Passive Vibration Control of Axially Moving Beams Using Distributed Nonlinear Energy Sinks

In this paper, a control equation with nonlinear energy sink (NES) coupling is established for simply supported axial motion beams, and three arrangements (single-point local, distributed along the beam, and parallel at the end) are constructed. The Galerkin truncation and Runge–Kutta are used for solution, and the steady-state response calculation process is obtained through [Formula: see text] truncation convergence verification. The values show that moderately increasing the nonlinear stiffness can significantly reduce the first-order resonance, while excessively high stiffness induces narrowband complex responses and additional peaks. Increasing viscous damping significantly enhances attenuation and suppresses abnormal responses in the first, second, and third order resonance regions. Reducing the NES mass enhances the first-order vibration suppression but may trigger nonlinear anomalies. In terms of the number and structure of the layout, the multi-NES distribution is generally better, and the irregular dynamics can be gradually eliminated as the number increases. However, for some parameters, [Formula: see text] is not as good as [Formula: see text] in the first-order region. The above results provide quantitative basis and reproducible passive control paths for NES parameter and position optimization.