Flutter Behavior Research Articles

Flutter behavior of a flexible airfoil: Multiparameter experimental study

The flutter behavior of a flexible airfoil is experimentally studied, with the goal to increase the flutter stability boundary due to the airfoil flexibility effect. The flexible airfoil concept is realized as an elastically supported symmetrical airfoil with a laminated composite plate attached to its trailing edge. A series of multiparameter wind tunnel flutter tests were conducted to investigate the flutter behavior of a flexible airfoil at various aeroelastic system configurations. The airfoil flexibility effect on the flutter behavior is studied in terms of two main dynamic properties of a flexible plate, the flexural stiffness and the areal density, which are introduced through two non-dimensional laminate design parameters. It is shown that the flutter behavior of a flexible airfoil is characterized by two types of flutter, namely the classical airfoil flutter and the plate flutter. The increase in the critical flutter speed due to airfoil flexibility effect is significant for aeroelastic system configurations with high plunge to pitch natural frequency ratios in the region of the aeroelastic system bimodal behavior, where the two types of flutter occur simultaneously. Furthermore, the experimental evidence of the bimodal behavior of the observed aeroelastic system is presented.

Analysis of Supersonic and Transonic Panel Flutter Using a Fluid-Structure Coupling Algorithm

In order to analyze the supersonic and transonic panel flutter behaviors quantitatively and accurately, a fluid-structure coupling algorithm based on the finite element method (FEM) is proposed to study the two-dimensional panel flutter problem. First, the Von Kármán's large deformation is used to model the panel, and the high speed airflow is approached by the Euler equations. Then, the equation of panel is discretized spatially by the standard Galerkin FEM, and the equations of fluid are discretized by the characteristic-based split finite element method (CBS-FEM) with dual time stepping; thus, the numerical oscillation encountered frequently in the numerical simulation of flow field could be removed efficiently. Further, a staggered algorithm is used to transfer the information on the interface between the fluid and the structure. Finally, the aeroelastic behaviors of the panel in both the supersonic and transonic airflows are studied in details. And the results show that the system can present the flat and stable, simple harmonic oscillation, buckling, and inharmonic oscillation states at Mach 2, considering the effect of the pretightening force; at Mach 1.2, as the panel loses stability, the ensuing limit cycle oscillation is born; at Mach 0.8 and 0.9, positive and negative bucklings are the typical states of the panel as it loses its stability. Further, the transonic stability boundary is obtained and the transonic bucket is precisely captured. More, this algorithm can be applied to the numerical analysis of other complicated problems related to aeroelasticity.

Flutter instability analysis of bridge decks using the step-by-step method

The branch switch characteristics of coupled flutter are clarified by use of Step-by-Step flutter analysis. In the case of typically coupled flutter instability, the branch switch characteristic from torsional branch to heaving branch is observed. In this paper, a revised step-by-step analysis method is proposed and a calculating program using MATLAB is built. Finally, the flutter behavior of the Cao Lanh Bridge, which is the long bridge in Vietnam, is studied from the point of view of flutter in two-degrees of freedom, namely torsional and heaving motion.

On bimodal flutter behavior of a flexible airfoil

The dynamic aeroelastic behavior of an elastically supported airfoil is studied in order to investigate the possibilities of increasing critical flutter speed by exploiting its chord-wise flexibility. The flexible airfoil concept is implemented using a rigid airfoil-shaped leading edge, and a flexible thin laminated composite plate conformally attached to its trailing edge. The flutter behavior is studied in terms of the number of laminate plies used in the composite plate for a given aeroelastic system configuration. The flutter behavior is predicted by using an eigenfunction expansion approach which is also used to design a laminated plate in order to attain superior flutter characteristics. Such an airfoil is characterized by two types of flutter responses, the classical airfoil flutter and the plate flutter. Analysis shows that a significant increase in the critical flutter speed can be achieved with high plunge and low pitch stiffness in the region where the aeroelastic system exhibits a bimodal flutter behavior, e.g., where the airfoil flutter and the plate flutter occur simultaneously. The predicted flutter behavior of a flexible airfoil is experimentally verified by conducting a series of systematic aeroelastic system configurations wind tunnel flutter campaigns. The experimental investigations provide, for each type of flutter, a measured flutter response, including the one with indicated bimodal behavior.

비틀림 비선형성을 갖는 2차원 익형의 Critical Slowing Down 을 이용한 Limit Cycle Flutter 예측 인자

In this paper, limit cycle flutter induced by Hopf bifurcation is studied with nonlinear system analysis approach and observed for the critical slowing down phenomenon. Considering an attractor of the dynamics of a system, when a small perturbation is applied to the system, the dynamics converge toward the attractor at some rate. The critical slowing down means that this recovery rate approaches zero as a parameter of the system varies and the size of the basin of attraction shrinks to nil. Consequently, in the pre-bifurcation regime, the recovery rates decrease as the system approaches the bifurcation. This phenomenon is one of the features used to forecast bifurcation before they actually occur. Therefore, studying the critical slowing down for limit cycle flutter behavior would have potential applicability for forecasting those types of flutter. Herein, modeling and nonlinear system analysis of the 2D airfoil with torsional nonlinearity have been discussed, followed by observation of the critical slowing down phenomenon.

About the Aerothermoelastic Stability of Panels in Supersonic Flows

This article provides new insights into the aerothermoelastic stability of thin plates. Particularly, the issue of loss of stability of an isotropic plate-strip of constant thickness immersed in a supersonic flow field and subjected to a variable temperature field through the thickness is examined. Using the basic principles of the theory of aerothermoelasticity of isotropic bodies, the theories of flexible panels, and the linear law of temperature field through the thickness of the panel, the stability equations and associated boundary conditions are obtained. As expected, the coefficients of the aerothermoelastic governing equations depend on the thermal load, and consequently the panel-flutter critical speed depends on temperature. The model takes into account quadratic and cubic aerodynamic non-linearities as well as cubic geometric non-linearities. Due to the inhomogeneity of the temperature field distribution across the thickness plate buckling instability occurs. This instability accounts for the deformed shape of the plate and the stability boundary depends on the variables characterizing the flow speed, the temperature of the middle plane and the temperature gradient in the direction normal to the plane. It is shown that the combined effect of the temperature field and free-stream regulates the process of stability and the temperature field can significantly change the flutter critical speed and flutter behavior. The problem of stability is also considered in the non-linear framework. The existence and behavior of flutter-type vibrations is investigated at pre- and post-critical speeds. The influence of the temperature field on the dependency of the limit cycle amplitude as a function of speed is studied. Results and discussions are presented along with pertinent concluding remarks.

Flutter of a two-dimensional wing with asymmetry at low Mach numbers

A two-dimensional wing aeroelastic model with a modified Leishman–Beddoes model in state-space form is performed to investigate the flutter behavior at low Mach numbers. The two-dimensional wing aeroelastic system employs highly aerodynamic non-linear features. The modifications to the Leishman–Beddoes model are validated by comparing with the experimental results of airfoil airloads at low Mach numbers, and the wing flutter experimental results also verify the model of the two-dimensional wing aeroelastic system. Results demonstrate that a fold bifurcation, which is related to the high-amplitude limit cycle oscillation, stems from the phenomenon of dynamic stall and the emergence of the period-2 limit cycle oscillation is due to the asymmetry of the aeroelastic system.

Dynamic stability analysis of shear-flexible composite beams

Dynamic stability behavior of the shear-flexible composite beams subjected to the nonconservative force is intensively investigated based on the finite element model using the Hermitian beam elements. For this, a formal engineering approach of the mechanics of the laminated composite beam is presented based on kinematic assumptions consistent with the Timoshenko beam theory, and the shear stiffness of the thin-walled composite beam is explicitly derived from the energy equivalence. An extended Hamilton’s principle is employed to evaluate the mass-, elastic stiffness-, geometric stiffness-, damping-, and load correction stiffness matrices. Evaluation procedures for the critical values of divergence and flutter loads of the nonconservative system with and without damping effects are then briefly introduced. In order to verify the validity and the accuracy of this study, the divergence and flutter loads are presented and compared with the results from other references, and the influence of various parameters on the divergence and flutter behavior of the laminated composite beams is newly addressed: (1) variation of the divergence and flutter loads with or without the effects of shear deformation and rotary inertia with respect to the nonconservativeness parameter and the fiber angle change, (2) influence of the internal and external damping on flutter loads whether to consider the shear deformation or not.

Flutter Analysis of a supersonic composite AirFoil skin by using the Differential Quadrature Method

The differential quadrature method is extended to deal with an aeroelastic problem. A structural model is presented based on Hamilton’s principle, and the piston theory is used for modeling supersonic aerodynamic loads. A solution for the flutter of a composite wing skin is obtained by using the differential quadrature method. The validity of this method is confirmed by comparing its results with FEM solutions for the natural frequencies and flutter speed. Then, a detailed parametric study is carried out to examine the influence of the thickness, area, ply-angle, and aspect ratio of composite wings skins on their supersonic flutter behavior. It is shown that the flutter speed of a composite wing skin strongly depends on the area, thickness, ply angle, and aspect ratio of the structure.

Stability of Flexible Orthotropic Rectangular Plates in Supersonic Flow: Amplitude-Speed Dependency in Precritical and Postcritical Flight Conditions

AbstractThis paper provides insights into the stability of flexible orthotropic rectangular plates in supersonic flow by revealing the amplitude-speed dependency behavior for such panels in precritical and postcritical flight conditions. Flutter and postflutter behaviors are discussed to highlight the important effect of the structural and aerodynamic nonlinearities inherently present for panels in high-speed flows. The influence of transversal shear on stability is also illustrated. Depending on the plate’s geometrical parameters, soft- and hard-type flutter behaviors are possible, and a graphical interpretation is provided along with pertinent conclusions.

Flutter analysis of high-aspect-ratio wings based on a third-order nonlinear beam model

In this study, the effects of geometric structural nonlinearity on flutter of high-aspect-ratio wings are examined. The aeroelastic model used is based on (a) a set of governing differential equations describing the motion of an inextensional beam, previously formulated and (b) the semiempirical ONERA aerodynamic model. Galerkin method is implemented to solve dynamic perturbation equations about a nonlinear static equilibrium state. The small perturbation flutter boundary is determined by these perturbation equations. The effect of geometric structural nonlinearity of the beam model on the flutter behavior is significant. Especially, static deformations in the flapwise direction caused by a static force generally decrease system’s flutter speed and frequency.

Analysis of Coupled Flutter of Parallel Plates in Axial Flow by Using Monolithic Finite Element Method

In the present paper, we use a monolithic finite element method to simulate the flutter behavior of two, three and four parallel plates experimentally studied by Schouveiler and Eloy (Phys. Fluids 21, 081703(2009)). Different coupled fluttering modes of the parallel plates are successfully reproduced. Although the results are preliminary, the essential physics of this strongly coupled system are successfully captured. No artificial constraints (i.e., the virtual spring connections between the plates) are needed to predict the in-phase mode of flutter. To the authors' best knowledge, this is the first time that one can capture all the coupled modes of flutter of multiple plates through direct numerical simulations.

Static/Dynamic Edge Movability Effect on Non-Linear Aerothermoelastic Behavior of Geometrically Imperfect Curved Skin Panel: Flutter and Post-Flutter Analysis

This paper addresses the problem of the aerothermoelastic modeling behavior and analyses of skin curved panels with static and dynamic edge movability effect in high supersonic flow. Flutter and post-flutter behavior will be analyzed toward determining under which conditions such panels will exhibit a benign instability, that is a stable limit cycle oscillation, or a catastrophic instability, that is an unstable LCO. The aerothermoelastic governing equations are developed from the geometrically non-linear theory of infinitely long two dimensional curved panels. Von Kármán non-linear strain-displacement relation in conjunction with the Kirchhoff plate-hypothesis is adopted. A geometrically imperfect curved panel forced by a supersonic/hypersonic unsteady flow is numerically investigated using Galerkin approach. These equations are based on the third-order piston theory aerodynamic for modeling the flow-induced forces. Furthermore, the effects of thermal degradation and Kelvin’s model of structural damping independent of time and temperature are also considered in this model. Computational analysis and discussion of the finding along with pertinent conclusions are presented.

Flutter of buckled shape memory alloy reinforced laminates

The effect of shape memory alloys (SMA) on the linear and nonlinear flutter behaviors of buckled cross-ply and angle-ply laminates was investigated in the frequency and time domains using the finite element method. In particular, this study takes the first move toward examining the effect of varying the SMA fiber spacing. Von Karman large deformation assumptions and quasi-steady aerodynamic theory were employed. The flutter boundary, stability boundary, time history response, and phase plane plots of SMA reinforced cross-ply and angle-ply laminates are presented. The numerical results show that increase in the SMA fiber volume fraction and prestrain may generate more recovery stress, and increase the stiffness of the SMA reinforced laminates. Therefore, the flutter boundary and critical load of the plate may be increased significantly. All five types of panel behavior, namely flat, buckled, limit-cycle, periodic, and chaotic motion, are clearly displayed and successively identified. This study sheds light on improving the flutter boundary efficiently by increasing the SMA fiber volume fraction to reinforce the center of the plate.

A Miniaturized Piezoelectric Wind Flutter Generator

A novel miniaturized piezoelectric wind flutter generator is proposed which consisted of a flexible beam and a PZT cantilever. The working principle is based on flexible beam flutter, which can amplify the PZT cantilever vibration. A prototype was tested in a wind tunnel. It is found that there are three behavior states with wind speed increasing, and flutter behavior takes place when wind speed varies between the critical wind speed Uc1and Uc2, an empirical formula was obtained about the critical speed Uc1. The open circuit voltage and power were measured. The device can generate 794μW output power with 30kΩ resistor in a wind of speed 20m/s, power density is 139μW/cm3.

Aerothermoelastic analysis of composite laminated plates

The flutter behavior of a thermally buckled composite laminated plate is investigated in the frequency and time domains using the finite element method. Von Karman large deformation assumptions and quasi-steady aerodynamic theory are employed for the analysis. The effects of temperature gradient, panel length-to-width ratio, fiber orientation, and stacking sequence on aerothermoelastic behavior of the plate are studied in detail. The flutter boundary, buckling boundary, time history response, and phase plane plots of cross-ply and angle-ply laminates are presented. The numerical results show that temperature gradient induces thermal moments and increases the overall stiffness of the plate, and thus may increase the flutter boundary significantly. When the buckle pattern of the plate changes, the eigenvalues of the natural modes are changed suddenly and the sequence of the natural modes may be altered. Therefore, the change in the buckle pattern postpones the coalescence and the flutter boundary may increase. The change in the coalescence pair may also postpone the coalescence and increase the flutter boundary.

Experimental determination of unsteady aerodynamic coefficients and flutter behavior of a rigid wing

In this paper, unsteady aerodynamic forces acting on a three-dimensional wing and its aeroelastic behavior are determined experimentally using a novel semi-experimental method. Towards this end, a rigid wing specimen was fabricated and tested in a low speed, subsonic wind tunnel with two motion sensors for plunging and pitching. Time history samples of the wing motion were obtained at a single air speed and processed using the “Aerodynamics is Aeroelasticity Minus Structure” (AAEMS) system identification method to generate a reduced-order aerodynamic model in discrete-time, state-space format. Coupling the aerodynamic model with the structural model, obtained from the ground vibration test (GVT), results in a reduced-order aeroelastic model that can be analyzed with a variable dynamic pressure. Despite the absence of pressure measurements the model yields a good prediction of aeroelastic behavior, especially for lightly damped modes and for a wide range of dynamic pressures, including the flutter point. It is shown that when the dynamic pressure is at 29.6% of the critical flutter value the method estimates the flutter speed with less than 2% error. However, as the reference dynamic pressure is lowered (relative to the flutter dynamic pressure) the flutter prediction becomes less accurate due to the lack of pressure data. The experimental procedure outlined in this paper can be useful when predicting flutter based on data obtained at sub-critical dynamic pressures.

3D Flutter Analysis of Cable Supported Bridges Including Aeroelastic Effects of Cables

For 3D flutter analysis of cable supported bridges, the aeroelastic effects of cables include the aerodynamic forces acting on cables and local lateral vibrations of cables, as well as the interaction of both. In order to investigate the aeroelastic effects of cables, a 3D flutter analysis method by a commercial structural analysis software package is developed and verified by the simply supported thin plate example and two actual bridges. The developed method can treat the cable as a multi-link model, instead of a single link model, and therefore can show the lateral degrees of freedom along the cable. Also it can simulate the structural damping perfectly and solve the flutter modes successfully. The flutter behaviors including aeroelastic effects of cables of two example bridges, Yangpu Bridge and Jiangyin Bridge in China, are investigated based on the developed method. The calculated results show that for the Yangpu cable-stayed bridge with a 602 m main span, the flutter critical wind velocity can be increased by 20.2% with the consideration of aeroelastic effects of cables. For the Jiangyin suspension bridge of 1385 m main span, however, the impact of the aeroelastic effects of cables on the flutter critical wind velocity is neglectable. The mechanisms of the aeroelastic effects of cables are discussed in this paper.

Flutter Analysis of Wing, Booster Fin and Vertical Tail

Aerospace vehicles are subjected to various types of severe environmental loads. The basic design criterion includes the minimum weight configuration that results in very flexible structures, which leads to various types of structural interaction problems like flutter, divergence etc. Hence every aerospace vehicle should be analysed for its aeroelastic instabilities. In the present work the flutter analysis of a typical space vehicle was carried out in substructure level with the interface fixed condition. The doublet lattice, zona51 and piston theories are used in the unsteady aerodynamic calculations for the subsonic, supersonic and hypersonic speed regimes. As there is no theoretical procedure for transonic speeds, doublet lattice method has been used in the present analysis. Frequency and damping versus velocity are presented to identify the flutter velocities and the flutter behavior.

Prediction of flutter characteristics for a transport wing with wingtip devices

Flutter characteristics of a transport wing with winglet and C-type wingtip were investigated using a high-fidelity aeroelastic analysis method. Unsteady aerodynamics was simulated by a computational fluid dynamics (CFD) solver where the Euler equations were presented as fluid governing equations, and structural vibration was calculated by a computational structural dynamics (CSD) solver where the modeling included geometric nonlinearity. Besides, aeroelastic analysis consisted of an effective coupling of CFD and CSD. Flutter and limit cycle oscillation (LCO) behavior of basic transport wing were predicted first, and the results were compared with the existing experiment. It was found that large-amplitude shock-wave motion provided the proper physical mechanism for the LCO. Then, flutter analyses of wingletted transport wing and C-wing were sequentially conducted. Also aerodynamic and mass effects of wingtip devices were identified separately by way of setting virtual mass. The study demonstrated that wingtip devices could produce substantial adverse effects on flutter characteristics of basic transport wing. The winglet addition, which could alter flutter mode in subsonic flow, decreased the flutter speed more than 10%. Major contributors of the winglet to variations of flutter behavior were aerodynamics and mass, respectively, for subsonic and transonic states. As for a C-wing configuration, the C-type wingtip generated a reduction of wing flutter speed up to 19%, but has a minor impact on flutter frequency. The mass of C-type wingtip dominated the effect on flutter behavior of basic transport wing.