Modeling and Vibration Characteristics Analysis of the NES-Plate Coupling System Under Arbitrary Elastic Boundary Conditions

In practical engineering applications, flexible plates exhibit a variety of boundary conditions. When a nonlinear energy sink (NES) is affixed to a plate, the resulting NES-plate system forms a high-dimensional, nonlinear vibration model. Repeated modeling and computation of the NES-plate system’s vibration characteristics under differing boundary conditions can be both labor-intensive and intricate. Consequently, developing a unified nonlinear vibration analytical model for the NES-plate coupled system with arbitrary elastic boundary conditions is highly valuable. This study establishes such a unified model for analyzing the vibration characteristics of the NES-plate coupling system across varied boundary conditions. Here, the NES is affixed to the plate structure’s surface to mitigate vibration. To represent arbitrary elastic boundaries of the plate, the model incorporates rotational and transverse springs. The investigation analyzes the nonlinear vibration responses of the NES-equipped plate under general elastic boundaries and assesses the NES’s effectiveness in vibration control. Furthermore, the effects of boundary stiffness variations on the coupling system are evaluated. Finally, the study explores the influence of NES parameter adjustments on the system’s vibration characteristics and complex nonlinear dynamic behaviors under general elastic boundary conditions. The results show that changing the NES parameters significantly alters the vibration state of the plate, and adjusting the NES nonlinear stiffness appropriately is more effective in reducing plate vibration than changing the NES damping.