Propagation of compression solitary waves on tensegrity-like lattices made of truncated octahedrons

This work studies the properties of compression solitary waves propagating through one-dimensional mass–spring lattices, whose unit cells show an interaction law mimicking that of a truncated tensegrity octahedron. Analytic methods based on the Weierstrass criterion for compact solitary waves, and the long wave approximation theory are employed to demonstrate that the analyzed systems support compression solitary waves in a suitable range of wave speeds. These systems exhibit an initially soft response, which progressively turns into an elastically hardening behavior ending with a linear branch in the pre-buckling regime of the units cells. Explicit formulae are given for the lower and upper bounds of the wave speed interval that produce compact solitary waves, together with analytic laws of the shape of the traveling wave. Numerical simulations provide a validation of the presented theory.