## 3 Experimental Investigation  
### Experimental Program and Setup  
According to the main aim of the research--experimental investigation of critical tensile force and its comparison with an analytical value--the following problems were solved experimentally:  
* measuring the moment of inertia of rotating masses in order to obtain the equivalent mass M;
* finding the modulus of elasticity of the rod;
* studying the influence of semi-rigidity in the rod ends connection, caused by the elasticity of the connection elements at the rod ends to the guide and slider;
* obtaining the buckling load for all investigated types of end connections. To solve the above-mentioned problems, a stand, corresponding to a general scheme shown in Figure 1, was used. The view of the stand, presenting its construction, is shown in Figure 7a. The axis of wheel 1 with bearings and the linear guiding elements of the direction slide 2 are connected to the basic rod 3. Joint 4 that connects the elastic rod 5 to the wheel allows a rigid or a pinned connection. Connection joint 6 between elastic rod and \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & & \multicolumn{2}{c}{\(D\%\)} \\ \cline{3-5} R/L & \(L\)/\(R\) & **Rigid-Rigid** & **Pinned-Rigid** & **Rigid-Pinned** \\ \hline  & 0.80 & 1.250 & 4.71 & 0.05 \\  & 0.75 & 1.333 & 2.31 & 0.06 \\  & 0.67 & 1.500 & 0.63 & 0.11 \\  & 0.60 & 1.667 & 0.11 & 0.23 \\  & 0.50 & 2.000 & 0.04 & 0.51 \\  & 0.40 & 2.500 & 0.11 & 1.23 \\  & 0.33 & 3.000 & 0.63 & 2.29 \\  & 0.25 & 4.000 & 2.29 & 5.47 \\  & 0.80 & 1.250 & 4.71 & 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Maximum deviation of \(\omega^{2}/\omega_{0}^{2}\) from linear dependence in the range of \(0\leq u\leq u_{\sigma}\) for various \(L/R\) ratios. Figure 6: Variation of maximum deviation of \(\omega^{2}/\omega_{0}^{2}\) from linear dependency in the range of \(0\leq u\leq u_{\sigma}\) vs. the \(R/L\) ratio. direction slide has a screw stopper that allows a rigid or a pinned connection. According to the construction of the elastic rod connection joint to the wheel, the radius \(r\) of the rod end displacement was 305 and 295 mm for the rigid and pinned connections, respectively. The elastic rod was made of a hardened steel strip with a section of 19.5 \(\times\) 1.47 mm\({}^{2}\); the working length L was controlled by measuring, according to the selected \(L/R\) ratio. For the rigid connection, the working distance was measured from contact A (Figure 7b,c), and for the pinned one, from the rotation axis (Figure 7d). The extension of the traction cable 7 (pulley block and weights at the end) are not shown in Figure 7a and were used as a typical solution for loading. Figure 7: (**a**) Upper view on the horizontal stand for testing systems, including a tensile rod with an end moving along a circular trajectory: 1—wheel, 2—direction slide, 3—basic rod, 4—connection joint to the wheel, 5—elastic rod, 6—connection joint to the direction slide, 7—traction cable; (**b**) rigid joint connection of the elastic rod to the wheel; (**c**) connection joint between elastic rod and direction slide with a screw stopper that allows a rigid or a pinned connection; (**d**) pinned connection of the elastic rod to the wheel. To obtain the vibration frequency, the wheel circular velocity was measured by an inductive gage, including a permanent magnet located on the wheel and a stationary coil. The signal was transmitted from a data logger to a PC each 0.01 s. This transmission allowed transferring the data at the maximum measured frequency with an error of 0.8%. For linear measurements of static displacements, the error for a standard gage was 0.05 mm. In the proposed testing stand design, the reduction of the rod movable end resistance to movement was achieved by the increased movement radius and structural design of mobility by wheel rotation. If the radius of the rolling balls in the central bearing assembly is 12 mm and the wheel radius is 295 mm, the decrease in friction resistance to rod end movement is 24.6 times.