Natural frequencies and damping ratios of Norway spruce (Picea abies (L.) Karst) growing on subalpine forested slopes

Abstract

We investigated the natural frequencies and damping ratios of 24 Norway spruce trees (Picea abies (L.) Karst) growing on subalpine forested slopes using swaying experiments. Trees were winched to the release position using a manually operated cable winch. Before release, the stem base rotation was approximately 2 degrees. All trees were tested in both fall-line and cross-slope direction if possible to reveal the difference between the two perpendicular directions. A new method based upon the Hilbert transformation for evaluating the damping ratio for trees was used. It enabled us to investigate the damping ratio for all excited modes of vibration in the tree structure during the swaying experiments and to study if velocity proportional damping (viscous damping) is a reasonable assumption when predicting the tree response to different external actions using mechanical models. No difference in first natural frequency and damping ratio was found between the fall-line and cross-slope direction for all tested trees. The first natural frequencies correlated best with the diameter at breast height and squared total tree height DBH/H 2. For the damping ratio, no significant correlation with different tree characteristics could be found. A non-velocity proportional damping ratio was observed for two trees. This indicates that using a viscous damping for all frequencies is an appropriate simplification when modelling the wind-tree interaction.