Forced Vibration of Supercritical Axially Moving Beam with an Intermediate Spring Support

[Purposes] This work is conducted to understand the nonlinear vibration response characteristics of axially moving beams with intermediate support constraints. [Methods] The dynamic equation of the system was established on the basis of Hamilton principle, and the motion equation was discretized into a nonlinear ordinary differential equation by using the Galerkin method. By combining the improved arclength extension method with the incremental harmonic balance method, the dynamic equations of the system were solved, and the dynamic response characteristics of the system under different parameters were analyzed. [Findings] It is shown that the overall system response exhibits a hard spring characteristic. The support spring has a significant impact on the dynamics of the axially moving beam. In addition, when the axial movement speed is within a certain range, the system exhibits internal resonance, and the system shows more complex response characteristics.