# Damping of Beam Vibrations Using Tuned Particles Impact Damper
## 3 Test Stand  
To reveal the extraordinary features of the TPID prototype, the special laboratory test stand was designed (Figure 2). It was aimed to conduct the research on the kinematically excited cantilever beam equipped with the TPID device. Various TPID damper parameters were taken into consideration during the experiments. In the first stage of empirical investigations, to fully understand the features of the investigated system the values of TPID such as the volume of container, mass of the grains or type of granular material were systematically changed. Subsequently, the tip of the vibrated beam amplitudes for the resonant range were measured for the various parameters configuration.  
The features of the investigated system, including the geometry of the grains and the dimensions of the test stand, are presented in Table 1. The range of laboratory tests included three different granular media (Figure 3). The spherical shape of particles having diameter \(D=6\) [mm] were tested in laboratory tests. Additionally, five different filling ratios (grains volume to total volume) were taken  
Figure 1: Scheme of the tests stand and the Tuned Particles Impact Damper (TPID) prototype.  
into account. At the current stage of investigations the authors did not concern the wear of grains material process and its influence on the damping properties of the device. The whole research plan is presented in Figure 4.  
The measuring system consisted of LabJack and National Instruments data acquisition cards. The beam tip displacements were measured by Emron laser sensor and additional accelerometer located at the end of the beam. The signals were recorded on a personal computer with dedicated recording and analyzing software. The previously mentioned beam was clamped in a special handle and mounted in the individually designed exciter (Figure 2). A special arrangement of gears, belt transmissions and eccentric disks were transforming the rotary movement of the electric rotor into a reciprocating movement of the exciter. The kinematic excitation rule including variable frequencies (up to 60 Hz) and fixed amplitude level (\(\pm\)5 mm) were considered. The data was sampled at 0.5 kHz.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Component** & **Parameter** & **Value** \\ \hline \multirow{2}{*}{Cantilever beam} & Size & Length: 600 [mm], Width: 35 [mm], High: 2 [mm] \\  & Material & Steel \\ \hline \multirow{2}{*}{PID} & Size & Length: 63 [mm], Width: 63 [mm], High: 200 [mm] \\  & Material & Plastic and steel \\ \hline \multirow{2}{*}{Grains-case 1} & Size & \(D=6\) [mm] \\  & Material & Plastic \\  & Density & \(\rho_{p}=1000\) [\(\frac{kg}{m}\)] \\ \hline \multirow{2}{*}{Grains-case 2} & Size & \(D=6\) [mm] \\  & Material & Steel \\  & Density & \(\rho_{s}=7860\) [\(\frac{kg}{m}\)] \\ \hline \multirow{2}{*}{Grains-case 3} & Size & \(D=6\) [mm] \\  & Material & Mixed (plastic and steel) \\ \hline \multirow{4}{*}{Balloon} & Size & \(Volume_{1}=0.20\) [dm\({}^{3}\)] \\  & Size & \(Volume_{2}=0.35\) [dm\({}^{3}\)] \\ \cline{1-1}  & & \(Volume_{3}=0.50\) [dm\({}^{3}\)] \\ \cline{1-1}  & Material: rubber & \(Volume_{4}=0.65\) [dm\({}^{3}\)] \\ \cline{1-1}  & & \(Volume_{5}=0.79\) [dm\({}^{3}\)] \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters used in experiments.  
Figure 2: Test stand.  
For rapid changes of the rubber balloon volume the compressor equipped with pressure sensors was used. The volume changing of the TPID compartment consisted of inflating and deflating the balloon that tightly filled the working chamber of the granular shock absorber. Recorded data were analyzed in the SageMath environment based on Phyton programing language.