  In this paper, lightweight metastructures are designed consisting of
prismatic tensegrity building blocks which have excellent strength-to-weight
ratio and also enable unique compression-torsion coupling. A theoretical model
with coupled axial-torsional stiffness matrix is first developed to study the
band structures of the proposed lightweight metastructures. Unit cell designs
based on both Bragg scattering and local resonance mechanism are investigated
to generate bandgaps at desired frequency ranges. Broadband full-wave
attenuation is found in the tensegrity metastructure with special
opposite-chirality unit cells. Furthermore, tunable stiffness in the prismatic
tensegrity structure is investigated and 'small-on-large' tunability in the
tensegrity metastructure is achieved by harnessing the geometrically nonlinear
deformation through an external control torque. Prestress adjustment for fine
tuning of the band structure is also investigated. Finally, frequency response
tests on finite metastructures are preformed to validate their wave attenuation
ability as well as their wave propagation tunability. The proposed tensegrity
metastructures could be very useful in various engineering applications where
lightweight and tunable structures with broadband vibration suspension and wave
attenuation ability are in high demand.
