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.

翻译：摩擦诱发振动（FIV）在工程领域极为常见。分析含多点接触摩擦界面的系统动力学行为是重要课题，然而准确模拟由摩擦引起的非光滑/不连续动力学行为极具挑战性。本文提出一种全新的物理信息神经网络方法，用于求解非光滑摩擦诱发振动或含摩擦振动问题。相较于传统时间步进方法，该新型计算框架将非光滑多体动力学的理论公式进行变换并嵌入神经网络训练过程。主要发现包括：新框架不仅能精确模拟非光滑动力学行为，还能消除传统多体系统时间步进方法所需的极小时间步长限制，从而在保持高精度的同时大幅节省计算量。具体而言，本文提出四类高精度PINN方法：（1）单PINN；（2）双PINN；（3）高级单PINN；（4）高级双PINN。测试了两种典型非光滑接触动力学问题：一维含粘滑接触问题与二维含分离-再附着及粘滑振荡接触问题。单PINN与双PINN方法在处理一维粘滑问题时均展现出优势，在传统时间步进方法难以模拟的摩擦模型上表现优于传统方法。针对二维问题，展示了高级单PINN与高级双PINN在精度提升方面的能力，即使在传统方法失效的工况下仍能获得良好结果。