Low-dimensional dynamical modeling and vibration control of flexible telescopic masts

Flexible telescopic masts (FTMs) exhibit complex dynamical behavior, characterized by significant large-scale transverse deformation and axial motion. The dynamical coupling between numerous flexible beams results in high computational costs when simulating the FTM's nonlinear dynamical characteristics. To address this challenge, this study introduces a parametric global mode method (PGMM) that is well-suited for the model of multiple nested hollow flexible beams. It models the large-scale elastic deformation of all flexible components using a unified set of modal coordinates, leading to a low-dimensional representation and significantly improving computational efficiency. The accuracy of the PGMM is validated through comparisons with results from the assumed mode method, finite element analysis, and experiments. The nonlinear dynamic responses of FTMs composed of multiple beams (n = 3, 5, 10) are simulated under harmonic excitation, where the variations of the displacement-frequency curves and the 1:3 internal resonance phenomenon are characterized. The comparative study of transient responses indicates that an effective PGMM model achieves a 98.82 % reduction in computational cost compared to the finite element model while maintaining high accuracy. Benefiting from the high accuracy and efficiency, an input shaping technique based on the average operating frequency is employed to reduce residual vibrations in the FTMs, where the peak displacements are reduced by over 85.3 %. This work provides a new way of developing advanced dynamical modeling methods of FTMs and time-varying nonlinear combined structures for their dynamics design, optimization, and system control.