Nonlinear waves in lattice materials: Adaptively augmented directivity and functionality enhancement by modal mixing

R. Ganesh, S. Gonella

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)272-288
Number of pages17
JournalJournal of the Mechanics and Physics of Solids
StatePublished - Feb 1 2017

Bibliographical note

Funding Information:
The authors acknowledge the support of the National Science Foundation (CAREER Award CMMI-1452488 ).

Publisher Copyright:
© 2016 Elsevier Ltd


  • Harmonic generation
  • Modal mixing
  • Mode hopping
  • Nonlinear waves
  • Phononic crystals
  • Spatial Directivity


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