• DOI:10.1098/RSTB.2003.1348
• Corpus ID: 40409040

Oscillations of plants' stems and their damping: theory and experimentation.

@article{Brchert2003OscillationsOP,
  title={Oscillations of plants' stems and their damping: theory and experimentation.},
  author={Franka Br{\"u}chert and Olga Speck and H C Spatz},
  journal={Philosophical transactions of the Royal Society of London. Series B, Biological sciences},
  year={2003},
  volume={358 1437},
  pages={
          1487-92
        }
}

• F. Brüchert, O. Speck, H. Spatz
• Published 29 September 2003
• Mathematics
• Philosophical transactions of the Royal Society of London. Series B, Biological sciences

Free oscillations of upright plants' stems, or in technical terms slender tapered rods with one end free, can be modelled by considering the equilibrium between bending moments and moments resulting from inertia. For stems with apical loads and negligible mass of the stem and for stems with finite mass but without top loading, analytical solutions of the differential equations with appropriate boundary conditions are available for a finite number of cases. For other cases approximations leading to an upper and a lower estimate of the frequency of oscillation omega can be derived. For the limiting case of omega = 0, the differential equations are identical with Greenhill's equations for the stability against Euler buckling of slender poles. To illustrate, the oscillation frequencies of 25 spruce trees (Picea sitchensis (Bong.) Carr.) were compared with those calculated on the basis of their morphology, their density and their static elasticity modulus. For Arundo donax L. and Cyperus alternifolius L. the observed oscillation frequency was used in turn to calculate the dynamic elasticity modulus, which was compared with that determined in three-point bending. Oscillation damping was observed for A. donax and C. alternifolius for plants' stems with and without leaves or inflorescence. In C. alternifolius the difference can be attributed to the aerodynamic resistance of the leaves, whereas in A. donax structural damping in addition plays a major role.