An Experimental Study and Mathematical Modeling of Vibration Transfer in Pistachio Trees Using an Inertia-Type Trunk Shaker and Field-Adapted Wireless Sensors

Trunk shakers are the most widely used mechanical harvesting machines for harvesting nut trees, including pistachio in California. Improvement of these machines requires a better understanding of the shaking dynamics of the existing trunk shakers during harvest. In this study, the effects of four different shaking patterns on three sizes of pistachio trees of different ages, shapes, and sizes were investigated under field conditions. The vibration acceleration of the real pistachio tree was measured using a wireless network of 3-axis accelerometers installed on the shaker head and different parts of the trees during the shaking harvest. Changes in acceleration and the effect of tree morphology on the magnitude of acceleration in each pattern are presented and discussed. A new location index λ, which is based on the distance of the sensor from the shaking point and diameter of the branch at each sensor location, is introduced. This study focused on mathematical modeling of the variation and distribution of the acceleration throughout the tree canopy. The sensor location index, relative force ratio (RFR), and relative kinetic energy ratio (RKER) were defined to better understand the energy damping in each part of the tree. The results showed that the relationship between the acceleration peaks and the sensor location index could be expressed by a third-degree polynomial function with an acceptable coefficient of determination. Under different shaking patterns, similar changes in the RFR of the tree at different locations and for different trees were observed. This finding indicates that the vibration force is significantly damped as the distance from the shaker clamps increases. However, the RKER values at the same shaking pattern result in different effects at different points on the branches according to tree morphology.