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Real applications in structural mechanics, where the dynamic behavior islinear, are rare. Usually, structures are made of components assembled togetherby means of joints whose behavior maybe highly nonlinear. Depending on theamount of excitation, joints can dramatically change the dynamic behavior ofthe whole system, and the modelling of this type of constraint is thereforecrucial for a correct prediction of the amount of vibration.  The solution of the nonlinear equilibrium equations by means of the HarmonicBalance Method (HBM) is widely accepted as an effective approach to calculatethe steady state forced response in the frequency domain, in spite of DirectTime Integration (DTI). The state of the art contact element used to model thefriction forces at the joint interfaces is a nodal contact element, where thelocal contact compliance is modelled by means of linear springs and Coulomb lawis used to govern the friction phenomena.  In the literature, when the HBM is applied to vibrating systems with jointinterfaces and the state-of-the-art contact model is used, an uncoupledapproach is mostly employed: the static governing equations are solved inadvance to compute the pre-stress effects and then the dynamic governingequations are solved to predict the vibration amplitude of the system. As aresult, the HBM steady-state solution may lead to a poor correlation with theDTI solution, where static and dynamic loads are accounted for simultaneously.  In this paper, the HBM performances are investigated by comparing theuncoupled approach to a fully coupled static/dynamic approach. In order tohighlight the main differences between the two approaches, a lumped parametersystem, characterized by a single friction contact, is considered in order toshow the different levels of accuracy that the proposed approaches can providefor different configurations.

Nonlinear dynamics of mechanical systems with friction contacts: coupled static and dynamic Multi-Harmonic Balance Method and multiple solutions