Existence of periodic orbits and multistability dynamics in axially accelerating beams

The axially accelerating beam systems are widely used in engineering fields, which have abundant dynamical phenomena. In this work, we studied the periodic orbits and the phenomena of multistability of the system. The necessary and sufficient conditions for the existence of periodic orbits are derived by Schauder's fixed point theorem and the averaging method. The theoretical results are in good agreement with the numerical analysis. Multistability is discussed in some set of parameter values. To predict the dynamical behaviors of the system in the long-term run, the effects of external excitation amplitude on the structures of basins of attraction are studied. The results reveal the influences of the physical parameters and initial values on the complex dynamical behaviors of the system, which can offer some guidance for selecting parameter values in engineering application of axially accelerating beams.