## 3 Results and Discussions
### Power Spectral Density Plots (PSDs)  
The measured data were analyzed to determine the PD levels of vibration in field and laboratory measurements. Figure 8 shows the developed PSDs of each layer of the stacked unit and floor and supplemented with the spectrum of ASTM D7386. It can be seen that the measured PD levels are almost the same in each layer between 1-8 Hz in the case of field measurements, and 1-6 Hz in the laboratory. Except for the laboratory, the PD levels in that frequency range did not reach the level of the test spectrum, but they increased in the function of the road condition. The observed vibration levels on the floor decreased from about 18 Hz on all road conditions, but in the case of country and urban roads between 29-48 Hz this vibration level almost coincides with the test spectrum of ASTM D7386. It is worth noting that each stacked layer shows higher PD levels in a difference frequency range than in the field measurement data, where they are higher than the other layers and the test spectrum; the highest PD levels were recorded on the 3 rd layer between 9-14 Hz and 19-33 Hz, on the 2 nd layer between 16-19 Hz, and on the 1 st layer between 35-51 Hz. All stacked layers rapidly decreased above 50 Hz, and they were below the floor vibration intensity above 55-60 Hz. These phenomena can also be observed in the laboratory, with the difference that the frequency ranges of the phenomena are different. In this case the highest PD levels are recorded on the 3 rd layer between 8-22 Hz, on the 2 nd layer between 22-33 Hz, and on the 1 st layer between 33-56 Hz. At this point it is so important to emphasize that the vibration simulation protocol generally uses time-compression method by increasing the vibration magnitude during simulation [16; 17], presumably ASTM protocol also applies this. However, it can be clearly seen in Figure 9 that this artificial gain is not evenly distributed over the entire frequency range studied. The PD levels of the layers in the stacked unit reached or exceeded the ASTM spectrum levels in the frequency range of 7-50 Hz, so here the artificial amplification of the test spectrum cannot be interpreted. In the 1-6 Hz lower frequency range the field PD levels, even in the higher stacking level, are much lower than the protocol values. Over 50 Hz the response vibration of the unit rows is also lower than the test spectrum. So, in these two frequency regions, the assumed time-compression can be determined even for the top level of a stacked unit without fixation. Another observation is that the motion of the stacked unit deviates the motion of both vibration table and the delivery vehicle between 8-50 Hz. It should be emphasized here that the ASTM vibration test protocol is based on field measurements that were conducted in the US with parcel delivery vehicles [4] and are used as worldwide protocol in the packaging testing practice (as practically the only one for parcel package delivery vibration testing), but some former studies showed that the vehicles that used in outside of US produce slightly different PSD shape in the 1-200 Hz frequency range [4]. Furthermore, the PSD plot obtained for this study shows a little bit lower intensity than it was observed in former published research [4]. The reason can be that this paper used only one specific vehicle to observe the vibration event in the field focusing on the vibration levels in unit load, until the previous study applied several different parcel delivery vehicles to get information about the vibration levels. The overall G\({}_{\text{rms}}\) values were calculated for each layer of the stacked unit and also for the floor. These data are presented in Table 3. In the analyzed frequency range (1-200 Hz) the values increased upward except in the laboratory where this tendency was true for the stacked unit but in this case the highest G\({}_{\text{rms}}\) value was on the floor.