  Real applications in structural mechanics, where the dynamic behavior is
linear, are rare. Usually, structures are made of components assembled together
by means of joints whose behavior maybe highly nonlinear. Depending on the
amount of excitation, joints can dramatically change the dynamic behavior of
the whole system, and the modelling of this type of constraint is therefore
crucial for a correct prediction of the amount of vibration.
  The solution of the nonlinear equilibrium equations by means of the Harmonic
Balance Method (HBM) is widely accepted as an effective approach to calculate
the steady state forced response in the frequency domain, in spite of Direct
Time Integration (DTI). The state of the art contact element used to model the
friction forces at the joint interfaces is a nodal contact element, where the
local contact compliance is modelled by means of linear springs and Coulomb law
is used to govern the friction phenomena.
  In the literature, when the HBM is applied to vibrating systems with joint
interfaces and the state-of-the-art contact model is used, an uncoupled
approach is mostly employed: the static governing equations are solved in
advance to compute the pre-stress effects and then the dynamic governing
equations are solved to predict the vibration amplitude of the system. As a
result, the HBM steady-state solution may lead to a poor correlation with the
DTI solution, where static and dynamic loads are accounted for simultaneously.
  In this paper, the HBM performances are investigated by comparing the
uncoupled approach to a fully coupled static/dynamic approach. In order to
highlight the main differences between the two approaches, a lumped parameter
system, characterized by a single friction contact, is considered in order to
show the different levels of accuracy that the proposed approaches can provide
for different configurations.

Dynamical Systems