Physics-informed neural network for friction-involved nonsmooth dynamics problems

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.