Dynamic Behavior Study of a Twin Axially Moving Beam with a Nonlinear Coupled Oscillator System

As one of the most critical dynamic systems, axially moving beam structures are widely used in modern industry. Various engineering systems can be simplified as axially moving beams and their coupled systems, and controlling their vibration is necessary. Unfortunately, the current literature on coupled beam systems typically ignores the axial motion of each sub-beam, thereby limiting the development of nonlinear vibration control theory for axially moving beam systems. Motivated by the above limitations, this study establishes a dynamic analysis model for a twin axially moving beam using the nonlinear coupled oscillator system (NCOS). The influence of NCOS on the dynamic behavior of the twin axially moving beam is discussed. Numerical analysis shows that the dynamic behavior of the twin axially moving beam with the NCOS is correctly simulated using GTM. Under suitable parameters, NCOS can effectively suppress the vibration of a twin axially moving beam, with the working states of NCOS divided into linear and nonlinear. Under unsuitable parameter conditions, NCOS can amplify the lateral vibration of the twin axially moving beam and elicit complex responses. Choosing appropriate parameters for NCOS seems necessary to promote its engineering applications. Additionally, for different moving velocities of axially moving beams, within the same range of nonlinear stiffness variation, the influence of NCOS on the dynamic behavior of the twin axially moving beam varies. Overall, within a given parameter range, the introduction of NCOS enhances the twin axially moving beam's vibration suppression effectiveness. For different moving velocities of axially moving beams, the range of NCOS’s nonlinear stiffness changes should be specifically designed.