Studies of Store-Induced Limit-Cycle Oscillations Using a Model with Full System Nonlinearities

The authors investigate limit-cycle oscillations of a wing/store configuration. Unlike typical aeroelastic studies that are based upon a linearized form of the governing equations, herein full system nonlinearities are retained, and include transonic flow effects, coupled responses from the structure, and store-related kinematics and dynamics. Unsteady aerodynamic loads are modeled with the equations from transonic small disturbance theory. The structural dynamics for the cantilevered wing are modeled by the nonlinear equations of motion for a beam. The effects of general store-placement are modeled by the nonlinear equations of motion related to the position-induced nonlinear kinematics. Chordwise deformations of the wing surface, as well as pylon and store flexibility, are assumed negligible. Nonlinear responses are studied by examining bifurcation and related response characteristics using direct simulation. Particular attention is given to cases for which large-time, time-dependent behavior is dependent on initial conditions, as observed for some configurations in flight test. Comparisons of results in which selective nonlinearities are excluded indicate that the accurate prediction of nonlinear responses such as limit cycle oscillations (LCOs) may depend upon consideration of all nonlinearities related to the full system.     

Nonlinear Analysis of Store-Induced Limit Cycle Oscillations

Flight tests of modern high-performance fighter aircraft reveal the presence of limit cycle oscillation (LCO) responses for aircraft with certain external store configurations. Conventional linear aeroelastic analysis predicts flutter for conditions well beyond the operational envelope, yet these store-induced LCO responses occur at flight conditions within the flight envelope. Several nonlinear sources may be present, including aerodynamic effects such as flow separation and shock-boundary layer interaction and structural effects such as stiffening, damping, and system kinematics. No complete theory has been forwarded to accurately explain the mechanisms responsible. This research examines a two degree-of-freedom aeroelastic system which possesses kinematic nonlinearities and a strong nonlinearity in pitch stiffness. Nonlinear analysis techniques are used to gain insight into the characteristics of the behavior of the system. Numerical simulation is used to verify and validate the analysis. It is found that when system damping is low, the system clearly exhibits nonlinear interaction between aeroelastic modes. It is also shown that although certain applied forcing conditions may appear negligible, these same forces produce large amplitude LCOs under specific realizable circumstances.     

An Investigation of Internal Resonance in Aeroelastic Systems

Although the study of internal resonance in mechanical systems has been given significant consideration, minimal attention has been given to internal resonance for systems which consider the presence of aerodynamic forces. Herein, the investigators examine the possible existence of internal resonances, and the related nonlinear pathologies that such responses may have, for an aeroelastic system which possesses nonlinear aerodynamic loads. Evidence of internal resonance is presented for specific classes of aeroelastic systems, and such adverse response indicates nonlinearities may lead to aeroelastic instabilities that are not predicted by traditional (linear) approaches.     

Predictions of nonlinear viscoelastic behavior using a hybrid approach

An approach for nonlinear viscoelastic characterization is presented which uses the combined measurements from creep and dynamic mechanical tests. Although the methodology should extend to several materials and geometries, this research concentrates on thin film polymers used in the manufacture of high altitude scientific balloons. Typically, the constitutive behavior of these materials is characterized through the use of linear viscoelastic techniques. Although this linear approach provides an accurate model for small strains or loads, these materials have been shown to be highly stress dependent and, consequently, it is necessary to identify this nonlinear behavior. Traditional creep measurements require extensive laboratory test times, yet the results obtained from dynamic mechanical analysis provide the capability to predict long term material performance without a lengthy experimentation program. However, dynamic mechanical methods are currently limited to linear response; thus, an approach is presented in which the stress-dependent behavior is derived from short-term creep measurements in a manner analogous to time-temperature superposition. Predictions of material response using linear and nonlinear approaches are compared with experimental results obtained from traditional long-term creep tests. Although linear pre-dictions deteriorate for large stresses, excellent agreement is shown for the nonlinear model.     

Adaptive Feedback Linearization for the Control of a Typical Wing Section with Structural Nonlinearity

Earlier results by the authors showed constructions of Lie algebraic, partial feedback linearizing control methods for pitch and plunge primary control utilizing a single trailing edge actuator. In addition, a globally stable nonlinear adaptive control method was derived for a structurally nonlinear wing section with both a leading and trailing edge actuator. However, the global stability result described in a previous paper by the authors, while highly desirable, relied on the fact that the leading and trailing edge actuators rendered the system exactly feedback linearizable via Lie algebraic methods. In this paper, the authors derive an adaptive, nonlinear feedback control methodology for a structurally nonlinear typical wing section. The technique is advantageous in that the adaptive control is derived utilizing an explicit parameterization of the structural nonlinearity and a partial feedback linearizing control that is parametrically dependent is defined via Lie algebraic methods. The closed loop stability of the system is guaranteed to be stable via application of La Salle's invariance principle.