Degree Type


Date of Award


Degree Name

Doctor of Philosophy


Mechanical Engineering

First Advisor

Atul Kelkar

Second Advisor

Umesh Vaidya


Under the right parameters, flutter occurs in an airfoil when aerodynamic forces drive a dynamic structure to an oscillatory, possibly divergent condition. The presence of a rotational stiffness nonlinearity at the root of an all-moving airfoil has been shown to decrease the freestream velocity at which flutter occurs. Since this is a somewhat common configuration for flight structures and other aerodynamic machinery, a large amount of research has been devoted to understanding it over the several decades. Attempts to characterize it, however, have mostly resulted in methods that provide numerical simulation, validated by experimental results, rather than a nonlinear systems analysis approach. This research addresses the problem of characterizing the phenomenon of flutter in an all moving airfoil that has a rotational stiffness free-play nonlinearity. Application is made to both a rigid two-dimensional model and a flexible three-dimensional model. A system theory approach is used to model a typical airfoil system with rotational free-play nonlinearity so that analysis can be performed with necessarily conducting numerical time domain simulations of the model. The main contributions of this research are the introduction and validation of a nonlinear freeplay model that allows better exploitation of nonlinear systems analysis techniques, the design and validation of the subsequent two-dimensional model, the application of new system identification tools to provide an aerodynamic reduced order model that is reasonably accurate for three-dimensional modeling and computationally efficient, and the introduction of two new approaches to the three-dimensional modeling problem. This research introduces the use of a hyperbola function to model the free-play nonlinearity, allowing a system that is both continuous, responsive to changes in the free-play region width, and physically representative. For the two-dimensional case, the nonlinearity is modeled as a feedback interconnection of linear system and static nonlinearity. The feedback interconnection structure is exploited to analyze the system dynamics, consisting of unique stable fixed points, multiple steady states and limit cycle oscillations. A Hopf bifurcation is identified by analysis, and the results of the derivation are demonstrated to provide accurate predictions of flutter behavior. For the three-dimensional model, two candidate models are presented and analyzed. The first addresses the nonlinearity as a rigid body input, which is then superimposed upon the structural and aerodynamic systems, themselves connected in a loop. The second separates the nonlinearity out within a contained structural model, which is in turn looped with the aerodynamic model. In both cases, the aerodynamics are modeled by providing dynamic modal airfoil motion to a panel method flow code, and using the resulting aerodynamic force outputs in a system identification scheme. Finally, the results of the three-dimensional modeling are compared to experimental wind tunnel data for a flutter airfoil of similar physical properties.


Copyright Owner

David C. Asjes



File Format


File Size

108 pages