A novel approach for analyzing the dynamic properties of trees with fractal sympodial branching architecture: A group tree modeling

It is remarkable that trees with high slenderness ratios are able to survive regular strong wind events. This phenomenon is motivating the exploration of the inherent vibration mitigation mechanisms of trees. This study examines the role of trees' hierarchical branching architecture on their modal properties. Its particular focus is on the modal frequencies and mode shapes of sympodial trees. This study idealizes trees as fractal structures with sympodial branching architecture and proposes a new group tree modeling approach to analyze their modal properties. Analytical closed-form solutions are derived to estimate the modal properties of trees. The analysis shows that sympodial trees localize vibrations on higher order branches. Furthermore, the modal properties of trees with a specific fractal level could be self-similar, and repetitive and form recursive relations with that of the previous level. Overall, the results offer a possible explanation of how fractal branching architecture prevents trees from excessive vibration.