Abstract:
The behavior of coniferous trees subjected to wind loading was investigated
through a series of experiments and also through simulation modeling. Previous
studies that measured the natural oscillation frequencies and damping ratios were
reviewed and equations were developed for predicting the natural frequency of a
tree from the ratio of diameter at breast height to total tree height squared (i.e.,
DBHJH2). Experiments were performed on nine plantation-grown Douglas-fir
(Pseudotsuga menziesii Mirb. Franco) trees to quantify the effects of crown
removal on natural frequency and damping ratio. Results showed that pruning
increased natural frequency; however at least 80% of the crown mass needed to be
removed before this increase was noticeable. This effect was consistent across all
trees and a single equation was developed that enabled the natural frequency of a
tree of given size and pruning intensity to be predicted.
The dynamic behavior of three Douglas-fir trees was modeled with the
finite element method (FEM). Bole and branch geometry were measured in detail
for each tree, enabling the first order branches from each tree to be represented as
individual cantilever beams attached to the bole. Predicted natural frequencies of
the three trees were in close agreement with observed values, and both natural
frequencies and damping ratios were very sensitive to branch modulus of elasticity.
Damped free vibration tests were conducted on two instrumented Douglas-fir
trees by displacing the bole and measuring the oscillations of the bole and
selected branches. Results showed that branch oscillation frequency was similar to
the natural frequency of the tree, but different from the natural frequency of the
individual branches themselves. In this situation the branches behaved as forced
damped harmonic oscillators with the forcing frequency equal to the natural
frequency of the whole tree. Measurement of the oscillations of selected branches
during strong winds indicated that branches primarily oscillated at frequencies
below their natural frequency. Some higher frequency oscillations were observed,
however these may be noise in the data. Results did not appear to support the
theory that branch natural frequencies are similar to the first harmonic of whole tree
natural frequency.
