# On the compact wave dynamics of tensegrity beams in multiple dimensions

## TL;DR

This paper investigates the nonlinear wave dynamics in multi-dimensional tensegrity beams, revealing the existence of compact compression waves and their potential for innovative sound focusing applications.

## Contribution

It introduces the first numerical analysis of wave behavior in 2D and 3D tensegrity lattices, extending previous 1D findings to higher dimensions.

## Key findings

- Discovery of compact compression waves in 2D and 3D tensegrity lattices.
- Waves propagate with nearly constant speed and are resilient to collisions.
- Potential application in designing advanced sound focusing devices.

## Abstract

This work presents a numerical investigation on the nonlinear wave dynamics of tensegrity beams in 1D, 2D and 3D arrangements. The simulation of impact loading on a chain of tensegrity prisms and lumped masses allows us to apply on a smaller scale recent results on the propagation of compression solitary waves in 1D tensegrity metamaterials. Novel results on the wave dynamics of 2D and 3D beams reveal - for the first time - the presence of compact compression waves in two- and three-dimensional tensegrity lattices with slender aspect ratio. The dynamics of such systems is characterized by the thermalization of the lattice nearby the impacted regions of the boundary. The portion of the absorbed energy moving along the longitudinal direction is transported by compression waves with compact support. Such waves emerge with nearly constant speed, and slight modifications of their spatial shape and amplitude, after collisions with compression waves traveling in opposite direction. The analyzed behaviors suggest the use of multidimensional tensegrity lattices for the design and additive manufacturing of novel sound focusing devices.