Detection of nonlinear modal interactions based on time series

Abstract

Nonlinear modal interactions are frequently encountered in the dynamic responses of aerospace structures due to the activation of nonlinearities when submitted to large amplitudes of excitation. These peculiar nonlinear interactions create internal resonances, leading to an increase in the response amplitude not predicted by the linear theory. While modal interactions have been studied on numerical models and reported on real-life structures, no algorithm for their automatic detection has been proposed so far. In this context, the present work aims at developing an algorithm for the automatic detection of modal interactions, based on experimental time series recorded during industrial test campaigns. The proposed algorithm focuses on the analysis of structural responses to sinesweep excitations, which are commonly used in the industry.

The detection algorithm is based, on the one hand, on the study of the frequency content of the responses with an adaptive filter; and, on the other hand, on the assessment of the correlation between the phases and deflection shapes of higher harmonics and linear modes. The linear modal shapes are approximated by their deflection shapes at resonance during low-energy testing.

The algorithm is first discussed and validated on simulated data, using a nonlinear mass-spring system and the finite element model of a spacecraft with strong nonlinearities and high non-proportional damping. The performance of the algorithm is then demonstrated using experimental data from the spacecraft shaker test campaign.

This automatic method is fast and robust to detect the presence of modal interactions during spacecraft shaker test or aircraft ground vibration test. Therefore, it paves the way for broadening the scope of modal interaction study to industrial applications, and can be used in the design stage of mechanical structures to avoid unexpected failures during their operational lifespan.