Predicting Aeroelastic Limit-Cycle Oscillations Due to Freeplay Nonlinearity Using Pre-Critical Output Data
Author(s)
Hartin, Michael Bruce
Advisor(s)
Editor(s)
Collections
Supplementary to:
Permanent Link
Abstract
This thesis introduces a novel output-based approach for predicting limit-cycle oscillations caused by freeplay, a stiffness nonlinearity resulting in no or highly reduced restoring elastic effects within specific motion ranges of actuated structures. This nonlinearity can affect moving parts of aerospace vehicles, such as control surfaces or tilting propellers and rotors, as well as other engineering systems that feature components in relative motion. The resulting self-excited, bounded periodic oscillations can degrade system performance and induce structural damage, fatigue, or failure. These issues require computationally efficient and accurate methods to predict the onsets and amplitudes of freeplay-induced limit-cycle oscillations in the design phase.
The proposed approach uses output data from free-decay time histories at pre-critical operating conditions, before limit-cycle oscillations develop, to estimate the recovery rate to equilibrium as a function of a monitored response variable and a varying (control) parameter. Recovery rate data points are then fitted and extrapolated to predict the values of the response variable and control parameter associated with limit-cycle oscillation solutions, which correspond to a recovery rate of zero. This approach preserves the non-intrusive nature of direct time-marching simulations while offering higher computational efficiency and numerical robustness. In addition, its output-based nature enables application to both computational and experimental data.
Building on previous research on systems with geometrical or polynomial stiffness nonlinearities, this thesis investigates the effectiveness of this output-based approach for predicting limit-cycle oscillations due to freeplay for the first time. Novel theoretical developments to the original output-based formulation are introduced to address the unique complexities of freeplay nonlinearity, which introduces nearly amplitude-discontinuous stiffness properties into the system. These developments are demonstrated by predicting limit-cycle oscillations of an idealized, elastically mounted tilting propeller in airplane mode, with freeplay in the tilting mechanism. Predictions are based on output data from simulations of an analytical, two-degree-of-freedom model and are verified against reference limit-cycle oscillation solutions from direct time marching. The sensitivity of the predictions to parameters in the approach is explored to understand its accuracy and numerical robustness. The proposed approach effectively captures regions of the parameter-amplitude plane where limit-cycle oscillations develop using output data from as few as one time history at pre-critical operating conditions. Prediction accuracy regularly improves as one uses output data collected closer to the onset of limit-cycle oscillations. These results pave the way for investigating applications to more complex configurations in future research.
The novel contributions from this thesis have the potential to streamline limit-cycle oscillation calculations in the design phase of nonlinear aeroelastic systems, enabling higher performance and safety in shorter, more cost-effective cycles. For example, the proposed approach can help ensure acceptable limit-cycle oscillations in systems such as aircraft lifting surfaces and emerging air vehicle configurations for regional and urban air mobility. In addition, while this study focuses on computational applications, the output-based nature of the proposed approach makes it suitable for future experimental applications in wind-tunnel or flight testing. Lastly, the approach may be applied to other nonlinear dynamical systems with freeplay or physics that can be modeled using a similar mathematical form.
Sponsor
Date
2025-12
Extent
Resource Type
Text
Resource Subtype
Thesis (Masters Degree)