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In many systems of interest, most of the structure is well approximated as linear but some parts must be treated as nonlinear to get accurate response predictions: significant nonlinear effects are due to the connections between coupled subsystems, such as in automotive or aerospace structures. The present work aims at predicting the nonlinear behavior of coupled systems using a substructuring technique in the modal domain. This study focuses on the effects of nonlinear connections on the dynamics of an assembly in which the coupled subsystems can be considered as linear. Each connection is instead considered as a quasi-linear substructure with stiffness that is function of amplitude or energy. The iterative procedure used here is enhanced with respect to previous works by enforcing a better control of the total energy at each iteration allowing to obtain the solution for a prescribed set of energy levels. Also, the initial guess and the convergence criterion have been modified to speed up the procedure. This technique is applied to a system made of two continuous linear subsystems coupled by nonlinear connections. The numerical results of the coupling are first compared to the ones obtained by using the Harmonic Balance technique on the model of the complete assembly to evaluate its effectiveness and understand the effects of modal truncation. Besides, a nonlinear connecting element, specifically designed in order to have a nearly cubic hardening behavior, is used in an experimental setup. Substructuring results are compared to experimental results measured on the assembled system, in order to evaluate the correlation between mode shapes and the accuracy in the resonance frequency at several excitation levels.

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Substructure decoupling techniques, defined in the frame of Frequency Based Substructuring, allow to identify the dynamic behaviour of a structural subsystem starting from the known dynamics of the coupled system and from information about the remaining components. The problem of joint identification can be approached in the substructuring framework by decoupling jointed substructures from the assembled system. In this case, information at the coupling DoFs of the assembled structure are necessary and this could be a problem if the interface is inaccessible for measurements. Expansion techniques can be used to obtain the dynamics on inaccessible (interface) DoFs starting from accessible (internal) DoFs. A promising technique is the System Equivalent Model Mixing (SEMM) that combines numerical and experimental models of the same component to obtain a hybrid model. This technique has been already used in an iterative coupling-decoupling procedure to identify the linear dynamic behaviour of a joint, with a Virtual Point description of the interface. In this work, a similar identification procedure is applied to the Brake Reus Beam benchmark to identify the linear dynamic behaviour of a three bolted connection at low levels of excitation. The joint is considered as a third independent substructure that accounts for the mass and stiffness properties of the three bolts, thus avoiding singularity in the decoupling process. Instead of using the Virtual Point Transformation, the interface is modelled by performing a modal condensation on remote points allowing deformation of the connecting surfaces between subcomponents. The purpose of the study is to highlight numerical and ill-conditioning problems that may arise in this kind of identification.