Natural sway frequencies and damping ratios of trees: influence of crown structure.

Natural frequency and damping ratio were measured for nine plantation-grown Douglas-fir (Pseudotsuga menziesii Mirb. Franco) trees from the Oregon Coast Range under different levels of crown removal. Natural frequency of trees, in both their unpruned and completely de-branched states, was linearly related to the ratio of diameter at breast height to total tree height squared (i.e., DBH/H2), as expected from the theory governing the oscillation of a cantilever beam. Pruning resulted in an increase in natural frequency; however, at least 80% of the crown mass needed to be removed before this increase was noticeable. A single equation was developed that enabled the natural frequency of a tree of given size and pruning intensity to be predicted. Damping ratios of unpruned trees varied considerably from 8% to almost critical, while those for completely de-branched trees ranged from 1% to 8%. Two different trends in damping ratio were observed during pruning. Some trees exhibited an increase in damping ratio with initial crown removal, followed by a sharp decrease when the uppermost portion of the crown was removed. Others showed little or no change in damping ratio followed by a sharp reduction upon removal of the uppermost portion of the crown. Damping was mainly due to aerodynamic drag and preventing interference with neighbouring trees had little effect. Theoretical analysis using the finite element method indicated that changes in natural frequency as a result of pruning are not due to changes in damping ratio, but rather changes in mass distribution. This analysis also suggested that treating branches as lumped masses rather than individual cantilevers attached to the main stem may not be appropriate