An analytic study on the properties of solitary waves traveling on tensegrity-like lattices

TL;DR

This paper analytically investigates solitary waves in 1D tensegrity-like lattices, revealing their existence, shape dependence on wave speed, and localization behavior, aligning with prior numerical findings.

Contribution

It provides an analytical framework for understanding solitary wave properties in tensegrity-inspired chains, extending previous numerical results.

Findings

Solitary waves exist in tensegrity-like chains.

Wave shape depends on wave speed.

Increased wave speed causes pulse localization.

Abstract

This paper develops an analytic study on the existence and properties of solitary waves on 1D chains of lumped masses and nonlinear springs, which exhibit a mechanical response similar to that of tensegrity prisms with locking-type response under axial loading. Making use of the Weierstrass' theory of 1D Lagrangian conservative systems, we show that such waves exist and that their shapes depend on the wave speed. A progressive localization of the traveling pulses in narrow regions of space is observed as the wave speed increases up to a limit value. A comparative analysis illustrates that the presented study is able to capture the wave dynamics observed in previous numerical studies on tensegrity mass-spring chains.