Nonlinear Waves in Lattice Materials: Adaptively Augmented Directivity and Functionality Enhancement by Modal Mixing

TL;DR

This paper explores how nonlinear elastic waves in periodic lattice structures can be engineered to activate adaptive functionalities and wave manipulation capabilities by leveraging modal mixing and higher harmonic generation.

Contribution

It introduces a novel approach to design lattice structures that utilize nonlinearity and modal complexity to achieve adaptive wave control and multifunctionality at low frequencies.

Findings

Higher harmonics generate secondary wave packets with multiple characteristics.

Designing unit cells geometrically and topologically enables control over wave features.

Nonlinear effects activate high-frequency functionalities at low-frequency excitation.

Abstract

The motive of this work is to understand the complex spatial characteristics of finite-amplitude elastic wave propagation in periodic structures and leverage the unique opportunities offered by nonlinearity to activate complementary functionalities and design adaptive spatial wave manipulators. The underlying assumption is that the magnitude of wave propagation is small with respect to the length scale of the structure under consideration, albeit large enough to elicit the effects of finite-deformation. We demonstrate that the interplay of dispersion, nonlinearity and modal complexity involved in the generation and propagation of higher harmonics gives rise to secondary wave packets that feature multiple characteristics, one of which conforms to the dispersion relation of the corresponding linear structure. This provides an opportunity to engineer desired wave characteristics through a geometric and topological design of the unit cell, and results in the ability to activate complementary functionalities, typical of high frequency regimes, while operating at low frequencies of excitation - an effect seldom observed in linear periodic structures. The ability to design adaptive switches is demonstrated here using lattice configurations whose response is characterized by geometric and/or material nonlinearities.