Modal degeneracy and oblique bending modes in ultra-long cable-strut deployable space masts

Abstract

With the increasing application of large-scale ultra-long space deployable structures in aerospace engineering, low-order modal degeneracy and the resulting oblique bending modes have become critical issues affecting structural dynamic performance and on-orbit stability. This paper investigates low-order modal degeneracy and the evolution of oblique bending mode orientation in ultra-long cable-strut deployable articulated masts. A prestress-dependent transfer matrix model is established that incorporates key local structural effects, including joint rotational inertia and concentrated masses from locking mechanisms. Based on this model, the effects of cable stiffness and tip mass distribution on low-order modal frequencies and mode orientations are systematically studied. The results show that uniform changes in cable stiffness mainly affect natural frequencies, while mode orientations remain nearly unchanged. In contrast, local stiffness reductions break structural symmetry, lift modal degeneracy, and induce noticeable mode rotation. Under ideal symmetry, bending modes in two orthogonal directions form a degenerate pair, and the mode shapes can be expressed as linear combinations of two orthogonal basis modes. When stiffness variations or asymmetric tip masses are introduced, modal energy redistributes within the degenerate subspace, leading to mode separation along the weaker stiffness direction and forming oblique bending modes dominated by a single direction. Asymmetric tip masses produce similar effects by lifting degeneracy and rotating mode orientation. Overall, the results show that oblique bending modes are governed by symmetry-breaking mechanisms, providing guidance for parameter tuning in practical engineering applications.

The authors' abstract, as published at the source. Journal of Vibration and Control, 2026 · DOI ↗