Abstract:
Abstract: Most existing finite element models of a fruit tree used the trunk-branch model to simulating vibration response, ignoring the effects of fruit and leaves. But the fruitless and leafless model had many differences with the actual fruit tree and could not accurately calculate the vibration characteristics. In this study, a method for constructing a tree's vibration model with fruits and leaves had been proposed. This method combined laser scanning technology and finite element calculation methods, having the ability to calculate the vibration characteristics of fruit trees based on the accurate shape of fruit trees. The first step in constructing the model with fruits and leaves was to extract the skeleton points and branch radius from the laser scanning point cloud information of the fruit tree. The next step was using the extracted fruit tree skeleton points as the nodes of the finite element model to construct a fruitless and leafless fruit tree model. Adding mass to the nodes based on the fruits and leaves natural laws with the assumption that some kind of fruit trees had the consistent distribution of fruits and leaves during the harvest period, the 6-degree-of-freedom beam element vibration model was constructed finally. A fruit-and-leaf vibration finite element model was applied to a fruit-leafed the ginkgo tree. A small laser scanner was used to scan the experimental ginkgo tree three times to obtain complete point cloud information. Through a statistic of 8 factors for the leaves and fruits distribution of the ginkgo tree, this study analyzed the number and quality of leaves and fruits on branches of unit length and based on the regular pattern above to build the ginkgo tree vibration model. The Ginkgo fruit distribution obtained from the analysis was that the average spacing of axillary buds was about 4.2 cm, an average of 6 fruits grow on each axillary bud, and the weight of each fruit was about 6 grams on branches with a diameter of less than 10 mm. The Ginkgo leaves distribution was that the average spacing of axillary buds was about 4 cm, an average of 5 leaves grow on each axillary bud, and the weight of each leaf was about 0.4 g on branches with a diameter of less than 12 mm. To verify the accuracy of the calculation results, the ginkgo trees were tested in three states of fruit-leaf, fruit-free, and trunk-branches. By comparing the three testing spectral curves, this study found that there were many differences at the number of natural frequencies and acceleration amplitude, which meant leaves and fruits significantly affected the spectral characteristics. Comparing the calculation results of the first 15 models and calculation results in 15-25 Hz with sample test results, this study found that the number of natural frequencies obtained from simulation results was more than the number of natural frequencies obtained from test results. The natural frequencies from test results could find very close values in the simulation results. The amplitude and the acceleration response of each branch in the tested spectrum curve were consistent with the simulation vibration mode shape. The corresponding maximum relative errors of natural frequencies in the three states of fruit-leaf, fruit-free, and trunk-branches were 5.76%, 2.06%, and 1.98% Hz, respectively. The average relative errors of natural frequencies were 2.32%, 0.82%, and 0.95%. By analyzing the calculation model's accuracy, this study found that adding the leaves and fruits weight to the trunk-brank model could improve the calculation accuracy when the tree's shape and analysis elements' quality of the trunk-brank model had not changed. The modeling method described in this study could obtain the natural frequencies of the fruit tree accurately and quickly. This study had a guiding significance for resonance method harvesting in practical applications.