A Fruit Tree Stability Model for Static and Dynamic Loading

Static and dynamic tests were carried out on the trunk and main roots of cherry trees to obtain their important elastic and viscous properties. The horizontal and vertical displacement of the stem was measured at horizontal forces 80 cm above ground level. Force relaxation tests were carried out in the same way for 15 min. Main root samples were taken from a felled tree for bending, stressing and force relaxation tests. Accelerations of pre-stressed and released trunks were recorded for whole trees and for trunks when the limb was totally removed above 85 cm. From the static and dynamic test results a common model was composed of two Maxwell elements, a damping element and a spring, all coupled in parallel. During static loading, i.e. at force relaxation, the damping of the two Maxwell elements was active. During dynamic loading, when the trunk is swinging at its own frequency, only the single damping element acts together with the three parallel springs. The damping of the Maxwell elements is too high to influence the oscillations at the natural frequency.