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

## TL;DR

This paper explores how local and global prestress can be used to tune the acoustic band gaps of tensegrity metamaterials, enabling control over their wave propagation properties without changing material composition.

## Contribution

It introduces a method to adjust frequency band gaps in tensegrity metamaterials through prestress tuning, based on Bloch-Floquet theory and linearized response analysis.

## Key findings

- Band gaps can be effectively tuned by prestress adjustments.
- Numerical simulations confirm band gap presence in elastically hardening regime.
- Prestress tuning offers a new way to control wave propagation in metamaterials.

## Abstract

This work studies the acoustic band structure of tensegrity metamaterials, and the possibility to tune the dispersion relation of such systems by playing with local and global prestress variables. Building on established results of the Bloch-Floquet theory, the paper first investigates the linearized response of chains composed of tensegrity units and lumped masses, which undergo small oscillations around an initial equilibrium state. The stiffness of the units in such a state varies with an internal self-stress induced by prestretching the cables forming the tensegrity units, and the global prestress induced by the application of compression forces to the terminal bases. The given results show that frequency band gaps of monoatomic and biatomic chains can be effectively altered by the fine tuning of local and global prestress parameters, while keeping material properties unchanged. Numerical results on the wave dynamics of chains under moderately large displacements confirm the presence of frequency band gaps of the examined systems in the elastically hardening regime. Novel engineering uses of the examined metamaterials are discussed.