Computation of limit cycle oscillations and their stabilities in nonlinear aeroelastic systems using harmonic balance methods

Abstract

Understanding the aeroelastic behaviour of aerospace systems is critical in aircraft design. The presence of structural nonlinearities can have a significant impact on these behaviours causing the onset of Limit Cycle Oscillations (LCO) and shifts in stability. Numerical continuation techniques have been implemented to detect and track the behaviour of these solutions. However, due to the complexity nonlinearities bring it is common practice to simplify the analysis to linear models that can underestimate the impact nonlinearities have. Nonlinear analysis tools can often be inefficient especially for large scale systems. Studies have shown that modelling nonlinear steady state vibrational behaviour in the frequnncy domain with Harmonic Balance Methods (HBM) can significantly improve the efficiency of nonlinear analysis. In this paper, the architecture of a HBM based continuation tool for analysis of nonlinear aeroelastic systems is presented. A simple 2D aerofoil case study featuring a freeplay nonlinearity is investigated with the tool and compared to state of the art alternative software that operate in the time domain. With this case study, it was shown that HBM provided both faster running times and less data storage requirements than alternative software. The devised HBM operated 11 times faster than MATCONT and 3 times faster than COCO for the same test case. Stability data obtained using Hill's method was also in agreement with COCO and time history comparisons. The significance of the freeplay nonlinearity is also demonstrated, shifting the safety margin of the design by 18% when compared to purely linear aeroelastic analysis.

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

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