A finite element model for investigating effects of aerial architecture on tree oscillations.

A finite element model was developed to study the influence of aerial architecture on the structural dynamics of trees. The model combines a complete description of the axes of the aerial architecture of the plant with numerical techniques suitable for dynamic nonlinear analyses. Trees were modeled on the basis of morphological measurements that were previously made on three 4-year-old Pinus pinaster Ait. saplings originating from even-aged stands. Calculated and measured oscillations were compared to evaluate model behavior. The computations allowed the characteristics of the fundamental mode of vibration to be estimated with satisfactory accuracy. Inclusion of a topological description of the aerial system in a mechanical model provided insight into the effect of tree architecture on tree dynamic behavior. Simplifications of the branching pattern in the model led to overestimations of the natural swaying frequency of saplings by 10 to 20%. Inadequate values of stem and root anchorage stiffness resulted in errors of 10 to 20%. Modeling results indicated that aerodynamic drag of needles is responsible for 80% of the damping in the studied trees. Additionally, damping of stem movement is reduced by one half when branch oscillations are not considered. It appears that the efficiency of the dissipative mechanisms depends directly on crown topology.