Abstract: S. Oberst, S. Tuttle (2018)

Driven by the need for multi-functionality and increasing demands for low mass and compact-stowing, unfolding, self-deploying or -morphing smart mechanical structures have become popular space engineering designs for flexible appendages. Extensive research has been conducted on the use of tape springs as hinge deployment mechanisms for space booms, solar sails, or optical membranes or directly for used as antennas. However, the vibrational behaviour of tape springs and its related dynamics have rarely been addressed in detail, even though missions are underway with similarly flexible appendages installed.

By conducting quasi-static bending tests on a tape spring antenna, we evidence hysteresis behaviours in both the opposite- and equal sense bending directions. Apart from the well-known snap-through buckling, the structure exhibits torsional buckling in the equal sense bending direction before collapsing. Micro-vibrational excitation triggers nonlinear jump phenomena and the period-doubling route to chaos. Using a computational tape spring model and simplified environmental loads similar to those encountered in near-Earth orbits, coupling between the first bending and torsional modes generates a dynamic instability which is predicted by a complex eigenvalue analysis step. The current study highlights that high perturbation sensitivity and system-inherent nonlinearities can lead to stability issues.

In the course of designing a spacecraft with thin-walled appendages, system-level trade-offs are routinely performed. Since it is unclear how severely the vibrations of flexible appendages might affect their proper functioning or the control of the spacecraft, it is of paramount importance to validate experimentally thin-walled structures thoroughly for their dynamic and stability behaviours.

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Nonlinear dynamics of thin-walled elastic structures for applications in space