Substructuring using NNMs of nonlinear connecting elements

The behaviour of real systems is in general significantly difficult to achieve due to their implicit nonlinear nature. For ordinary studies, they are assumed to behave linearly obtaining rough information regarding their main features. However, in most cases this is not enough to properly design them, thus the introduction of some nonlinearities becomes necessary. In most cases, real structures can be modeled as linear substructures jointed through nonlinear connections to evaluate how the nonlinearities affect the global system. The connecting element is modeled as an additional substructure to be included in the substructuring process. Substructuring methods are here used together with Nonlinear Normal Modes (NNMs) theory to achieve the behaviour of these types of systems. The nonlinearities, even if localised in a small portion of the system, play a crucial role and their effects on the dynamics of the whole system are different whether the connection has a softening or hardening behaviuor. Two cases involving lumped parameters systems are analysed, showing that the method can be applied considering both hardening and softening nonlinear laws and it provides reliable results.