Experimental Evidence of Directivity-Enhancing Mechanisms in Nonlinear Lattices

TL;DR

This study experimentally demonstrates how nonlinear effects in lattice materials can enhance directional wave control by generating higher harmonics that conform to linear dispersion relations, expanding the functional capabilities of mechanical metamaterials.

Contribution

It provides the first experimental evidence of how nonlinearity can be engineered to improve wave directionality and modal control in lattice structures.

Findings

Nonlinear higher harmonics follow the linear dispersion relation.

Nonlinear wave features exhibit unique modal and directional characteristics.

Nonlinearity enhances the functional design space of mechanical metamaterials.

Abstract

In this letter, we experimentally investigate the directional characteristics of propagating, finite-amplitude wave packets in lattice materials, with an emphasis on the functionality enhancement due to the nonlinearly-generated higher harmonics. To this end, we subject a thin, periodically perforated sheet to out-of-plane harmonic excitations, and we design a systematic measurement and data processing routine that leverages the full-wavefield reconstruction capabilities of a laser vibrometer to precisely delineate the effects of nonlinearity. We demonstrate experimentally that the interplay of dispersion, nonlinearity, and modal complexity which is involved in the generation and propagation of higher harmonics gives rise to secondary wave packets with characteristics that conform to the dispersion relation of the corresponding linear structure. Furthermore, these nonlinearly generated wave features display modal and directional characteristics that are complementary to those exhibited by the fundamental harmonic, thus resulting in an augmentation of the functionality landscape of the lattice. These results provide proof of concept for the possibility to engineer the nonlinear wave response of mechanical metamaterials through a geometric and topological design of the unit cell.