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This work studies the acoustic band structure of tensegrity metamaterials,and the possibility to tune the dispersion relation of such systems by playingwith local and global prestress variables. Building on established results ofthe Bloch-Floquet theory, the paper first investigates the linearized responseof chains composed of tensegrity units and lumped masses, which undergo smalloscillations around an initial equilibrium state. The stiffness of the units insuch a state varies with an internal self-stress induced by prestretching thecables forming the tensegrity units, and the global prestress induced by theapplication of compression forces to the terminal bases. The given results showthat frequency band gaps of monoatomic and biatomic chains can be effectivelyaltered by the fine tuning of local and global prestress parameters, whilekeeping material properties unchanged. Numerical results on the wave dynamicsof chains under moderately large displacements confirm the presence offrequency band gaps of the examined systems in the elastically hardeningregime. Novel engineering uses of the examined metamaterials are discussed.

Tuning frequency band gaps of tensegrity metamaterials with local and global prestress