The Effect of Structural Parameters on Response Characteristics of Aeroelastic System in the Presence of Dynamic Stall

The effect of structural paramters on the response and aerodynamic stiffness characteristics of the free aeroelastic system under the influence of dynamic stall is investigated adopting CFD (Computational Fluid Dynamics) method. The equilibrium angle of the spring and the structural stiffness are taken as parameters of interest. Systems with small equilibrium angles enter the symmetric limit-cycle state more quickly after a Hopf bifurcation and experience dynamic stall in both directions, rather than slowly decreasing in minimum angle of attack and remaining in the asymmetric limit-cycle state before dynamic stall in the opposite direction, as is the case with systems with large spring equilibrium angles. Thus, aerodynamic stiffness of system with large equilibrium angles can be more significantly influenced by the change in aerodynamic moment characteristics at the minimum angle of attack. Furthermore, by increasing the initial angular velocity, we find that the system response all becomes symmetric limit cycle and therefore the aerodynamic stiffness appears to have a monotonically increasing characteristic. As to the effect of structural stiffness, it is found that the limit cycle amplitude first increases with structural stiffness after bifurcation, then the amplitude is unchanged with varying structural stiffness at higher Mach number. Energy maps show that the parametric distribution of the energy transfer contributes to this phenomenon. Moreover, when entering the symmetric limit cycle state, the structural stiffness no longer has a significant effect on the aerodynamic stiffness of the system, as the increase in the aerodynamic stiffness is determined solely by the increase in dynamic pressure without the effect of changes in moment characteristics.

Mathematical modeling in problems about dynamics and stability of elastic elements of wing profiles

The mathematical models describing the dynamics of elastic elements of wing structures and representing the initial-boundary value problems for systems of partial differential equations are proposed. The dynamics and stability of elastic elements of wings, flown around by a gas or liquid stream in a model of an incompressible medium, are investigated. To study the dynamics of elastic elements and a gas-liquid medium, both linear and nonlinear models of the mechanics of a solid deformable body and linear models of the mechanics of liquid and gas are used. On the basis of the constructed functionals for partial differential equations, the sufficient stability conditions are obtained in analytical form. The conditions impose restrictions on the parameters of mechanical systems. The obtained stability conditions are necessary for solving the problems of controlling the parameters of the aeroelastic system. On the basis of the Galerkin method, a numerical study of the dynamics of elastic elements was carried out, the reliability of which is confirmed by the obtained analytical results.

Interpolation-Based Modeling Methodology for Efficient Aeroelastic Control of a Folding Wing

The aeroelastic model of a folding wing varies with different configurations, so it actually represents a parameter-varying system. Firstly, a new approach based on interpolation of local models is proposed to generate the linear parameter-varying model of a folding wing. This model is capable of predicting the aeroelastic responses during the slow morphing process and is suitable for subsequent control synthesis. The underlying inconsistencies among local linear time-invariant (LTI) models are solved through the modal matching of structural modes and the special treatment of the rational functions in aerodynamic models. Once the local LTI models are represented in a coherent state-space form, the aeroservoelastic (ASE) model at any operating point can be immediately generated by the matrix interpolation technique. Next, based on the present ASE model, the design of a parameterized controller for suppressing the gust-induced vibration is studied. The receptance method is applied to derive fixed point controllers, and the effective independence method is adopted and modified for optimal sensor placement in variable configurations, which can avoid solving ill-conditioned feedback gains. Numerical simulation demonstrates the effectiveness of the proposed interpolation-based modeling approach, and the parameterized controller exhibits a good gust mitigation effect within a wide parameter-varying range. This paper provides an effective and practical solution for modeling and control of the parameterized aeroelastic system.

A Combined Energy Method for Flutter Instability Analysis of Weakly Damped Panels in Supersonic Airflow

A combined energy method is proposed to investigate the flutter instability characteristics of weakly damped panels in the supersonic airflow. Based on the small damping assumption, the motion governing partial differential equation (PDE) of the panel aeroelastic system, is built by adopting the first-order piston theory and von Karman large deflection plate theory. Then by applying the Galerkin procedure, the PDE is discretized into a set of coupled ordinary differential equations, and the system reduced order model (ROM) with two degrees of freedom is obtained. Considering that the panel aeroelastic system is non-conservative in the physical nature, and assuming that the panel exhibits a single period oscillation on the flutter occurrence, the non-conservative energy balance principle is applied to the linearized ROM within one single oscillation period. The obtained result shows that the ROM modal coordinate amplitudes ratio is regulated by the modal damping coefficients ratio, though each modal damping coefficient is small. Furthermore, as the total damping dissipation energy can be eliminated due to its smallness, the He’s energy balance method is applied to the undamped ROM, therefore the critical non-dimensional dynamic pressure on the flutter instability occurrence, and the oscillation circular frequency amplitude relationship (linear and nonlinear form) are derived. In addition, the damping destabilization paradoxical influence on the system flutter instability is investigated. The accuracy and efficiency of the proposed method are validated by comparing the results with that obtained by using Routh Hurwitz criteria.

Fuzzy control of nonlinear aeroelastic system based on neural network identification

This article presents a fuzzy control method for the limit cycle oscillation (LCO) suppression of nonlinear aeroelastic systems based on the neural network identification algorithm. A prototypical 2D wing section with a single control surface at the trailing edge of the main wing, which contains a symmetrical free play nonlinearity in the pitch degree of freedom, is modeled to illustrate the proposed method. A neural network is used to identify the fuzzy control rules from the existing LCO suppression input and output data. A new fuzzy control rate of the nonlinear aeroelastic system is obtained by adjusting the parameters of the fuzzy control surface. Numerical simulations are conducted to verify the effectiveness of the proposed method.

Influence of Bistable Plunge Stiffness On Nonlinear Airfoil Flutter

Aeroelastic systems have nonlinearities that provide a wide variety of complex dynamic behaviors. Nonlinear effects can be avoided in practical applications, as in instability suppression or desired, for instance, in the energy harvesting design. In the technical literature, there are surveys on nonlinear aeroelastic systems and the different manners they manifest. More recently, the bistable spring effect has been studied as an acceptable nonlinear behavior applied to mechanical vibration problems. The application of the bistable spring effect to aeroelastic problems is still not explored thoroughly. This paper contributes to analyzing the nonlinear dynamics of a typical airfoil section mounted on bistable spring support at plunging motion. The equations of motion are based on the typical aeroelastic section model with three degrees-of-freedom. Moreover, a hardening nonlinearity in pitch is also considered. A preliminary analysis of the bistable spring geometry’s influence in its restoring force and the elastic potential energy is performed. The response of the system is investigated for a set of geometrical configurations. It is possible to identify post-flutter motion regions, the so-called intrawell, and interwell. Results reveal that the transition between intrawell to interwell regions occurs smoothly, depending on the initial conditions. The bistable effect on the aeroelastic system can be advantageous in energy extraction problems due to the jump in oscillation amplitudes. Furthermore, the hardening effect in pitching motion reduces the limit cycle oscillation amplitudes and also delays the occurrence of the snap-through.