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Multiple resonance damping or how do trees escape dangerously large oscillations?¹

Institut für Biologie III, University of Freiburg, D-79104 Freiburg, Germany; Forstliche Versuchs- und Forschungsanstalt Baden-Württemberg, D-79100 Freiburg, Germany

ABSTRACT

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.

Key Words: biomechanics • damping • Douglas fir • oscillations • resonance • theory of bending vibrations