Subharmonic dynamics of an axially accelerating beam

Geometrically nonlinear dynamics of an axially accelerating beam is investigated numerically in this paper. Employing the Galerkin scheme, the equation of motion is reduced to a set of nonlinear ordinary differential equations with coupled terms. The linear part of this set of equations is then solved to determine the linear natural frequencies. The frequency of the axial acceleration is set to twice the first or second linear natural frequency (subharmonic resonance), and bifurcation diagrams of Poincaré maps are obtained via direct time integration and choosing the amplitude of the speed variations as a bifurcation parameter. The results are presented for four different values of the mean value of the axial speed, specifically in the form of time traces, phase-plane portraits, fast Fourier transforms (FFTs), and Poincaré maps.