Prediction of limit cycle oscillations under uncertainty using a Harmonic Balance method

• We perform computations of limit cycle oscillations using a high-dimensional Harmonic Balance method.
• We perform uncertainty quantification for LCO using a non-intrusive polynomial chaos method.
• We predict super- and sub-critical bifurcations and limit cycle oscillation amplitudes on wing structures.
• Pentic stiffness is critical to wing subcritical LCO amplitude.

The Harmonic Balance method is an attractive solution for computing periodic responses and can be an alternative to time domain methods, at a reduced computational cost. The current paper investigates using a Harmonic Balance method for simulating limit cycle oscillations under uncertainty. The Harmonic Balance method is used in conjunction with a non-intrusive polynomial-chaos approach to propagate variability and is validated against Monte Carlo analysis. Results show the potential of the approach for a range of nonlinear dynamical systems, including a full wing configuration exhibiting supercritical and subcritical bifurcations, at a fraction of the cost of performing time domain simulations.