## 4 Discussion
The excellent fit is achieved for the reduced mass \(m_{r}=0.5m_{n}\), where the mass of the one node \(m_{n}\) is calculated by dividing the weight of the experimental model by six. In the curve fitting procedure, the formula (16) was treated as a parametric equation with the mass \(m_{r}\) as the parameter. The fitting procedure was constructed by changing the mass \(m_{r}\) to match the theoretical solution (16) to the experimental data. The non-linear least-squares fitting procedure was used, in which the best fit was found for the sum of squares to errors \(SSE=1.144\) and for the square of the multiple correlation the R-square \(R_{sq}=0.9745\). The statistics \(SSE\) is indicating a better fit with a value closer to zero. For the \(R\)_-square_ statistics the better the fit, the closer the values to one. The sensitivity of the frequency to the self-stress state is high enough to be successfully used to control the dynamic properties of the simplex. The results from the FEM are presented for a lumped-mass idealization of the finite element mass matrix with the diagonal terms \(m_{r}=0.5m_{n}\) and for the consistent-mass formulation with the calculated effective mass of the cables based on the weight of the experimental model. Very good agreement with formula (16) and with the experiment was found for the lumped-mass approach. In the case of the consistent-mass approach, the agreement is worse, although the change of the frequency has similar, non-linear characteristics during the prestress in the experiments and FEM calculations. In the FEM calculations the first frequency increases in proportion to the square root of the prestress force in the cross-cable. The difference between the experiments and numerical calculations for the consistent mass matrix decreases with the increase of the prestressing from approximately 60% for the first level through 30% for the fourth to 20% for the 13 th level. For the level greater than 1.5 kN the difference is less than 25%, which may be acceptable at the moment, considering the very complex mass distributions in the physical model. It was observed in the experiments when the structure was not prestressed, the gravity caused heavy elements such as nodes to create a little prestress, which is not taken into account in the numerical analysis. Considering both the FEM calculation, quite good agreement was found between results of the finite element method and experimental tests. It seems that the external loads should act similar to the prestressing. They cause the additional prestress. However, their effect should be greater with the lower prestress level due to the fact that with the increase of the prestressing the member forces caused by the external load gradually decrease relative to the prestress and their effect on the vibration frequency decreases. Although non-linear analysis should be used to calculate the static load response of the tensegrity structure, the dynamic response can often be linearized around the equilibrium state corresponding to a designed prestress level and small vibrations can be analyzed. It was shown in the paper that the natural frequencies and modes of the simplex can be obtained using the experimental modal analysis approach. Also, usage of the finite element method in numerical simulations, allows to control the stiffness by regulating the level of pre-stressing. However, practice shows that there are some difficulties and an experimental validation can bring useful information, especially if the natural frequencies of the structure are measured and filtered from the whole experimental vibration spectrum. The effect of self-stress on the overall stiffness of the tensegrity simplex was shown experimentally. The tendency of increasing the first natural frequency with an increase of the prestressing is clear visible in the experiments. It was also shown that adjustment of self-stress levels by means of the prestressing can also be used to control the dynamic properties of tensegrity simplex as the structures with one infinitesimal mechanism.