Post-buckling Behavior of Axially Moving Beams Under External Loads and Nonlinear Vibration Characterization

PurposeThe direction of the axial external load also affects the linear relationship between the intrinsic frequency of the system and the load. In this paper, we study the linear relationship between axial loads and the intrinsic frequency of the system. In this paper, the post-buckling behavior and nonlinear vibration of axially moving beams under axial loads are Investigated.MethodsAccording to Hamilton's variational principle, the dynamic equations of the axially moving beam under axial load are established. The post-buckling configuration of the beam was analyzed and predicted. The governing equations are rewritten in the form of Dufferin's equations using the truncated Galerkin method. The expression for the closed form of the nonlinear forced vibration of the beam is determined using the homography analysis method (HAM).ResultsThe numerical results show the dependence of axial velocity, initial axial stress on post-buckling configuration.ConclusionThe explicit expression for the nonlinear fundamental frequency derived by the homography analysis method shows that the direction of the initial axial force affects the nonlinear frequency with initial amplitude.