Wave-packet spreading in disordered soft architected structures

TL;DR

This study investigates how wave-packets spread in a disordered, nonlinear elastic lattice with coupled translational and rotational degrees of freedom, revealing complex energy transport behaviors and persistent chaos.

Contribution

It demonstrates the impact of nonlinear coupling between multiple degrees of freedom on wave-packet spreading in disordered lattices, extending understanding beyond single-DoF models.

Findings

Wave-packet spreading occurs due to nonlinear coupling of DoFs.

Strong nonlinearities lead to near ballistic energy transport.

Persistent chaos is observed during energy spreading, decreasing over time.

Abstract

We study the dynamical and chaotic behavior of a disordered one-dimensional elastic mechanical lattice which supports translational and rotational waves. The model used in this work is motivated by the recent experimental results of B. Deng et al., Nat. Commun. 9, 3410 (2018). This lattice is characterized by strong geometrical nonlinearities and the coupling of two degrees-of-freedom (DoFs) per site. Although the linear limit of the structure consists of a linear Fermi-Pasta-Ulam-Tsingou lattice and a linear Klein-Gordon (KG) lattice whose DoFs are uncoupled, by using single site initial excitations on the rotational DoF, we evoke the nonlinear coupling between the system's translational and rotational DoFs. Our results reveal that such coupling induces rich wave-packet spreading behavior in the presence of strong disorder. In the weakly nonlinear regime, we observe energy spreading only due to the coupling of the two DoFs (per site) which is in contrast to what is known for KG lattices with a single DoF per lattice site, where the spreading occurs due to chaoticity. Additionally, for strong nonlinearities, we show that initially localized wave-packets attain near ballistic behavior in contrast to other known models. We also reveal persistent chaos during energy spreading, although its strength decreases in time as quantified by the evolution of the system's finite-time maximum Lyapunov exponent. Our results show that flexible, disordered and strongly nonlinear lattices are a viable platform to study energy transport in combination with multiple DoFs (per site), also present an alternative way to control energy spreading in heterogeneous media.