Non-reciprocity in structures with nonlinear internal hierarchy and asymmetry

Matthew D. Fronk, Sameh Tawfick, Chiara Daraio, Alexander F. Vakakis, Michael J. Leamy

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Acoustic reciprocity is a property of linear, time invariant systems in which the locations of the source of a forcing and the received signal can be interchanged with no change in the measured response. This work investigates the breaking of acoustic reciprocity using a hierarchical structure consisting of internally-scaled masses coupled with cubically nonlinear springs. Using both direct results and variable transformations of numerical simulations, energy transmission is shown to occur in the direction of decreasing scale but not vice versa, constituting the breaking of acoustic reciprocity locally. When a linear spring connects the smallest scale of such a structure to the largest scale of another identical structure, an asymmetrical lattice is formed. Because of the scale mixing and transient resonance capture that occurs within each unit cell, it is demonstrated through further numerical experiments that energy transmission occurs primarily in the direction associated with the nonlinear coupling from the large to the small scale, thus signifying the breaking of reciprocity globally. This nonlinear hierarchical structure exhibits strong amplitude-dependency in which reciprocitybreaking is associated with specific ranges of excitation amplitudes for both impulse and harmonic forcing.

Original languageEnglish (US)
Title of host publication29th Conference on Mechanical Vibration and Noise
PublisherAmerican Society of Mechanical Engineers (ASME)
ISBN (Electronic)9780791858226
DOIs
StatePublished - Jan 1 2017
EventASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2017 - Cleveland, United States
Duration: Aug 6 2017Aug 9 2017

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
Volume8

Other

OtherASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2017
CountryUnited States
CityCleveland
Period8/6/178/9/17

Keywords

  • Non-reciprocity
  • Nonlinear wave propagation
  • Periodic structures
  • Resonance capture

ASJC Scopus subject areas

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modeling and Simulation

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  • Cite this

    Fronk, M. D., Tawfick, S., Daraio, C., Vakakis, A. F., & Leamy, M. J. (2017). Non-reciprocity in structures with nonlinear internal hierarchy and asymmetry. In 29th Conference on Mechanical Vibration and Noise (Proceedings of the ASME Design Engineering Technical Conference; Vol. 8). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/DETC2017-67965