###### Abstract  
In the last decade, there has been a significant increase in parcel delivery shipments all over the world due to online stores and consumer demand to receive the products in a shorter period of time. It is especially true when situations like COVID-19 limits personal purchases in shopping malls as well as grocery and pharmaceutical stores. This often means that courier operators try to deliver packages utilizing vehicles with racks or shelves, which during the COVID-19 epidemic are not there anymore. This study measured the vertical vibration levels that occur in stacked parcels during express delivery versus the simulation technique in the laboratory. The goal of this paper was to measure and compare the vibration levels between laboratory practice and field transportation. For the measurement a three-layer stacked unit was built to observe the vibration levels on different road conditions in a parcel delivery vehicle and ASTM vibration profile (ASTM International). Then the measured acceleration-time data were analyzed in terms of power spectral densities (PSD) and the presented statistical data provided an understanding of the variability of intensity in different levels in stacked unit. The results showed that the vibration level increases in the stacked load upwards and with worse road conditions, but even in the worst case it did not reach those vibration levels that the laboratory test showed. Moreover, the layers of the stacked unit are in out-of-phase motion in the field, while the stacked unit in the vibration simulation usually is in-phase motion. Results indicate that the proposed vibration simulation does not correlate well with typical field vibration. This is fundamentally true as during a forced vibration created by a single-axis shaker, do not account for additional inputs occurring simultaneously creating an off-balance to the loads and as a result are less severe than simulated conditions. These findings are limited to single axis vibration simulation and unsecured loads. vibration; power spectral density (PSD); stacked packages; parcel delivery +
Footnote †: journal: Applied Sciences  
parcels are stacked on top of each other. This situation is complicated further by the fact that the fixation accessories such as fixing straps or bands are virtually non-existent in this transportation mode. This is a common practice in Europe, but on some continents, this is different because the operators use vehicles equipped with shelves. Figure 1a,b shows some examples for parcel shipments during daily courier service. The shipments for courier parcel packages usually consist of small size, lightweight and time sensitive products. The vibration environment of these stacked shipments produces unique physical events due to free movement spaces around them [2]. Since they are not restrained as unitized loads with stretch wrap or banding. In the vertical direction these parcels practically can move freely. This physical condition is very important to analyze in order for packaging engineers to design suitable protective packaging systems. The vibration environment during distribution can be based on factors such as vehicle body structure, type of vehicle suspension and tires, road roughness, vehicle speed and actual payload, respectively [3]. Previous studies have measured and analyzed vibration levels for parcel delivery vehicles and CEP (Courier Express Parcel) modes of transportation [4; 5; 6; 7; 8; 9]. Factors regarding the effect of payloads, suspension system and road condition to vibration levels during express in delivery vehicles have also been previously studied [4; 9; 10]. However, all this previous research measured and analyzed the vibration levels on the floor of the vehicle and none of them took into consideration that most of these parcels are transported in \"unrestrained stacked configuration\" and without shelving due to the intensive flow of goods and relatively limited capacity of vehicles.