An Improved Physics-Informed Neural Network for Nonsmooth Stick–Slip Dynamic Analysis

Abstract In complex frictional systems, friction-induced vibration (FIV) and noise are ubiquitous and intricate issues. Achieving high-precision simulation of the vibration response is crucial for the diagnosis of system dynamic properties and vibration control. However, frictional surfaces with multiple contact points introduce nonsmoothness, resulting in unpredictable vibration responses and posing significant challenges for numerical methods to maintain accuracy over long-term analyses. This study proposes a new physics-informed neural network (PINN) method designed to enhance the adaptability between physical constraints and neural network training. The method introduces loss functions with state transition boundary modification (STBM) derived from the physical governing equations. Additionally, a data expansion and regression (DER) strategy for processing linear complementarity problem (LCP) is implemented in the optimizer, significantly improving simulation accuracy for complex stick–slip vibration processes in multicontact frictional systems. By combining these two innovations, the proposed method, referred to as BMDER-PINN, was validated through simulations of stick–slip vibration in a two-degree-of-freedom (2DoF) frictional system. Compared with conventional time-stepping methods, this approach ensures higher accuracy in longer simulations while also enabling large time steps, thereby offering a promising calculation method for improving nonsmooth dynamics simulations.