This dissertation focuses on the development of the fundamental understanding of the dynamic behavior of assemblies of periodic arrays of tensegrity unit cells (along one and two directions). The ultimate aim of the dissertation is to capitalize on the attractive attributes of tensegrity structures with the unique characteristics of periodic structures, which stem from their ability to impede the propagation of disturbances that fall within certain frequency bands (known as stop bands or bandgaps). A successful implementation of such periodic/tensegrity structures is envisioned to extend the usefulness of tensegrity to vibration isolation problems, as well as to the synthesis of tunable acoustic and elastic wave filters, in both the frequency and spatial domains.

In this dissertation, numerical analysis of the statics and kinematics of icosahedron tensegrity cells are developed. The developed relationships are utilized to conceive one- and two-dimensional periodic arrays by appropriate stacking of icosahedron tensegrity cells. Alternative configurations for the periodic tensegrity arrays are considered for improved band gap characteristics, and a novel design for a periodic, tensegrity-based damper/vibration isolator is presented and demonstrated.

Particular emphasis is placed here on investigating and demonstrating some of the very interesting elastic properties of the periodic/tensegrity structures. Among these properties is the ratio of the bulk modulus to the shear modulus which are shown to be on the order of 1000. These values are two orders of magnitude higher than any naturally-occurring bulk material, suggesting that the viable potential of the periodic/tensegrity structures as suitable candidates for the synthesis of practical and realizable “pentamode” metamaterials, with many potential applications in the novel areas of acoustic and elastic cloaking where the proposed periodic/tensegrity structures act as liquids to ensure proper impedance matching.