  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.
