Prediction and validation of aeroelastic limit cycle oscillations using harmonic balance methods and Koopman operator

Abstract

The presence of nonlinearities within aerospace systems often triggers self-sustaining oscillations known as Limit Cycle Oscillations (LCO), demanding costly analysis for identification, notably through the resource-intensive generation of bifurcation diagrams. Consequently, the expense incurred tends to sideline nonlinear analysis in initial design phases, constraining design possibilities and impeding data-driven methods for nonlinear aeroelastic analysis reliant on efficient data collection, which has garnered attention in the aerospace sector. This work proposes a computationally efficient numerical framework for calculating LCO amplitudes and determining stability in nonlinear aeroelastic systems. The framework consists of using Harmonic Balance Methods (HBM) combined with the Hill method for the stability analysis. To avoid the sorting problem, the Koopman operator-based data-driven method is implemented. The methodology is applied to numerical test cases, encompassing both smooth and nonsmooth nonlinearities, and validated against outcomes from MATCONT and COCO. Subsequently, an experimental validation of the framework is conducted, comparing its outcomes to existing LCO experimental data acquired through control-based continuation experiments.

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ORCID for Jie Yuan: orcid.org/0000-0002-2411-8789

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