A one degree of freedom damped fruit tree model

A simple tree structure model was composed of a trunk and main roots. It included mass, spring, and damping elements, all reduced to the external end of the main roots. The model parameters, such as virtual turning center, reduced mass, spring constant, and damping coefficient, were measured on a real cherry tree. The model was then virtually shaken at 800 mm trunk height, and acceleration and displacement amplitudes versus shaking frequency were calculated. The real cherry tree was also shaken at 800 mm trunk height by an inertia-type shaker machine, and the same data were recorded. The acceleration amplitude vs. frequency and displacement amplitude vs. frequency functions were similar for both the virtual and real trees, showing the accuracy of the model. Trunk amplitude, power consumption, and specific power consumption were then calculated and transferred to any trunk height between 0 and 800 mm as a function of shaking frequency. These data suggest that the optimal shaking height is a function of shaking frequency.