Dynamic analysis of the tensegrity structure of a rotary airborne wind energy machine

Abstract

The dynamic behavior of the tensegrity structure (helix) of a rotary airborne wind energy (RAWE) machine was investigated by combining experimental and numerical techniques. Taking advantage of the slenderness of the helix, a dynamic model for the evolution of its center line and the torsional deformation was developed by using Cosserat theory. The constitutive relations for the axial, bending, and torsional stiffness, which are a fundamental component of the model, were obtained experimentally by carrying out laboratory tests. Three scenarios of increasing complexity were then studied with the numerical tool. Firstly, a stationary solution of the model, i.e., with fixed ends and no rotation, was found numerically and used to verify the correct implementation of a numerical code based on finite elements. The stability analysis of this solution, which corresponds to the state of the structure just after deployment but before operation, showed that the natural periods of longitudinal, lateral, and torsional modes of the RAWE structure under consideration are around 0.03, 0.2, and 0.4 s, respectively. Secondly, the dynamics in nominal operation was investigated by keeping both end tips fixed and implementing a controller that adjusts the torque at the ground to reach a target angular velocity of 120 rpm. Key characteristic variables like the tension and the response times of the helix were obtained. Thirdly, the dynamics of the helix when the lower end is fixed and the upper end is driven in a circular motion of frequency f1 was studied experimentally and numerically. The tension of the helix in the experiment increased for f1 above a certain threshold, and the structure collapsed at f1≈5 Hz. Simulation analysis revealed a resonance of the structure at a higher frequency (around 13 Hz).