On the symmetries and vibration modes of layered space grids

Layered space grids (typically double-layer and triple-layer configurations) offer large-span roofing solutions for many modern facilities ranging from industrial warehouses to exhibition pavilions, places of public assembly and indoor sports complexes. These configurations often exhibit a high degree of symmetry not only at the modular level, but also at the global level, and the vibration characteristics of the structures are heavily influenced by the type of symmetries they possess. In this contribution, the symmetries of various configurations of layered space grids are described, and the associated vibration modes are explored using a group-theoretic approach. This allows insight to be gained, prior to any detailed analysis, on the number of distinct modes of vibration (and natural frequencies) of specific symmetry types, and some important observations are made in this regard. Computational aspects are also covered, and a numerical example included.