Subcritical parametric response of an axially accelerating beam

In this paper, the planar nonlinear dynamics of an axially accelerating beam in the subcritical speed regime is examined theoretically, via two different numerical techniques, employing a large enough number of modes in order to investigate modal interactions. The equation of motion is discretized via the Galerkin method which results in a set of coupled nonlinear ordinary differential equations (NODEs) with time-dependent coefficients. The set of NODEs is solved by means of the pseudo-arclength continuation technique and some of the results are tested and verified via direct time integration of the NODEs. The analyses include the system tuned to a three-to-one internal resonance, as well as for the case where it is not. Results are illustrated through frequency–response diagrams, time traces, phase–plane portraits, and fast Fourier transforms (FFTs).