The aeroelastic behaviour of an airfoil oscillating in large and small pitch amplitudes due to nonlinearity ‎in aerodynamics is examined. The phenomenon of stall flutter resulted in the Limit cycle oscillations of ‎NACA 0012 at low to intermediate Reynolds number is investigated numerically through the unsteady ‎two-dimensional aeroelastic simulation. The simulations employed unsteady Reynolds Average Navier ‎Stokes shear stress transport k-ω turbulent model with the low Reynolds number correction. The ‎simulations of the fluid-structure interaction were performed by coupling the structural equation of ‎motion with a fluid solver through the user-defined function utility. Numerical simulations were executed ‎at three different elastic axis positions, the leading-edge, 18% and 36% of the airfoil chord length. The ‎airfoil chord measures 0. 156 m. The simulations were executed at the free stream velocity ranging from ‎‎5. 0 m/s to 13 m/s corresponding to the Reynolds number between 51618 and 134207. Two types of ‎oscillation amplitudes were observed at each elastic axis position. At the leading-edge and 18% case, ‎small amplitude oscillations were observed while at 36%, the system underwent high amplitude ‎oscillations. The analysis revealed the cause for small oscillation amplitude is due to the separation of the ‎laminar boundary layer on the suction side of the airfoil starting at the trailing edge. High amplitude ‎oscillations occurred due to the existence of the dynamic stall phenomenon beginning at the leading-edge. ‎Small amplitude LCOs only occurred within a Limited range of airspeed before it disappeared due to ‎increasing airspeed‎‎.

In this study, the effect of the angle of attack on the aeroelastic characteristics of high aspect ratio wing models with structural nonlinearities in unsteady subsonic aerodynamic flows is investigated. The studied wing model is a cantilever wing with flag, lag and torsion vibrations and with large deflection capability, in accordance with the Hodges-Dowell wing model. An unsteady low speed incompressible air flow is assumed to include the flow time lags. Variations of the Limit cycle amplitudes and frequency with free stream velocity at different angle of attacks are carefully studied. For the considered model, the angle of attack has little effect on utter velocity but its effect on Limit cycle amplitudes and frequency is considerable. This study shows that the Limit cycle amplitudes are very sensitive to variations in angles of attack.

In this paper, the dynamic instability of swept wings by using the geometrically exact fully intrinsic beam equations and with considering the static stall effects is investigated. Study of variations of the Limit cycle amplitudes by using the fully intrinsic beam equations and ONERA unsteady aerodynamic model with static stall effects in swept wings is the achievement of this article. the geometrically exact fully intrinsic beam equations involve only moments, forces, velocity and angular velocity, and in these equations, the displacements and rotations will not appear explicitly. In this study, the aerodynamic loads on the wing in an incompressible flow regime are determined by using the ONERA unsteady aerodynamic model. In order to check the instability behavior of the system, first the resulting non-linear partial differential equations are discretized by using the central finite difference method, and then time responses are obtained. The obtained results are compared with those available in the literature. Furthermore, the effects of sweep angle are studied. Finally, it is observed that by using the geometrically exact fully intrinsic beam equations, the instability of the swept wings can be determined accurately and selection of suitable sweep angle can postpone the occurrence of Limit cycle oscillation.

Today, the development of unmanned aircrafts with specific performance characteristics, Including UAVs which capable to fly at high altitude and long endurance is very regarded. In this paper, we have analyzed a nonlinear aeroelastic wing with a high aspect ratio with and without store (tank) which attached to the wing. Also, the aerodynamic model and structural model have been coupled in steady states. The equations of motion have obtained from Hamilton's principle and the Lagrange equations have acquired from three modesof “bending outside the plate", "bending inside the plate" and "torsion". First of all, we have examined the aeroelastic stability analysis “k” approach and effect has been studied for several important parameters. Then, by considering the non-linear terms in equations by using fourth order Rung -Kutta approach, we have studied the results of the simulation and noticed to some phenomena like Limit cycle oscillations and Effect of geometric parameters on the amplitude of these fluctuations is discussed. The Nonlinear terms are structure and store types and aerodynamics flow have been studied in the linear modes. For solving the equations we have used Galerkin method. Also, the equations have governed in the domain time. By Comparing the results, acceptable accuracy of our modeling and undertaken analysis has observed.

This paper considers the problem of stable Limit cycles generating in a class of uncertain nonlinear systems which leads to stable oscillations in the system’s output. This is a wanted behavior in many practical engineering problems. For this purpose, first the equation of the desirable Limit cycle is achieved according to shape, amplitude and frequency of the required output oscillations. Then, the nonlinear control law is designed such that the phase portrait of the closed-loop system includes this stable Limit cycle. The design of controller is based on the Lyapunov stability theorem which is suitable for stability analysis of the positive Limit sets (the stable Limit cycle is a positive Limit set for the nonlinear dynamicl system). The proposed robust controller consists of two parts: nominal control law and additional term which guarantees the robust performance and vanishing the effect of uncertain terms. Finally, to show the applicability of the proposed method, an inertia pendulum system (with parametric uncertainties in its dynamical equations) is considered and the robust output oscillations are achieved by creating the desirable Limit cycle in the close-loop system.

In this paper governing aeroelastic equations of the two degree of freedom airfoil containing cubic nonlinearity in an incompressible flow are presented in the both time and frequency domains.Numerical solution and harmonic balance methods are applied for the solution of govening aeroelastic equations in the time domain to obtain amplitude and frequency of Limit cycle oscillations (LCO). Also, describing function method is modified and presented for the pediction of theLCO amplitude and frequency in the frequency domain.LCO frequency and amplitude are obtained via applying three methods as harmonic balance, describing function and numerical solution methods for two different cases. Comparision between the results of these three methods shows a very good agreement.

Flutter and Limit cycle oscillations (LCO) control of a structural non-linear wing with actuator saturation is considered in this paper. For this purpose composite nonlinear feedback (CNF) theory is used The CNF theory accounts for the effect of actuator saturation and here it can be shown, this control method can effectively suppress the flutter and LCO of a structural nonlinear wing with constrained input. The aeroelastic model is a low aspect ratio rectangular wing in a low subsonic flow with structural nonlinearities. The structural nonlinearity arises from double bending in both chord-wise and span-wise directions (Von Karman plate theory). For aerodynamics modeling a full and reduced order aerodynamics model based on the modified vortex lattice method is used Results from simulations show, with this simple controller, we can effectively suppress LCO and extend flutter boundary.

In this paper, by defining a new paradigm for nonlinear aerodynamic equations of flow separation and static stall, a new form of nonlinear aeroelastic equations for two degrees of freedom airfoils (torsional and bending) are presented. Structural equations are based on the nonlinear mass-spring model which includes the nonlinear quadratic and cubic terms. Aerodynamic equations are obtained by combining the unsteady Wagner model and the nonlinear lift coefficient-angle of attack for simulating stall using a cubic approximation. Hamilton’s principle and Lagrange equations were used to derive the aeroelastic equations. The obtained integro-differential nonlinear aeroelastic equations are solved using a timehistory integration method. The aeroelastic behavior of the airfoil is compared in both unsteady and quasi-steady flow. Using the time-history method compared to the phase space method leads to fewer equations. The results show that the aeroelastic behavior of airfoil with a linear structure, using a nonlinear aerodynamic theory for the stall, causes oscillations with a Limit cycle in unsteady and quasisteady flow compared to other linear aerodynamic theories. Also, the use of the cubic curve instead of the piecewise linear curves which are commonly used in other references, causes an apparent complication of the equations, reduces the computational time due to faster convergence in solution and makes the reduction in errors. The results show that the use of nonlinear aerodynamic static stall not only reduces the instability velocity, but also reduces the amplitude of Limit cycle oscillations in both unsteady and quasi-steady regimes.

In this study the centre manifold is applied for reduction and Limit cycle calculation of a highly nonlinear structural aeroelastic wing. The Limit cycle is arisen from structural nonlinearity due to the large deflection of the wing. Results obtained by different orders of centre manifolds are compared with those obtained by time marching method (fourth-order Runge-Kutta method). These comparisons show zero, third and fifth order manifolds are very good approximation of this system. The aeroelastic model is a low aspect ratio rectangular cantilevered wing in a low subsonic flow which is structurally modeled by the Von Karman plate theory. A continuous time reduced order modified vortex lattice aerodynamics model is utilized in aerodynamics modeling.