Flutter Problem Research Articles

Finite-time fault-tolerant control for flutter of wing

In this paper, we use the radial basis function neural network and the finite-time H∞ adaptive fault-tolerant control technique to deal with the flutter problem of wings with propulsion system, which is affected by input saturation, time delay, time-varying parameter uncertainties and external disturbances. Then sensor and actuator faults are both considered in the control design. The theory content of this article includes the trajectory optimization, modeling of wing flutter and fault-tolerant controller design. The stability of the finite-time H∞ adaptive fault-tolerant controller is theoretically proved. Finally, simulation results are given to demonstrate the effectiveness of the scheme.

Flutter suppression of plates subjected to supersonic flow using passive constrained viscoelastic layers and Golla–Hughes–McTavish method

The present study involves the application of surface viscoelastic damping treatments to remedy panel flutter problems in existing aircraft components in which active control strategies cannot be easily performed. The rationale for such study is the fact that as the viscoelastic materials are often used to solve a variety of resonant noise and vibration problems in aerospace industry, it becomes important to quantify the increase of aeroelastic stability that can be obtained by the inclusion of viscoelastic treatments. The flutter boundaries of the aeroviscoelastic system accounting for the frequency- and temperature-dependent behavior of the viscoelastic material are computed by adopting the so-named Golla–Hughes–McTavish model. Since the inclusion of internal variables in the viscoelastic model leads to an augmented coupled system of equations of motion, a numerical pre-processing is found to be necessary prior to the resolution of the complex eigenvalue problem for the purposes of flutter analysis. After the theoretical foundations, the stability analysis of a three-layer sandwich plate under supersonic flow is addressed. The results show that it is possible to increase the critical flutter speeds of flat panels using surface viscoelastic damping treatments. However, the temperature and the thicknesses of the layers have significant effect on the flutter boundary.

Uncertainty Quantification of Subcritical Nonlinear Aeroelastic System Using Integrated Interpolation Method and Polynomial Chaos Expansion

The present paper is about analyzing and quantifying parametric uncertainties in a nonlinear aeroelastic system. The response surface of a subcritical system has discontinuities which makes it difficult to analyze using spectral approaches. A quadrature based spectral parametric uncertainty tool called nonintrusive spectral projection (NISP) can capture discontinuities in the response surface only by infinite number of points. As the number of random variable increases, the order of expansion has to increase drastically in order to capture the response accurately. Hence an alternate approach using integrated interpolation scheme which was earlier applied for a thermoacoustic problem is being applied to a classical flutter problem. It is found to be accurate and computationally cheaper than traditional Monte Carlo simulations (MCS) in capturing the response surface. This paper intends to apply the interpolation scheme to the nonlinear aeroelastic model and compares it with quadrature based polynomial chaos expansion (PCE) approach and MCS.

多体气动弹性系统超声速颤振分析

The supersonic flutter of aeroelastic multibody systems was investigated. Based on the theory of multibody dynamics and the piston theory for unsteady aerodynamic forces, the governing differential algebraic equations (DAEs) for the aeroelastic multibody system were established. The supersonic flutter analysis was conducted through solution of the eigenvalue problem in the form of DAEs to discuss the stability of the perturbed motion and the equilibrium of the multibody system. The approach was used for the supersonic flutter problems of a plate wing and a wing with control surfaces. The flutter speed of the wing was obtained with the control surfaces in different positions. The agreement between the simulation results and the experimental ones shows that, the present method has high computational accuracy, and is suitable for the flutter analysis of engineering structures consisting of multiple components.

Transonic flutter analysis of an AGARD 445.6 wing in the frequency domain using the Euler method

ABSTRACTA method based on the Euler equations is proposed for solving transonic flutter problems. The transonic nonlinear flow field with local shock wave/boundary layer interaction is obtained by the Euler/boundary layer equations, and the aerodynamic forces are converted from the time domain to the frequency domain using system identification techniques. The structural dynamic equations in generalized coordinates are adopted for solving structure problems. The method is validated by a flutter boundary prediction of the AGARD 445.6 wing model. The simulation results show that the method presented in this paper is accurate for the prediction of transonic flutter boundary through comparison with experimental data and other simulation results. Furthermore, the present frequency domain method is also much more efficient than the time domain method.

Flutter of conical shells under external flow of a supersonic gas

The well-known piston theory formula for the excess aerodynamic pressure is used in the majority of works devoted to the flutter of shells. In this paper we solve the flutter problem in a new formulation for conical shells under external flow of a supersonic gas and discuss the effect degree of new terms on the critical Mach number.

Транзиторный сдвиг в задаче о флаттере

Транзиторный сдвиг в задаче о флаттере

Characteristics Analysis and Optimization of Flying-Wing Vehicle Structure

To study structural characteristics of flying-wing vehicle, static and dynamic model of half wing span, static and dynamic model of all wing span, optimization model were established. Based on associated static test and ground resonance test data, these models were modified to implement static, dynamic and optimization analysis. Results demonstrated that structural bending and torsional deformations are mainly at outer wing surface. Torsion at inner wing is positive, while torsion at outer wing is negative. Total spar axial force along the wing span increases gradually from inner wing to outer wing and then decreases gradually after reaching the inner-outer wing interface. After axial force is transmitted to the inner wing, it is going to concentrate at the rear spar obviously. Structural bending rigidity and torsional rigidity satisfy requirements of both static force and flutter, without flutter problem of main structural mode. Viewed from the optimization size, ±45° and 0° skin at inner-outer wing turn thickens significantly. This can increase structural bending and torsional rigidity, which is good for satisfying multiple constraints comprehensively.

Nonlinear Thermal Flutter Analysis of Supersonic Composite Laminated Panels Using Differential Quadrature Method

In this paper, the differential quadrature method (DQM) was extended to deal with the nonlinear thermal flutter problem of supersonic composite laminated panel. Based on Hamilton's principle, the nonlinear thermal flutter model of composite panels was first established. The model adopted the von Karman large deflection plate theory for the geometrical nonlinearity, and the third order piston theory for the supersonic aerodynamic loads. Convergence and accuracy studies were carried out to verify the proposed approach. Finally, the nonlinear thermal flutter characteristics of a supersonic composite panel were studied. Uniform temperatures were first applied to the model in order to determine general heating effects on the stability of the composite panel. Owing to the varying structural stiffness of composite panels when subjected to thermal stresses, the thermal load reduced the frequency of composite panel, as well as the frequency interval between the first frequency and the second frequency; thereby hastening the flutter of composite panel. The nonlinear thermal flutter velocity ratio was decreased with respect to increasing temperature load for all aspect ratios. However, the influence of thermal loadings on flutter with various cross angles was different. Cases of unequal temperatures were considered. The average temperature load was kept constant which differs from the temperature gradient form of loading. The results show that the nonlinear thermal frequencies are affected in the presence of different temperature distributions. The changes in the temperature distribution have a slightly greater effect than changes in the average temperature. These effects due to temperature distribution changes do not have a substantial effect on the flutter dynamic pressure.

Scaling parameters and modeling flutter of a cylindrical shell

The similarity parameters in the problem of flutter of a cylindrical shell were studied. As a mathematical theory of shells there was adopted a technical theory in mixed form. For a manometric pressure either formula of piston theory or formula of linearized potential flow theory is accepted. Physical conditions of modeling were derived from the equation of similarity parameters of the model and full-scale processes.

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 of an elastic strip in a longitudinal supersonic flow

An elastic strip in a longitudinal supersonic gas flow is considered. An excess pressure formula is obtained on the basis of the linearized theory of supersonic potential flow. It is shown that, in the case of high-speed supersonic flow, the critical flutter velocity is equal to the phase velocity of perturbation waves propagated along the strip. In the framework of the classical piston theory, the flutter problem is solved for the case of a rigidly fixed strip in a longitudinal flow.

О флаттере упругой прямоугольной пластинки, обтекаемой сверхзвуковым потоком газа, набегающим на её свободный край.

О флаттере упругой прямоугольной пластинки, обтекаемой сверхзвуковым потоком газа, набегающим на её свободный край.

Frequency- and time-domain methods related to flutter instability problem

Bridge flutter phenomenon presents an important criterion of instability, which should be considered in the bridge design phase. This paper presents different bridge flutter methods which can be used to solve the flutter problem. Most commonly used frequency-domain approach is based on the formulation of aero elastic forces with frequency dependent coefficients called flutter derivatives. The critical wind speed, as the main critical condition for the onset of flutter is obtained based on these aero elastic forces. Aero elastic forces can be also expressed in the time-domain, using so-called indicial functions. These functions are usually determined from the corresponding flutter derivatives. In situations when fluid-memory effects tend to become small the quasi-steady theory can be used as an approximation of aero elastic forces. A numerical example related to the typical bridge cross-section follows presented approaches. .

The Time Domain Analysis of the Flutter of Wind Turbine Blade Combined with Eigenvalue Approach

The aeroelasticity and the flutter of the wind turbine blade have been emphasized by related fields. The flutter of the wind turbine blade airfoil and its condition will be focused on. The eigenvalue method and the time domain analysis method will be used to solve the flutter of the wind turbine blade airfoil respectively. The flutter problem will be firstly solved using eigenvalue approach. The flutter region, where the flutter will occur and anti-flutter region, where the flutter will not occur, will be obtained directly by judging the sign of the real part of the characteristic roots of the blade system. Then the time domain analysis of flutter of wind turbine blade will be carried out through the use of the four-order Runge-Kutta numerical methods, the flutter region and the anti-flutter region will be gotten in another way. The time domain analysis can give the changing treads of the aeroelastic responses in great detail than those of the eigenvalue method. The flap displacement of wind turbine blade airfoil will change from convergence to divergence, and change from divergence to convergence extremely suddenly. During the flutter region, the flutter of wind turbine blade will occur extremely dramatically. The flutter region provided by the time domain analysis of the flutter of the blade airfoil accurately coincides with the results of eigenvalue approach, therefore the simulation results are reliable and credible.

Dynamic Response of Flexible Wind Turbine Blade

Aiming at the non-stationary and stall flutter problems of wind turbine blade caused by transient load fluctuations, the dynamic properties of wind turbine were studied, the blade was simplify to a cantilever beam in case of the action of shear deformation and cross section rotating effect were considered in this analysis, equations of the blade were established based on D'Alemberts' principle and the principle of virtual displacement. The dynamic response of the wind turbine was solved by using the finite element method under the transient load environment. A 29.2 m rotor blade, previously reported in specialized literature, was chosen as a case study to validate dynamic behaviour predicted by a Timoshenko beam model. It is concluded that despite its simplicity, The cross-sectional shear-deformation has great influence on dynamic response of the blade.Dynamic model is sufficiently accurate to serve as a design tool for the recursive analyses required during design and optimization stages of wind turbines using only readily available computational tools. DOI: http://dx.doi.org/10.11591/telkomnika.v11i12.3329

Prediction of bridge flutter under a crosswind flow

This paper presents a number of approximated analytical formulations for the flutter analysis of long-span bridges using the so-called uncoupled flutter derivatives. The formulae have been developed from the simplified framework of a bimodal coupled flutter problem. As a result, the proposed method represents an extension of Selberg\' s empirical formula to generic bridge sections, which may be prone to one of the aeroelastic instability such as coupled-mode or single-mode (either dominated by torsion or heaving mode) flutter. Two approximated expressions for the flutter derivatives are required so that only the experimental flutter derivatives of (H*2A*1) are measured to calculate the onset flutter. Based on asymptotic expansions of the flutter derivatives, a further simplified formula was derived to predict the critical wind speed of the cross section, which is prone to the coupled-mode flutter at large reduced wind speeds. The numerical results produced by the proposed formulas have been compared with results obtained by complex eigenvalue analysis and available approximated methods show that they seem to give satisfactory results for a wide range of study cases. Thus, these formulas can be used in the assessment of bridge flutter performance at the preliminary design stage.

The computation of Jordan blocks in parameter-dependent matrices

This paper extends the implicit determinant method introduced by Spence & Poulton (2005, J. Comput. Phys., 204, 65–81) to obtain a numerical technique for the calculation of a two-dimensional Jordan block in a parameter-dependent matrix. An important feature of this technique is that the theory is straightforward to understand and an efficient numerical implementation is suggested naturally by the theory. Three interesting physical problems are presented, arising from the panel flutter problem in aerodynamics, the stability of electrical power systems and a problem in quantum mechanics.

Frequency-domain identification of time-varying systems for analysis and prediction of aeroelastic flutter

In this paper a different approach to wind tunnel flutter testing is presented. This procedure can now be performed as one continuous test, resulting in a major time saving. Both analysis of the current behaviour of the structure, and prediction towards higher velocities, are important for flight flutter testing, and are dealt with in this paper.The recently developed time-varying weighted non-linear least-squares estimator (TV-WNLS) (Lataire and Pintelon, 2011 [1]) is applied to the aeroelastic flutter problem. Smooth variation of the transfer function coefficients is forced through the TV-WNLS estimator, and the obtained polynomials are used as basis for predicting the damping ratio towards higher velocities. Selection of the model order is based on linear variation of the airspeed and the evaluation of Theodorsen's unsteady aerodynamics for the frozen time-varying aeroelastic system at a certain constant velocity. Therefore, providing a physical justification for the extrapolation of the damping ratio towards higher velocities. The method is applied to wind-tunnel measurements on a cantilevered wing. It is shown that the proposed method outperforms flutter speed prediction by classic damping ratio extrapolation and a non-parametric analysis of the time-varying signal.

Nonlinear flutter of viscoelastic rectangular plates and cylindrical panels of a composite with a concentrated masses

The problem of flutter of viscoelastic rectangular plates and cylindrical panels with concentrated masses is studied in a geometrically nonlinear formulation. In the equation of motion of the plate and panel, the effect of concentrated masses is accounted for using the δ-Dirac function. The problem is reduced to a system of nonlinear ordinary integrodifferential equations by using the Bubnov-Galerkin method. The resulting system with a weakly singular Koltunov-Rzhanitsyn kernel is solved by employing a numerical method based on quadrature formulas. The behavior of viscoelastic rectangular plates and cylindrical panels is studied and the critical flow velocities are determined for real composite materials over wide ranges of physicomechanical and geometrical parameters.