Dynamics analysis of a nonlinear system with Bingham model under stochastic excitation

This article examines the stochastic response of a system with a Bingham model magneto-rheological damper under random excitation. The application of the stochastic averaging method yielded the averaged stochastic Itô equation. The system’s steady-state response probability density function (PDF) is obtained by solving the corresponding Fokker–Planck–Kolmogorov equation. Theoretical calculations are confirmed through numerical simulation. Additionally, the study produced graphs depicting the steady-state probability density functions for system energy, amplitude, displacement, and velocity, along with time history graphs, joint probability density functions for displacement and velocity, and continuous wavelet coefficient energy distribution graphs. The paper also examines the impacts of viscous damping, Coulomb damping, and noise intensity on the steady-state response from both time-domain and frequency-domain perspectives. The findings indicate that in this stochastic model, when velocities are relatively low, an equivalent increase in Coulomb damping has a more pronounced effect on the steady-state response than viscous damping. These results provide a theoretical basis for understanding and addressing the behavior of Bingham model magnetorheological dampers in nonlinear systems under stochastic excitation.