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

摘要

The motive of this work is to understand the complex spatial characteristicsof finite-amplitude elastic wave propagation in periodic structures andleverage the unique opportunities offered by nonlinearity to activatecomplementary functionalities and design adaptive spatial wave manipulators.The underlying assumption is that the magnitude of wave propagation is smallwith respect to the length scale of the structure under consideration, albeitlarge enough to elicit the effects of finite-deformation. We demonstrate thatthe interplay of dispersion, nonlinearity and modal complexity involved in thegeneration and propagation of higher harmonics gives rise to secondary wavepackets that feature multiple characteristics, one of which conforms to thedispersion relation of the corresponding linear structure. This provides anopportunity to engineer desired wave characteristics through a geometric andtopological design of the unit cell, and results in the ability to activatecomplementary functionalities, typical of high frequency regimes, whileoperating at low frequencies of excitation - an effect seldom observed inlinear periodic structures. The ability to design adaptive switches isdemonstrated here using lattice configurations whose response is characterizedby geometric and/or material nonlinearities.