Influence of the Initial Prestress Level on the Distribution of Regions of Dynamic Instability of Geiger Domes

This paper provides a parametric analysis of cable–strut tensegrity domes subjected to periodic loads. This analysis aims at determining the main regions of dynamic instability (unstable regions). From the point of view of the physical interpretation of the phenomenon, if the load occurs in these regions, the amplitudes of the resulting vibrations increase, posing a risk to the durability of the structures. The consideration includes cable–strut structures called Geiger domes. Four dome design solutions known from the literature are compared, i.e., regular (patented by Geiger) and modified domes with a closed and an open upper section. In contrast to conventional cable–strut structures, Geiger domes are characterized by a self-equilibrated system of internal forces (initial prestress), which affects the shape and range of unstable regions. The main purpose is to answer the question as to which type of design solution is more sensitive to the risk of excitation vibrations. A nondimensional parameter λ is introduced for this quantitative assessment. This parameter reliably determines the change in the area of unstable regions as the initial prestress level increases. The range of the parameter λ is defined as a value between 1 and 0. In the case of λ=1, there is potential for the excitation of unstable motion, whereas in the case of λ=0, such a risk is absent. The analysis presented in this paper can be employed in the process of optimizing the initial prestress level, which will constitute the subsequent stage of this research. A geometrically non-linear model is used to evaluate the behavior of the considered structures.