Identification of primary and secondary resonances: experimental continuation and broadband data-based modeling

Abstract This paper presents a comparative study of two sets of techniques for identifying primary and secondary resonances in nonlinear dynamic systems: experimental continuation and broadband data-based modeling. The former refers to methods integrating control and continuation processes to empirically derive the bifurcation diagram of a nonlinear system. These approaches do not require a model, but the need for a controller introduces complexity in the experiments. Conversely, broadband data-based modeling uses wide-spectrum excitation data to develop a nonlinear model of the system. Proper model validation is crucial in this process to ensure accurate results. In this work, the comparison is carried out using two different setups: an electronic Duffing system and a thin-walled nonlinear beam. The findings demonstrate that both methods, when properly applied, can effectively identify not only primary resonances, but also the more challenging secondary ones. Measuring and predicting these resonances constitutes an ambitious task for data-based approaches. Moreover, the direct comparison between experimental continuation and broadband data-based techniques highlights the complementary strengths and limitations of each approach, providing new insights and perspectives on the identification of nonlinear resonances.