Platonic tensegrities: Dynamic aspects and characterization

Abstract

Biotensegrity is the natural extension of the tensegrity principles, developed by Fuller in the early 60’s, into the biologic field. With the singular properties of these structures, these principles have gained renewed attention in the scientific and technologic fields, both as models for theorizing the behavior of biological structures at different scales, and as useful tools in a wide variety of applications, ranging from the matrix biomaterials to extreme bionics. Therefore, understanding the dynamic behavior of these structures becomes a fertile field, enabler of future applications in the field of Bioengineering. Platonic Solids represent recurrent morphologies in nature, with well-studied symmetries. This work is part of a broad research dedicated to the study of Biotensegrity. Among the Platonic Solids, the Tetrahedron, Octahedron and Icosahedron were translated into tensegrities (Platonic Tensegrities), using the Rot-Umbela Manipulation and Symmetry methods. In this work, we present the results obtained after instrumentation and processing of the aqcired signals from homologues and nonhomologues nodes of these Platonic Tensegrities, when subjected to vibrations in the vertical axis, between 1.0 Hz and 60.0 Hz. These results indicate a close correspondence between Tetrahedral and Octahedral Tensegrities, which present resonant frequencies in the ranges of (8.0 ± 0.1) Hz; (15.0± 0.1) Hz to (21.0 ± 0.1) Hz and (40.0 ± 0.1) Hz to (45.0 ± 0.1) Hz. The Icosahedral Tensegrity presents more resonant frequencies compared to the previous two Tensegrities: (9.0 ± 0.1) Hz; (13.0 ± 0.1) Hz to (14.0 ± 0.1) Hz; (26.0 ± 0.1) Hz to (27.0 ± 0.1) Hz; (30.0 ± 0.1) Hz, to (35.0 ± 0.1) Hz and (41.0 ± 0.1) Hz to (42.0 ± 0.1) Hz. These differences are discussed from the perspective of symmetry groups associated to each of the Platonic Solids.