  Friction-induced vibration (FIV) is very common in engineering areas.
Analysing the dynamic behaviour of systems containing a multiple-contact point
frictional interface is an important topic. However, accurately simulating
nonsmooth/discontinuous dynamic behaviour due to friction is challenging. This
paper presents a new physics-informed neural network approach for solving
nonsmooth friction-induced vibration or friction-involved vibration problems.
Compared with schemes of the conventional time-stepping methodology, in this
new computational framework, the theoretical formulations of nonsmooth
multibody dynamics are transformed and embedded in the training process of the
neural network. Major findings include that the new framework not only can
perform accurate simulation of nonsmooth dynamic behaviour, but also eliminate
the need for extremely small time steps typically associated with the
conventional time-stepping methodology for multibody systems, thus saving much
computation work while maintaining high accuracy. Specifically, four kinds of
high-accuracy PINN-based methods are proposed: (1) single PINN; (2) dual PINN;
(3) advanced single PINN; (4) advanced dual PINN. Two typical dynamics problems
with nonsmooth contact are tested: one is a 1-dimensional contact problem with
stick-slip, and the other is a 2-dimensional contact problem considering
separation-reattachment and stick-slip oscillation. Both single and dual PINN
methods show their advantages in dealing with the 1-dimensional stick-slip
problem, which outperforms conventional methods across friction models that are
difficult to simulate by the conventional time-stepping method. For the
2-dimensional problem, the capability of the advanced single and advanced dual
PINN on accuracy improvement is shown, and they provide good results even in
the cases when conventional methods fail.
