Abstract
Tensegrity systems, defined as prestressed assemblies of tensioned cables and discrete compression struts, are attractive for lightweight, deployable and resilient structures. This paper presents a comparative dynamic study and geometry optimization of seven canonical modules [prism (P3), X-prism (P3X), tetrahedron (T4), octahedron (O6), icosahedron (I6), expanded octahedron (EO3) and double-expanded octahedron (DEO)] using a unified, reproducible computational pipeline. From a minimal parametric description, we generate geometry, perform form-finding via constrained force-density/energy minimization, linearize small-on-large motion about the prestressed equilibrium and evaluate modal properties, frequency response and axial stiffness, while estimating ultimate capacity from strut Euler buckling and cable rupture. Baseline members are high-modulus carbon fiber-reinforced polymer (CFRP) struts paired with high-modulus polyethylene (HMPE) cables, with light Rayleigh damping. The design space varies aspect ratio, twist angle, prestress ratio and cross-sectional parameters under a fixed overall envelope with a mass-aware objective. Numerical simulations show that the 6-strut icosahedron achieves the highest specific dynamic performance (fundamental frequency per unit mass) at moderate prestress, whereas the double-expanded octahedron offers the greatest strength-to-self-weight due to shorter effective strut lengths and enhanced load paths. Across topologies, optimal prism twist angles cluster around 30-36° and preferred cable pretension falls in the 1.8-2.5% engineering strain range. We provide quantitative rankings, optimal parameter sets and sensitivity maps that reveal trade-offs among stiffness, frequency and resistance to cable slackening. The results deliver actionable guidance for selecting topology and geometry in vibration-sensitive applications and outline limitations alongside avenues for experimental validation and nonlinear dynamic extensions.
Keywords: Geometry Optimization, Lightweight Structures, Modal Analysis, Prestress Tuning, Strength-to-weight Ratio, Tensegrity.