Nonlinear dynamics of mechanical systems with friction contacts: Harmonic Balance Method and multiple solutions

Real applications in structural mechanics where the dynamic behaviour is linear are rare. Usually, structures are made of components assembled together by means of joints whose behaviour may result highly nonlinear. Depending on the amount of excitation, joints can dramatically change the dynamic behaviour 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 the Direct Time Integration (DTI). Since the periodical nonlinear contact forces may depend on the history of the motion of the vibrating system, the HBM steady-state solution may lead to a poor correlation with the DTI solution. In this paper, the HBM performances are investigated by comparing two different approaches to each other: in the first case the static balance equations of the system are uncoupled from the dynamic balance equations, while in the second case a coupled static/dynamic approach is presented. A lumped parameter system characterized by a single friction contact is considered in order to show the different level of accuracy that the proposed approaches can give for different configurations.