Mayuresh J. Patil

Nonlinear Aeroelasticity and Flight Dynamics of High-Altitude Long-Endurance Aircraft

High-Altitude Long-Endurance (HALE) aircraft have wings with high aspect ratios. During operations of these aircraft, the wings can undergo large de∞ections. These large de∞ections can change the natural frequencies of the wing which, in turn, can produce noticeable changes in its aeroelastic behavior. This behavior can be accounted for only by using a rigorous nonlinear aeroelastic analysis. Results are obtained from such an analysis for aeroelastic behavior as well as overall ∞ight dynamic characteristics of a complete aircraft model representative of HALE aircraft. When the nonlinear ∞exibility efiects are taken into account in the calculation of trim and ∞ight dynamics characteristics, the predicted aeroelastic behavior of the complete aircraft turns out to be very difierent from what it would be without such efiects. The overall ∞ight dynamic characteristics of the aircraft also change due to wing ∞exibility. For example, the results show that the trim solution as well as the short-period and phugoid modes are afiected by wing ∞exibility.

Nonlinear aeroelastic analysis of complete aircraft in subsonic flow

Aeroelastic instabilities are among the factors that may constrain the flight envelope of aircraft and, thus, must be considered during design. As future aircraft designs reduce weight and raise performance levels using directional material, thus leading to an increasingly flexible aircraft, there is a need for reliable analysis that models all of the important characteristics of the fluid-structure interaction problem. Such a model would be used in preliminary design and control synthesis. A theoretical basis has been established for a consistent analysis that takes into account 1) material anisotropy, 2) geometrical nonlinearities of the structure, 3) unsteady flow behavior, and 4) dynamic stall for the complete aircraft. Such a formulation for aeroelastic analysis of a complete aircraft in subsonic flow is described. Linear results are presented and validated for the Goland wing (Goland, M., The Flutter of a Uniform Cantilever Wing, Journal of Applied Mechanics, Vol. 12, No. 4, 1945, pp. A197-A208). Further results have been obtained that highlight the effects of structural and aerodynamic nonlinearities on the trim solution, flutter speed, and amplitude of limit-cycle oscillations. These results give insight into various nonlinear aeroelastic phenomena of interest: 1) the effect of steady-state lift and accompanying deformation on the speed at which instabilities occur, 2) the effect on nonlinearities in limiting the amplitude of oscillations once an instability is encountered, and 3) the destabilizing effects of nonlinearities for finite disturbances at stable conditions.

Flight Dynamics of Highly Flexible Aircraft

An analysis and parametric study of the flight dynamics of highly flexible aircraft are presented. The analysis extends previous work of the authors, used to predict the atypical flight dynamic characteristics of highly flexible flying wings, to conventional configurations with one or more fuselages, wings, and/or tails. The aircraft structure is represented as a collection of geometrically exact, intrinsic beam elements, with continuity conditions enforced where beams intersect. The structural model is coupled with an aerodynamic model consisting of two-dimensional, large-angle-of-attack, unsteady theory for the lifting surfaces, and a fuselage model based on application of slender-body theory to a cylindrical beam. Influences of various design parameters such as wing flexibility, horizontal/vertical tail aerodynamics, and offset are investigated for aeroelasticity and flight dynamics of highly flexible aircraft. Results for prototype configurations illustrate the relationships between its design parameters and flight dynamic behavior.

Effect of Thrust on Bending -Torsion Flutter of Wings

The effect of thrust on the flutter of a high-aspect-ratio wing is investigated. The wing is represented by a beam using a nonlinear mixed finite element method. Aerodynamic forces are calculated using a finite-state, two-dimensional unsteady aerodynamic model. The effect of thrust is modeled as a follower force of prescribed magnitude. Without the thrust force, the wing is shown to become unstable for freestream airspeeds greater than the flutter speed. On the other hand, in the absence of aerodynamic forces, the wing becomes unstable for values of the thrust in excess of a critical magnitude of the force. When both effects are present, the airspeed at which the instability occurs depends on the thrust magnitude. For validation, an analytical solution for the en vacuo case (accounting only for the effect of thrust) was developed and shown to closely match results from the numerical method. Parametric studies show that the predicted stability boundaries are very sensitive to the ratio of bending stiffness to torsional stiffness. Indeed, the effect of thrust can be either stabilizing or destabilizing, depending on the value of this parameter. An assessment whether or not the magnitude of thrust needed to influence the flutter speed is practical is made for one configuration.

Flight Dynamics of High Aspect-Ratio Flying Wings: Effect of Large Trim Deformation

Analysis of flight dynamics of conventional airplane configurations usually begins with a rigid body approximation of the undeformed airplane structure. However, for high aspectratio flying wing configurations, static aeroelastic eects generate significant structural deformation and thus the aircraft configuration in flight is significantly dierent from the initial undeformed shape. As a consequence, flight dynamic studies conducted on a rigid body model based on the initial undeformed structure do not give an accurate assessment of the behavior of the airplane in flight. To overcome this, the deformed shape generated when the flying wing is subjected to static aeroelastic forces at trim, is used to define the rigid body configuration used for flight dynamic analysis. This paper studies the flight dynamic characteristics of the new rigid body configuration in relation to those of the rigid undeformed flying wing, and in relation to the stability characteristics of the complete aeroelastic model. The flight dynamic roots and the stability boundaries of the statically deformed rigid body configuration and the complete aeroelastic model are compared. It is found that staic aeroelatic deformation has a significant influence on the flight dynamic characteristics of high aspect-ratio HALE configurations.

Aeroelastic Analysis of Composite Wings

An aeroelastic stability analysis is presented for high-aspect ratio composite wings. The structural model is based on an asymptotically correct crosssectional formulation and a nonlinear geometric exact beam analysis, both derivable from 3-D elasticity. A new 2-D unsteady in∞ow flnite-state theory is considered for the aerodynamic part of the solution. Theodorsen theory is also implemented and used for most of the preliminary tests. The paper discusses, among other things, the importance of using the right stifiness formulation in order to model material couplings, the variations of divergence and ∞utter speeds with the changes in the lamination angle of a box-beam model of a wing cross section, and some of the efiects of a nonlinear structural model on the aeroelastic stability of a slender wing.

Output Feedback Control of the Nonlinear Aeroelastic Response of a Slender Wing

This paper presents the design of optimal constant gain output feedback based controllers for a nonlinear aeroelastic system. Controllers are designed for flutter suppression as well as gust-load alleviation. This controller architecture is one of the simplest, using direct feedback of the sensor outputs, but its performance is highly dependent on sensor selection and placement. Also, optimal design of such controllers require an accurate knowledge of the expected disturbance mode and gust spectrum. This paper presents results pertaining to the performance of SOF controllers for aeroelastic control (linear and nonlinear) and compares it to that of LQR and LQG controllers. Controllers are designed for various sensor placement. The gain and phase margins of the various controllers are also presented to understand the robustness characteristics. For optimal sensor placement and with knowledge of the disturbance, the constant gain output feedback controller performance and robustness was found to be equivalent to that of linear quadratic regulator and linear quadratic Gaussian controllers for the example considered. These controllers were also shown to be very easy to alter and combine with other controllers/filters for better overall system response.

Energy-consistent, Galerkin approach for the nonlinear dynamics of beams using intrinsic equations

The paper presents a Galerkin approach for the solution of nonlinear beam equations. The approach is energy consistent, that is, it is shown that the weighted residual integral describes energy flow. The Galerkin approach gives accurate results with fewer degrees of freedom as compared to low-order finite-element formulation. The Galerkin approach also leads to a nonlinear order-reduction technique that can be used to further decrease the order of the system. The reduced-order model is shown to capture the dominant nonlinearities in the system and is ideal for preliminary design and control synthesis.

Unsteady Aerodynamics of Deformable Thin Airfoils

The paper presents a theory for the unsteady aerodynamics of deformable thin airfoils. It extends the theory developed by Theodorsen and Garrick, which is restricted to rigid body motion. Frequency-domain lift, pitching moment, and thrust expressions are derived for an airfoil undergoing harmonic oscillations and deformation in the form of the Chebychev polynomials. The first two polynomials give the rigid body motion, whereas the rest represent the deformation. The results are verified with the time-domain unsteady aerodynamic theory of Peters. Numerical results are presented for several combinations of airfoil motion, which identify various possibilities for thrust generation using a deformable airfoil.

Optimal Flapping-Wing Vehicle Dynamics via Floquet Multiplier Sensitivities

This work considers the trimmed periodic orbits of flapping-wing micro air vehicles, and details the tradeoff between the stability of those orbits (via Floquet theory), their size, and the power needed to sustain them. The nonlinear equations of motion of a body with two rigid flapping wings are coupled to a blade element aerodynamic method, and the periodic shooting method is used to locate the orbit. Analytical sensitivities of the relevant flight metrics, including the Floquet multipliers, are derived with respect to kinematic variables, which enables a gradient-based optimization for maximum stability, minimum power, or minimum orbit size. This is done for hovering, climbing, and forward flight; comparisons between the required kinematics and the resulting flight behavior for each optimal case provide insight into the conflicting metrics. Notably, the optimizer is able to locate designs that are stable in an open-loop sense. However, this effort is not meant to replace the inclusion of a dedicated cl...