Understanding tree stability under self-weight and applied loads from wind and snow is important when developing management strategies to reduce the risk of damage from these abiotic agents. In this paper, linear buckling analysis was conducted using the finite element method to identify the instability modes of a tree structure under a specified set of loads. A non-prismatic elastic circular column of height H was analysed, taking self-weight into account. Various scenarios were considered: column taper, base rigidity, radial and longitudinal stiffness, ellipticity and crown weight. The effect on the critical buckling height was assessed in each case. Validation against closed form solutions of benchmark problems was conducted satisfactorily. The results indicate that column taper, base rigidity and the stiffness/density ratio are particularly important for this problem. Further comparison was made using data from a 15-year old Pinus radiata stand in New Zealand, which contained both buckled and non-buckled trees. While the model predicted factors of safety against buckling that were close to unity, it was unable to differentiate between buckled and non-buckled trees. Further investigation is needed to examine the reasons why this occurred. Despite this, the current study provides an in-depth numerical investigation, which has aided our understanding of the effects that material properties, geometric properties and boundary conditions have on buckling phenomenon in trees.

Free vibration analysis of a Euler-Bernoulli tapered column was conducted using the finite element method to identify the vibration modes of an equivalent tree structure under a specified set of conditions. A non-prismatic elastic circular column of height L was analysed, taking distributed self-weight into account. Various scenarios were considered: column taper, base fixity, radial and longitudinal stiffness (E) and density (ρ) and crown mass. The effect on the first natural frequency was assessed in each case. Validation against closed form solutions of benchmark problems was conducted satisfactorily. The results show that column taper, base fixity and E/ρ ratio are particularly important for this problem. Comparison of predictions with field observations of natural sway frequency for almost 700 coniferous and broadleaved trees from the published literature showed that the model worked well for coniferous trees, but less well for broadleaved trees with their more complicated crown architecture. Overall, the current study provides an in-depth numerical investigation of material properties, geometric properties and boundary conditions to create further understanding of vibration behaviour in trees.