Damping by branching: a bioinspiration from trees

Abstract

Man-made slender structures are known to be sensitive to high levels of vibration, due to their flexibility, which often cause irreversible damage. In nature, trees repeatedly endure large amplitudes of motion, mostly caused by strong climatic events, yet with minor or no damage in most cases. A new damping mechanism inspired by the architecture of trees is here identified and characterized in the simplest tree-like structure, a Y-shape branched structure. Through analytical and numerical analyses of a simple two-degree-of-freedom model, branching is shown to be the key ingredient in this protective mechanism that we call damping-by-branching. It originates in the geometrical nonlinearities so that it is specifically efficient to damp out large amplitudes of motion. A more realistic model, using flexible beam approximation, shows that the mechanism is robust. Finally, two bioinspired architectures are analyzed, showing significant levels of damping achieved via branching with typically 30% of the energy being dissipated in one oscillation. This concept of damping-bybranching is of simple practical use in the design of slender flexible structures.

The Multimodal Dynamics of a Walnut Tree: Experiments and Models

“…By designing a structure with an adequate branching pattem, using Eq. (1), a high level of damping on the first mode may be expected by transfer of energy to higher modes [21].…”

Vibration attenuation performance of long-eared owl plumage

“…The feather can be analogical to the tree which repeatedly endures large amplitudes of motion but suffers minor or no damage in most cases, because both of them have multiple branched structures. 25 And inspired by the damping-bybranching mechanism studied for trees, we found two possible reasons as following to give rise to the feather damping. Firstly, feather materials, as biological materials, are known to have inherent viscoelastic behaviour.…”

Branching morphology, vascular bundle arrangement and ontogenetic development in leaf insertion zones and ramifications of three arborescent Araliaceae species

“…ontogenetic phases and numerous optimized stem-branch attachments have evolved to meet these challenging demands. The analysis of the morphology, anatomy and biomechanics of botanical ramifications has become of increasing interest in recent years (Mattheck 1991;Niklas 1992;Burgert and Jungnikl 2004;Achim et al 2006;Tomlinson et al 2005;Müller et al 2006;Jungnikl et al 2009;Masselter et al , 2015Masselter et al , 2016Theckes et al 2011;Müller et al 2013;Schwager et al 2013;Haushahn et al 2014). Comprehending the development of botanical ramifications and identifying the central concepts of their structure also allow for biomimetic implementations into technical fiberreinforced materials.…”