Vibration behavior of plantation-grown Scots pine trees in response to wind excitation

This paper deals with the dynamic responses of three plantation-grown Scots pine trees to turbulent wind loading. Although individual tree movement was complicated and irregular in the analyzed wind speed range (hourly mean wind speeds at canopy top below 4 m s−1), results from the cross-wavelet transform and wavelet coherence calculations demonstrate that wind-induced tree displacement strongly covaried with wind loads exerted on the trees by coherent structures. These wind loads caused largest tree displacements in the along wind direction as well as in the across wind direction. The absorption of energy available from wind loads in the range of the damped natural sway frequencies of the sample trees’ stems was of minor importance for tree displacement. The application of the bi-orthogonal decomposition provided insight into the resulting modal deformations of the sample trees’ stems. Based on measured stem displacement data, the mean mode shapes for the first eight stem vibration modes (four mean mode shapes in along wind direction and four mean mode shapes in across wind direction) could be identified. The shapes of these modes were quite similar to the normal mode shapes of a clamped-free beam. For the analyzed wind speed range it is shown that most of the energy absorbed by the trees from the wind is dissipated by tree sway in the first mode. Higher vibration modes localized on the sample trees’ stems were only of minor importance for the trees’ responses to wind.