# Damping of Beam Vibrations Using Tuned Particles Impact Damper
## 4 Experiments
### The Influence of Container Volume and Mass of Particles  
Five various volumes of the container were investigated in the laboratory tests. The lowest value corresponds to the fully compacted grains. Such a case results in loading of the system by the concentrated mass of the grains. The dissipative properties of TPID element is then reduced to the minimum. For the maximum value of volume the vibrating grains can freely collide between each other. Also the impacts of particles and walls of the container is observable, which results in increased dissipative properties of the granular damper. Three different compositions of the particles were tested. Consequently, three various masses were included in the described experiments. Typical laboratory tests results are depicted in Figures 5 and 6. Root Mean Square (RMS) values of the beam tip displacements (1) for various operating parameters were determined to reveal the recorded response of the considered system. Additionally the RMS data are presented in Table 2.  
\[D_{RMS}=\sqrt{\frac{\sum_{i=1}^{n}a_{i}(f_{j})^{2}}{n}}, \tag{1}\]  
where \(a_{i}\)--maximum displacement amplitude in \"\(i\)\" cycle of vibration, \(f_{j}\)--frequency of excitation, \(j\)--case number, \(n\)--number of amplitude values in each case. Diagrams depicted in Figure 5a,c,e illustrate the effect of variable container volume for three types (masses) of granular materials. The selection of appropriate mass of particles is of first importance. This parameter can not be easily changed in the presented TPID prototype. At this stage of the research it was assumed, that the total mass of the particles (\(M_{p}\)) was 5%, 10% and 20% of the whole system mass (\(M_{s}\)). The second and the most important aspect is the volume of the container, controlled by the volume of the inflatable balloon placed inside the casing. Data depicted in Figure 5 confirm that changing the volume of the container may lead to reduction of the resonance amplitudes. Lower number of particles (lower mass) is related to limited number of \"intergranular\" collisions what obviously decreases the dissipative properties of the TPIDs (Figure 5c,e). In Figure 5a,b it can be observed that the RMS amplitude for the case where the particles mass is 10% of the total mass of the system and for the lowest container volume (\(V_{min}\)) was 42.5 mm. The value of the considered parameter for the maximum volume of the container (\(V_{max}\)) was 22.5 mm, which can be described as a reduction of vibrations by 53%. Lower damping properties were observed for the remaining two cases of the particles mass. In experimental studies, in which the granular mass was 20% of the mass of the entire system, the recorded RMS amplitudes for minimal and maximal volumes were 46.3 mm and 31.5 mm respectively. Analyzing the presented data, it turns out that the system vibration amplitude decreased by 32%. In a situation where the TPID damper worked with the use of granules with a mass equal to only 5%, the reduction of system vibrations was much lower than in the first two cases and amounted to 12%. Analyzing the RMS amplitude for all cases also including the intermediate values of the damper volume, it can be observed that the amplitudes of the system response change nonlinearly, and thus the vibration damping effectiveness is also nonlinear as a function of the TPID damper working space variation. Switching \"on\" and \"off\" processes, which involves increasing the initial value of the operating volume slightly changes the natural frequencies of the considered system. This phenomenon is presented in Figure 5b,d,f. Nonlinear contact forces occur during collisions between the granules and the damper container. In the considered mechanical systems they are coupled with changes in the dynamics of the structure.