of such structures. The first stage of analysis involves the identification of initial prestress forces (system of internal forces, which holds structural components in stable equilibrium) and infinitesimal mechanisms. The second stage focuses on calculating natural frequencies, while in the last, the impact of time-independent external loads on vibrations is studied. The influence of initial prestress and external load on the dynamic response of the structures is considered. A geometrically non-linear model is used to analysis. Presented considerations are crucial for the next step in the analysis, i.e., dynamic stability analysis of the behaviour of tensegrity structures under periodic loads.

tensegrity domes with mechanisms are sensitive to the change of the level of initial prestress. Two tensegrity domes are considered. In addition, a standard single-layer dome is taken into account for comparison. The analysis is carried out in two stages. Firstly, the presence of the characteristic tensegrity features is examined (qualitative analysis). Next, the behavior under static external loads is studied (quantitative analysis). In particular, the influence of the initial prestress level on displacements, effort, and stiffness of the structure is analyzed. To evaluate this behavior, a geometrically non-linear model is used. The model is implemented in an original program written in the Mathematica environment. The analysis demonstrates that for a dome with mechanisms, the adjustment of pre-stressing forces influences the static properties. It has been found that the stiffness depends not only on the geometry and properties of the material but also on the initial prestress level and external load. In the case of the non-existence of mechanisms, structures are insensitive to the initial prestress level.

into account. Particularly, the impact of the number of girders on the natural frequencies is analysed. A geometrically quasi-linear model is used, implemented in an original program written in the Mathematica environment. The results confirm that the number of girders affects the number of infinitesimal mechanisms. However, the dynamic behaviour does not depend on the number of mechanisms. The most important is the nature of a dome and the type of load-bearing girder. Especially, the behaviour of Geiger domes with a closed upper section is specific. In this case, not only the frequencies corresponding to the infinitesimal mechanisms depend on the prestress. There are additional frequencies that depend on prestress. The number of them, and the sensitivity on the initial prestress changes, depends on the number of girders. Generally, for the same number of girders, the natural frequencies of regular domes are higher than for the modified ones.

uwagę dwa typy geometrii kopuły (zwykłą i zmodyfikowaną). Przedstawione rozważania odpowiadają na następne pytania tj. czy jest możliwa kontrola liczby mechanizmów poprzez zmianę liczby dźwigarów nośnych? Jaki typ kopuły (zwykła czy zmodyfikowana) jest łatwiejszy do kontroli? Czy zachowanie kopuł z taką samą liczbą mechanizmów infinitezymalnych jest podobne? Czy liczba częstotliwości drgań własnych, zależnych od wstępnego sprężenia, jest równa liczbie nieskończenie małych mechanizmów? Analiza potwierdziła, że liczba dźwigarów nośnych ma wpływ na liczbę nieskończenie małych mechanizmów. Jednak zachowanie dynamiczne kopuł zależy głównie od geometrii kopuły oraz od typu dźwigara nośnego, a nie od liczby mechanizmów.