Effect of Fractal Tree Structures on Fruit’s Vibration Amplitude in Mechanical Harvesting Process

Tree structures are complex and random in nature but they follow some specific rules according to their various kinds. The objective of this work is to model three fractal trees’ dynamic behavior in the mechanical shaking process and study the effect of the bifurcation ratio and the length-order ratio (pruning ratio) on the frequency response and the percentage of the harvested fruit. Experimentally the static loadings are carried out on the trunk and branches of the tree to obtain their important elastic properties. In order to obtain viscoelastic properties of the tree, its dynamic free vibration is examined. The fractal trees are modeled with an equivalent multi degree of freedom mass-spring models and the governing equations of motion are derived by means of Newton’s second law; then, they are solved numerically for some sample fractal trees. Consequently, for different values of the bifurcation ratio and the length-order ratio (fractal dimension), the displacement of the fruit is calculated and the displacement amplitude of the fruit is obtained. Also, the effects of the tree structures and pruning ratios on the displacement amplitude of the fruit are discussed.

کلیدواژه ها:

Fractal structures ، Fractal dimension ، Bifurcation ratio ، Pruning ratio ، Frequency response