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 reciprocity-breaking is associated with specific ranges of excitation amplitudes for both impulse and harmonic forcing.
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ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
August 6–9, 2017
Cleveland, Ohio, USA
Conference Sponsors:
- Design Engineering Division
- Computers and Information in Engineering Division
ISBN:
978-0-7918-5822-6
PROCEEDINGS PAPER
Non-Reciprocity in Structures With Nonlinear Internal Hierarchy and Asymmetry Available to Purchase
Matthew D. Fronk,
Matthew D. Fronk
Georgia Institute of Technology, Atlanta, GA
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Sameh Tawfick,
Sameh Tawfick
University of Illinois at Urbana-Champaign, Urbana, IL
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Chiara Daraio,
Chiara Daraio
California Institute of Technology, Pasadena, CA
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Alexander F. Vakakis,
Alexander F. Vakakis
University of Illinois at Urbana-Champaign, Urbana, IL
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Michael J. Leamy
Michael J. Leamy
Georgia Institute of Technology, Atlanta, GA
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Matthew D. Fronk
Georgia Institute of Technology, Atlanta, GA
Sameh Tawfick
University of Illinois at Urbana-Champaign, Urbana, IL
Chiara Daraio
California Institute of Technology, Pasadena, CA
Alexander F. Vakakis
University of Illinois at Urbana-Champaign, Urbana, IL
Michael J. Leamy
Georgia Institute of Technology, Atlanta, GA
Paper No:
DETC2017-67965, V008T12A023; 9 pages
Published Online:
November 3, 2017
Citation
Fronk, MD, Tawfick, S, Daraio, C, Vakakis, AF, & Leamy, MJ. "Non-Reciprocity in Structures With Nonlinear Internal Hierarchy and Asymmetry." Proceedings of the ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 8: 29th Conference on Mechanical Vibration and Noise. Cleveland, Ohio, USA. August 6–9, 2017. V008T12A023. ASME. https://doi.org/10.1115/DETC2017-67965
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