Dynamical stability of the cantilever beam with oscillating length

The dynamical stability and transverse vibration of the cantilever beam with oscillating length are analyzed in this study. The differential equation of motion with time-dependent coefficients is discretized by the Galerkin method, and then the method of multiple scales for multi-degree of freedom is applied to investigate the parametric resonances of the cantilever beam with oscillating length. The effects of the oscillation amplitude and frequency on the parametric resonance regions and the tip responses are discussed. Tip responses simulation by Runge–Kutta method confirms the parametric resonance regions obtained by multiple scales method. In addition, the ‘jump’ phenomenon on the tip response of the axially oscillating deploying cantilever beam is also discussed.