Buckling Induced Strongly Nonlinear Vibration of Supercritical Axially Moving Beam

Abstract

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