Production Practices and Quality Assessment of Food Crops. Vol. 1

278 M. Ruiz-Altisent et al.
M: total mass (equivalent mass of the tree + mass of the shaker), kg
c: damping factor, N.s/m
k: elastic constant, N/m
Being the maximum force:
F max = 2mr ω 2
in case where m 1 ≅ m 2; r 1 ≅ r 2 and ω 1 ≅ω 2 = ω
Approximately the amplitude of vibration results [12]:
s = 2mr/M
The equivalent mass of limbs M can be estimated as 0.2 kg per diameter-mm and
for trunks as 2 kg per diameter-mm. Natural frequency, damping factor and elastic
coefficient of the trees change with time of the year, between the following approximate
values:
f = 0.5–3.5 Hz
c = 0.1–0.7
k ≤ 2000 N/cm
Fruit detachment is, for any particular species and type of trees, the effect of a
combination of:
– stroke,
– frequency and
– pattern of vibration.
Figure 15. Directions of vibration, depending on ω 1 and ω 2.