Substructuring with nonlinear subcomponents: A nonlinear normal mode perspective

Abstract

Substructure coupling techniques allow one to predict the response of an assembly from dynamic models for each subcomponent. Linear substructures are routinely used in analysis (e.g. the Craig-Bampton method) to reduce the computational cost of vibration, noise and load predictions for structures. They also provide a designer with insight into the influence that each subcomponent has on the assembled system's natural frequencies, mode shapes and damping. These concepts are currently limited to assemblies of linear substructures. This work explores substructuring with nonlinear subcomponents (substructures), using the nonlinear normal modes of each substructure to seek to understand how those contribute to the nonlinear modes of the assembly. The goal is to extend the insights that have been developed over the past several years for linear substructures, to nonlinear ones. A specific type of describing function model, which captures the variation of the structure's natural frequencies and mode shapes with energy is introduced, which is here dubbed a Representative Linear Modal Model (RLMM). The results show that this type of model can be used with linear substructuring techniques to effectively predict the dynamics of a nonlinear assembly, suggesting that linear substructuring concepts may be applied advantageously to nonlinear assemblies. © The Society for Experimental Mechanics, Inc. 2012.