Insights into mechanical properties of certain bio-inspired branched structures

This study is concerned with the motion and displacement of points on branches of a bio-inspired sympodial tree-like structure of a different hierarchy. First, displacements of points of a sympodial-like tree are recorded in pull-and-release experiments to get a qualitative insight into their behaviour. Then, a sympodial-type structure is analyzed, starting from its trunk, along a first-order branch and along an external and internal second-order branch. Given the fact that each point on branches performs in-plane vibration, their corresponding mechanical model consists of two orthogonal springs of unknown directions and unknown stiffness coefficients. Their directions actually correspond to the principal axes, which are obtained for the first time in the analytical form in terms of system’s geometrical and material parameters. The additional novelty lies in demonstrating how the position of their principal axes changes along each branch. Extreme displacements along principal axes are obtained as well, defining the ellipse of displacement for each point on branches of different order and position. The advantages of branched structures with respect to T-shaped structures that are commonly used in engineering are discussed and emphasized.