This study presents a predictive dynamic model developed to analyse the mechanical response of trees submitted to a turbulent airflow. This finite-element model integrates a three-dimensional description of tree architecture and is driven by fluctuating drag forces applied on all parts. For validation purposes, instantaneous wind velocities and wind-induced stem displacements of two trees were recorded in a mature Maritime pine stand (Pinus pinaster) at several heights. The tree geometrical and physical characteristics were measured to describe their architecture. No model parameter was adjusted. Tree motions appear to be driven by wind pulses reflecting turbulence intermittency. No evidence is found for resonant behaviour. In the mean wind direction, the simulated oscillations agree well with the measured time series. The underestimation of tree movement in the cross-stream direction outlines the importance of torque behaviour on the predictive accuracy of the model. The mechanical transfer functions of the modelled trees show vibration peak frequencies very similar to the measured ones. At higher frequencies, the simulated damping appears overestimated, with the set of parameters used. The model provides a sound basis to further investigate the influence of tree aerial architecture and turbulence structure on tree stability to wind.

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.

The aim of this study was to investigate the influence of aerial architecture on the dynamic characteristics of young maritime pines (Pinus pinaster Ait.) using a mechanistic approach. For this purpose, three 4-year-old saplings with prominent differences in their branching patterns were submitted to free oscillation tests. The tests were carried out with different methods and directions of mechanical loading in order to initiate the movement of each sapling. The oscillations of the different architectural elements, i.e. stem and branches of different topological order, were measured with inclinometers and strain gauges fixed to saplings. Successive pruning of the architectural elements was carried out to evaluate their relative influence on the dynamic characteristics of the trees. The aerial systems were digitized before the mechanical tests in order to use 3D visualization techniques and to make architectural analyses of the crown structure. Two distinct modes of deformation were detected during free oscillations. The natural swaying frequency ranged from 0.6–0.8 Hz for the saplings tested at the same period of the year. The frequency variations were partly explained by the morphological differences of the experimental subjects. The motions of the axes were found to depend on their topology, i.e. the movement of the axes of a given branching order was forced by the movement of their respective bearing axis. The axes of third branching order had a significant and negative effect on the damping of the natural deformation mode. Results point out the major role played by foliage, qualitatively and quantitatively, on the damping of tree motions and on coupling the motions of the crown components.

Quantifying wind risk in planted forests is critical to ensure the provision of wood-based biomaterials and forest ecosystem services in the future. Tree sway dynamics play a major role in determining their vulnerability to wind storms. While structural engineering theory can greatly assist in predicting tree and branch motion accurately, the effects of forest aging and silvicultural treatments on motion and the likelihood of mechanical failure are still poorly understood. In this study, we simulate the growth of an individual model tree and its architecture for a managed, even-aged pure Cryptomeria japonica D. Don. stand. The dynamic behavior of the tree is predicted for a rotation period at a 5-year interval using finite element analysis. Results show that tree natural sway frequency is subject to a 5-fold decrease over the tree's lifetime. The tree is thus more susceptible to absorb turbulent kinetic energy from the wind as it grows older. The damping ratio, which measures how rapidly the tree can return to its rest position after being deflected, is predicted to increase by a factor of four. By simulating the mechanical response to a wind gust, the model predicts a quick transition from a low risk of failure in the juvenile phase to a high-risk situation in the mature phase. The transition occurs between ages 15 and 30 when canopy closure takes place, when juvenile wood formation stops in the lower stem region and when the first thinning is carried out. Wind risk plateaus after the transition period. The age-risk relationship shown by the model is consistent with post-typhoon damage patterns documented by inventories in Japanese planted forests, albeit with a sharper transition.