Buckling Induced Strongly Nonlinear Vibration of Supercritical Axially Moving Beam

In this paper, the postbuckling problem and free linear nonlinear vibration surrounding configuration are accurately analyzed. The placement of translating beams that undergo significant overall buckling deformations in high-speed region, leading to strongly vibration, is studied. Using Galerkin method, we found partial differential equation reduced an ordinary with cubic quadratic terms, which differs from previous literature. supercritical natural frequency analytically obtained, solved using homotopy analysis method (HAM), solution examined numerical results. Results show obtained analytical valid for both weakly cases.