COUPLING OF NON-LINEAR SUBSTRUCTURES USING VARIABLE MODAL PARAMETERS

This paper presents a general methodology for the coupling analysis of systems with relatively weak non-linearities by assuming that the response remains harmonic under harmonic excitation. Standard coupling methods and their current shortcomings were discussed first. Two ways of obtaining non-linear modal parameter variations, namely profile constructing and parameter extracting, were presented next. The profile constructing method uses the systemʹs spatial data directly, while the parameter extracting method is based on a non-linear modal analysis of measured response data. Through numerical test cases, it was shown that both methods yielded virtually identical results. An iterative algorithm for the coupling of non-linear subsystems was presented in a form compatible with profile building. A six-degree-of-freedom system with cubic stiffness non-linearity was chosen for a detailed numerical study. Two subsystems, one linear and the other non-linear, were coupled to obtain the modal parameter variations of the coupled system. Using the non-linear modal parameters, the response of the coupled system was predicted at various force levels and the findings were checked via direct simulations using the harmonic balance method. Finally, the methodology was validated by coupling experimentally derived non-linear modal models of two substructures. As for the numerical study, the response of the coupled non-linear structure was predicted at various force levels and the findings were checked against direct measurements. Very good agreement was obtained in all cases studied.