RESUMEN
To further understand the mechanics of trees under dynamic loads, we recorded damped oscillations of a Douglas fir (Pseudotsuga menziesii) tree and of its stem without branches. Eigenfrequencies of the branches were calculated and compared to the oscillation frequency of the intact tree. The term eigenfrequency is used here to characterize the calculated resonance frequency of a branch fixed at the proximal end to a solid support. All large branches had nearly the same frequency as the tree. This property is a prerequisite for the distribution of mechanical energy between stem and branches and leads to an enhanced efficiency of damping. We propose that trees constitute systems of coupled oscillators tuned to allow optimal energy dissipation.
RESUMEN
This paper reports on the effect of wind loading below damaging strength on tree mechanical and physical properties. In a wind-exposed Sitka spruce stand in western Scotland, 60 trees at four different levels of wind exposure (10 m, 30 m, 50 m, 90 m from edge) were characterized for stem and crown size and shape and mechanical properties, including structural Young's modulus (E(struct)), natural frequency, and damping ratio. E(struct) increased from the stand edge to the mid-forest, but with a large inter-tree variation. Swaying frequency and damping ratio of the trees also increased with distance from edge. Wind-exposed edge trees grew shorter, but more tapered with an overall lower E(struct), allowing for greater flexural stiffness at the stem base due to the larger diameter and for higher flexibility in the crown region of the stem. The trees at the middle of the stand compensated for their increased slenderness with a higher E(struct). Thus, for the different requirements for wind-firmness at stand edge and mid-forest, an adapted combination of tree form and mechanical properties allows the best withstanding of wind loads. The results show the requirement to understand the different strategies of trees to adapt to environmental constraints and the heterogeneity of their growth reactions in response to these strategies.
RESUMEN
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.
