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A framework of numerical formulations for the aeroelastic analysis of helicopter rotor is presented in this paper. The blade structural dynamics are modeled by an open source multibody dynamic software MBDYN, which solves finite element equation of elastic bodies in general motions. Then the structural deformation is transformed to blade surface grid by radial base function (RBF) interpolation, and volume grids are regenerated by RBF and TFI methods. Lastly, the fluid governing equations are solved. By integrating the above methods, S76 hovering rotors are simulated and compared to the test data. Results show that elastic torsion decreases local angle of attack. For status at $M_{\mathrm{\text{tip}}}=0.65$ and $𝜃>10^0$, the shock and shock-induced separation are reduced on the outboard blade, which has remarkable effects on the prediction of rotor hovering performance.

The static aeroelastic characteristics of a flexible V-tail airplane were studied by the analyses of the variations of aerodynamic derivatives and flight loads versus flight dynamic pressure. The results show that the variation trends of aerodynamic derivatives and flight loads of the flexible airplane are different from those of the rigid airplane. Therefore, it is necessary to consider the static aeroelastic effects during the flexible airplane design.

Flight vehicles experience aeroelastic problems due to the interaction between structures and aerodynamic forces. Aeroelastic instability is usually a critical problem in transonic and lower supersonic regions. In present study, the aeroelastic analyses of several flight vehicles have been performed using the coupled techniques of computational fluid dynamics (CFD) and computational structural dynamics (CSD). The aeroelastic characteristics based on several aircraft models are investigated using the developed aeroelastic analysis system. On the other hand, structural nonlinearities always exist in flight vehicles. Structural nonlinearities such as freeplay and large deformation effects are considered in the present aeroelastic analysis system. Finally, aeroelastic characteristics of several flight vehicles will be explained considering both aerodynamic and structural nonlinearities.

An aeroelastic analysis of bearingless rotor systems with trailing edge flaps was conducted using large deflection-type beam theory for forward flight conditions with a focus on reducing vibration while minimizing control effort. The aerodynamic forces of the rotor blade were calculated using two-dimensional quasi-steady strip theory. For the analysis of forward flight, the nonlinear periodic blade steady response was obtained by integrating the full finite element equation in time through a coupled trim procedure with a vehicle trim. The objective function, which includes vibratory hub loads and active flap control inputs, was minimized by an optimal control process. Numerical simulations were performed for the steady-state forward flight of various advance ratios. Numerical results of the steady blade and flap deflections as well as the vibratory hub loads were also presented for various advance ratios and were compared with previously published analysis results obtained from modal analyses based on a moderate deflection-type beam theory.

Flutter phenomenon is one of the most dangerous problems in aeroelasticity. When it occurs, the aircraft structure can fail in a few second. In recent aeroelastic research, computational fluid dynamics (CFD) techniques become important means to predict the aeroelastic unstable responses accurately. Among various flow equations like Navier-Stokes, Euler, full potential and so forth, the transonic small disturbance (TSD) theory is widely recognized as one of the most efficient theories. However, the small disturbance assumption limits the applicable range of the TSD theory to the thin wings. For a missile which usually has small aspect ratio wings, the influence of body aerodynamics on the wing surface may be significant. Thus, the flutter stability including the body effect should be verified. In this research an inverse design method is used to complement the aerodynamic deficiency derived from the fuselage. MGM (modified Garabedian-McFadden) inverse design method is used to optimize the aerodynamic field of a full aircraft model. Furthermore, the present TSD aeroelastic analyses do not require the grid regeneration process. The MGM inverse design method converges faster than other conventional aerodynamic theories. Consequently, the inverse designed aeroelastic analyses show that the flutter stability has been lowered by the body effect.

This paper investigates the effects of the unsteady nonlinear aerodynamic, plunge/pitch cubic nonlinearities, flap free-play nonlinearity, and coupled nonlinear aeroelasticity on the dynamics of the three-dimensional blade section. The dynamic stall model is developed based on the unsteady Wagner aerodynamics. Coupling the developed nonlinear aerodynamic model and nonlinear elasticity model results in the nonlinear aeroelastic model. The nonlinear aeroelastic equation of motion is converted into a state-space form. The resulting nonlinear state-space equation of motion is simulated by a standard Runge–Kutta algorithm in MATLAB. The proposed model is validated against test data of distinct two- and three-degrees-of-freedom studies and is compared to the ONERA model. Bifurcation diagrams show that there is distinct airspeed, in which the system experiences limit cycle oscillations (LCOs) or chaos. Both hysteresis air loads and structural nonlinearity make the system unstable at airspeed less than linear flutter speed. The nonlinearity of the structure causes supercritical pitchfork bifurcation. Elastic-aerodynamic nonlinearity interaction causes sub-supercritical bifurcation at the lower airspeed and chaotic motion at a higher airspeed. Furthermore, the effects of the initial condition on the response of the nonlinear aero-servo-elastic system are investigated by the Lyapunov exponent method.

The strong asymptotic stabilization of 3D hyperbolic dynamics is achieved by a damped 2D elastic structure. The model is a Neumann wave-type equation with low regularity coupling conditions given in terms of a nonlinear von Karman plate. This problem is motivated by the elimination of aeroelastic instability (sustained oscillations of bridges, airfoils, etc.) in engineering applications. Empirical observations indicate that the subsonic wave-plate system converges to equilibria. Classical approaches which decouple the plate and wave dynamics have fallen short. Here, we operate on the model as it appears in the engineering literature with no regularization and achieve stabilization by microlocalizing the Neumann boundary data for the wave equation (given through the plate dynamics). We observe a compensation by the plate dynamics precisely where the regularity of the 3D Neumann wave is compromised (in the characteristic sector).

In this paper, multibody dynamic modeling and flutter analysis of a flexible slender vehicle are investigated. The method is a comprehensive procedure based on the hybrid equations of motion in terms of quasi-coordinates. The equations consist of ordinary differential equations for the rigid body motions of the vehicle and partial differential equations for the elastic deformations of the flexible components of the vehicle. These equations are naturally nonlinear, but to avoid high nonlinearity of equations the elastic displacements are assumed to be small so that the equations of motion can be linearized. For the aeroelastic analysis a perturbation approach is used, by which the problem is divided into a nonlinear flight dynamics problem for quasi-rigid flight vehicle and a linear extended aeroelasticity problem for the elastic deformations and perturbations in the rigid body motions. In this manner, the trim values that are obtained from the first problem are used as an input to the second problem. The body of the vehicle is modeled with a uniform free–free beam and the aeroelastic forces are derived from the strip theory. The effect of some crucial geometric and physical parameters and the acting forces on the flutter speed and frequency of the vehicle are investigated.

Aeroelastic response and control of airfoil-flap wing exposed to unsteady aerodynamic loads is addressed. The aim is to suppress flutter and to maintain stability of the system. The analytical aerodynamic model is featuring plunging–pitching–flapping coupled motion. Both linear and nonlinear models are developed. Linear quadratic regulator theory is used to design a full state feedback controller in state-space. The control law is implemented through the flap torque to suppress flutter instability and enhance the aeroelastic response. The system response is investigated when it is flying beyond the flutter speed and the control is delayed by a few seconds. The effects of aircraft propeller excitation and the variation of the aspect ratio on the intitiation of flutter are investigated. Numerical simulations are complemented by experimental measurements in a wind tunnel for NACA0012 airfoil.

In this paper, a new modified harmonic balance method is presented for the nonlinear aeroelastic analysis of two degree-of-freedom airfoils. Using this method, the nonlinear problem is first translated into a minimization problem, and the Particle Swarm Optimization which has high calculation efficiency is adopted to solve the problem. The proposed method is used to solve the nonlinear aeroelastic behavior of supersonic airfoil, with the unsteady aerodynamic load evaluated by the piston theory. Three examples of nonlinear aeroelasticity with significantly different coefficients are prepared, in which the frequencies and amplitudes of the limit cycles are obtained. The results show that the present current method is computationally more efficient.

Elastically mounted double aerodynamic pendulum is an aeroelastic system with two rotational degrees of freedom. A wing is attached to the second link of the pendulum. It is shown that it is possible to select values of parameters in such a way as to make the trivial equilibrium (where both links of the pendulum are stretched along the flow) unstable. Numerical simulation of behavior of the system in such situations is performed, and arising limit cycles are studied. Experimental investigation of such aerodynamic pendulum is performed in the subsonic wind tunnel of the Institute of Mechanics of Lomonosov Moscow State University. Characteristics of periodic motions are registered for different values of parameters of the system. It is shown that experimental data are in qualitative agreement with results of numerical simulation.

In this work, we devise solution algorithms for nonlinear multiparameter eigenvalue problems arising in the analysis of aeroelastic flutter. Two iterative algorithms are devised, as well as a restriction method for simplifying the system behavior away from the desired flutter points. The algorithms are tested on a sectional model and on the Goland wing. Both are found to have fast and reliable convergence properties, yielding flutter point solutions which are validated by the literature. The definition of the eigenvalues is found to have a significant influence on the convergence properties of the algorithm; preferable choices for eigenvalue definitions are noted. The computational costs of the algorithms are tested and discussed; they are found to be favorable relative to other approaches from the literature. Opportunities for extending these methods are also tested and discussed.

This paper studies the aeroelastic behavior of telescopic, multi-segment, span morphing wings. The wing is modeled as a linear, multi-segment, stepped, cantilever Euler–Bernoulli beam. It consists of three segments along the axis and each segment has different geometric, mechanical, and inertial properties. The aeroelastic analysis takes into account spanwise out-of-plane bending and torsion only, for which the corresponding shape functions are derived and validated. The use of shape functions allows representing the wing as an equivalent aerofoil whose generalized coordinates are defined at the wingtip according to the Rayleigh–Ritz method. Theodorsen’s unsteady aerodynamic theory is used to estimate the aerodynamic loads. A representative Padé approximation for the Theodorsen’s transfer function is utilized to model the aerodynamic behaviors in state-space form allowing time-domain simulation and analysis. The effect of the segments’ mechanical, geometric, and inertial properties on the aeroelastic behavior of the wing is assessed. Finally, the viability of span morphing as a flutter suppression device is studied.

When the amplitude of the oscillation of the unsteady flow is large or there is large perturbation relative to the mean background flow, the traditional proper orthogonal decomposition/reduced order model (POD/ROM) based on linearized time or frequency domain small disturbance solvers cannot capture the main nonlinear features well such as limit cycle oscillation (LCO), which is very dangerous for the structure. Therefore, the traditional linear ROMs are not good enough for limit cycles prediction and active control law design. A new nonlinear ROM based on dynamically nonlinear flow equation NPOD/ROM was investigated. The nonlinear second-order snapshot equation in time domain for POD basis construction is obtained from the Taylor series expansion of the flow solver. The simulation results indicate that the NPOD/ROM can capture LCO very well and is also very convenient for active control law design, while the traditional POD/ROM lose effectiveness.

A reduced-order model (ROM) based on block Arnoldi algorithm to quickly predict flutter boundary of aeroelastic system is investigated. First, a mass–damper–spring dynamic system is tested, which shows that the low dimension system produced by the block Arnoldi method can keep a good dynamic property with the original system in low and high frequencies. Then a two-degree of freedom transonic nonlinear aerofoil aeroelastic system is used to validate the suitability of the block Arnoldi method in flutter prediction analysis. In the aerofoil case, the ROM based on a linearized model is obtained through a high-fidelity nonlinear computational fluid dynamics (CFD) calculation. The order of the reduced model is only 8 while it still has nearly the same accuracy as the full 9600-order model. Compared with the proper orthogonal decomposition (POD) method, the results show that, without snapshots the block Arnoldi/ROM has a unique superiority by maintaining the system stability aspect. The flutter boundary of the aeroelastic system predicted by the block Arnoldi/ROM agrees well with the CFD and reference results. The Arnoldi/ROM provides an efficient and convenient tool to quick analyze the system stability of nonlinear transonic aeroelastic systems.

This paper presents a parametric study on aeroelastic stability analysis of multi-layered functionally graded carbon nanotubes reinforced composite (FG-CNTRC) cylindrical panels subjected to a yawed supersonic flow. The panel is considered to be composed of different layers reinforced by carbon nanotubes arranged in different directions with various patterns and different volume fractions. Reddy’s third-order shear deformation theory (TSDT) is employed to model the structure and external pressure is estimated based on the linear supersonic piston theory. The set of governing equations and boundary conditions are derived using Hamilton’s principle and are solved numerically using generalized differential quadrature method (GDQM). Convergence and accuracy of the presented solution are confirmed and effect of volume fraction, distributions and orientation of carbon nanotubes (CNTs), yaw angle and geometrical parameters of the panel on the flutter boundaries are investigated. Results of this paper can be considered as a useful tool in design and analysis of supersonic airplanes and missiles.

In this study, the optimization of free vibration and flutter analysis of a composite plate with the implementation of different boundary conditions is investigated. The governing equations of a composite plate are obtained using the first shear deformation theory (FSDT) of plates. The first-order piston theory is utilized to simulate aerodynamic loads, including arbitrary yaw angle over the panel area. The coupled method of genetic algorithm with well-known generalized differential quadrature (GDQ) method is then developed to obtain optimal layup, which led to maximum fundamental frequency and optimized critical flutter aerodynamic pressure. To achieve this aim, the free vibration and flutter analysis of a composite plate will be conducted via the obtained eigenvalue problem by establishing the discretized governing equations and applying boundary conditions. The obtained results are compared and validated with the available results in the literature, which show high accuracy and a fast rate of convergence. Also, the influence of changing in the yaw angle, number of layers, thickness-to-length ratio, boundary conditions and turning symmetric layup to asymmetric layup is studied.