that the relationship between stresses and strains for the shell material is linear-hereditary, a thin shell is used, which obeys the Kirchhoff-Love hypothesis. The aerodynamic force is written according to the linearized piston theory. A system of nonlinear integro-differential equations in partial derivatives is obtained to describe nonlinear oscillations of a thin isotropic viscoelastic shell. The system of nonlinear integro-differential equations is solved numerically by the method proposed by F. Badalov, which is based on the Bubnov-Galerkin methods, finite differences, and power series. When using an exponential kernel, the flutter rate increases to approximately 1.5%. Therefore, when using an exponential kernel, the flutter velocity of a viscoelastic shell practically coincides with the critical flutter velocity for ideally elastic plates. It was also found that the critical flutter velocity increases with an increase in the number of pinched sides of the shell.

Nonplanar vibration and flutter analysis of vertically spinning cantilevered piezoelectric pipes conveying fluid

In this paper a dynamical model for vertically spinning cantilevered piezoelectric pipes conveying fluid is proposed. The partial differential equations of motion are derived by the Hamilton's principle in two different planes. The gyroscopic coupling, electromechanical coupling and gravitational effects are considered. The partial differential equations are discretized by the Galerkin's procedure. The complex eigenvalue calculation is used to find the critical flutter velocities. Then, dynamic trajectories and stability are discussed with regard to the flow velocity, resistive load, spinning speed and piezoelectric layer spanning angle. The results show that various stability evolution can be attainable by use of different flow velocities, resistive loads and spinning speeds. Attachment of piezoelectric layer can improve the stability of the pipe conveying fluid. Also, it is found that, depending on the resistive load, the system can be stabilized or destabilized by decreasing the spinning speed. The results of this study can be useful in designing electromechanical systems.

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.

The Impact of Critical Flutter Velocity in Composite Wind Turbine Blade with Prebend Condition

The present work focuses on the effect of flutter in prebend 100 m horizontal axis wind turbine blade (HAWT) within the stability limits. The study was carried out with an advanced beam model for idyllic structure in a DU-97-W-300 cross-sectional area. A Galerkin type of approach has been applied to derive the equations, and the analysis was performed using a standard FEA code which involves the PK method and double lattice method for calculating flutter solution and aerodynamic loads respectively. The results reveal the significance of inducing prebending to improve the stability of the blade structures, and hence, the flutter velocity has moved from 11 m/s to 23 m/s. Furthermore, the output highlights the effect of prebending on the structural stability and also the flutter limit was found to be lengthened.