Nonlinear lateral vibrations of a deploying Euler–Bernoulli beam with a spinning motion

Abstract

The nonlinear lateral vibrations of a beam deploying from a fixed rigid hub are analyzed when the beam has a spinning motion. Previous studies do not consider the nonlinear coupled effect between axial and lateral displacements when analyzing the vibration behavior of a deploying beam with spin. In contrast, the present study considers the nonlinear coupling effect of the axial and lateral displacements for a deploying beam with spin to investigate the vibration behavior more exactly and comprehensively. The Euler–Bernoulli beam theory and von Karman nonlinear strain theory are used together to develop a new nonlinear model. The differences in dynamic response between the linear and nonlinear models are compared, and the effects of physical parameters on the differences are investigated. In addition, the beat phenomenon of a deploying beam with spin is studied. Significant differences in dynamic responses are observed between the proposed nonlinear and previous linear models. It is found that the beat phenomenon is caused by the interference of two close natural frequencies: the first and second natural frequencies of a spinning beam.