Acoustic non-reciprocity in lattices with nonlinearity, internal hierarchy, and asymmetry: Computational study

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

Research output: Contribution to journalArticle

Abstract

Reciprocity is a property of linear, time-invariant systems whereby the energy transmission from a source to a receiver is unchanged after exchanging the source and receiver. Nonreciprocity violates this property and can be introduced to systems if time-reversal symmetry and/or parity symmetry is lost. While many studies have induced nonreciprocity by active means, i.e., odd-symmetric external biases or time variation of system properties, considerably less attention has been given to acoustical structures that passively break reciprocity. This study presents a lattice structure with strong stiffness nonlinearities, internal scale hierarchy, and asymmetry that breaks acoustic reciprocity. Macroscopically, the structure exhibits periodicity yet asymmetry exists in its unit cell design. A theoretical study, supported by experimental validation, of a two-scale unit cell has revealed that reciprocity is broken locally, i.e., within a single unit cell of the lattice. In this work, global breaking of reciprocity in the entire lattice structure is theoretically analyzed by studying wave propagation in the periodic arrangement of unit cells. Under both narrowband and broadband excitation, the structure exhibits highly asymmetrical wave propagation, and hence a global breaking of acoustic reciprocity. Interpreting the numerical results for varying impulse amplitude, as well as varying harmonic forcing amplitude and frequency/wavenumber, provides strong evidence that transient resonant capture is the driving force behind the global breaking of reciprocity in the periodic structure. In a companion work, some of the theoretical results presented herein are experimentally validated with a lattice composed of two-scale unit cells under impulsive excitation.

Original languageEnglish (US)
Article number051011
JournalJournal of Vibration and Acoustics, Transactions of the ASME
Volume141
Issue number5
DOIs
StatePublished - Oct 1 2019
Externally publishedYes

Fingerprint

Wave propagation
hierarchies
Acoustics
nonlinearity
asymmetry
acoustics
Periodic structures
cells
Stiffness
wave propagation
receivers
exchanging
symmetry
excitation
narrowband
impulses
periodic variations
stiffness
parity
broadband

Keywords

  • Hierarchical materials
  • Nonlinear wave propagation
  • Nonreciprocity
  • Periodic structures

ASJC Scopus subject areas

  • Acoustics and Ultrasonics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Acoustic non-reciprocity in lattices with nonlinearity, internal hierarchy, and asymmetry : Computational study. / Fronk, Matthew D.; Tawfick, Sameh H; Daraio, Chiara; Li, Shuangbao; Vakakis, Alexander F; Leamy, Michael J.

In: Journal of Vibration and Acoustics, Transactions of the ASME, Vol. 141, No. 5, 051011, 01.10.2019.

Research output: Contribution to journalArticle

@article{1762acffd7754e45ba8b797674e5ed42,
title = "Acoustic non-reciprocity in lattices with nonlinearity, internal hierarchy, and asymmetry: Computational study",
abstract = "Reciprocity is a property of linear, time-invariant systems whereby the energy transmission from a source to a receiver is unchanged after exchanging the source and receiver. Nonreciprocity violates this property and can be introduced to systems if time-reversal symmetry and/or parity symmetry is lost. While many studies have induced nonreciprocity by active means, i.e., odd-symmetric external biases or time variation of system properties, considerably less attention has been given to acoustical structures that passively break reciprocity. This study presents a lattice structure with strong stiffness nonlinearities, internal scale hierarchy, and asymmetry that breaks acoustic reciprocity. Macroscopically, the structure exhibits periodicity yet asymmetry exists in its unit cell design. A theoretical study, supported by experimental validation, of a two-scale unit cell has revealed that reciprocity is broken locally, i.e., within a single unit cell of the lattice. In this work, global breaking of reciprocity in the entire lattice structure is theoretically analyzed by studying wave propagation in the periodic arrangement of unit cells. Under both narrowband and broadband excitation, the structure exhibits highly asymmetrical wave propagation, and hence a global breaking of acoustic reciprocity. Interpreting the numerical results for varying impulse amplitude, as well as varying harmonic forcing amplitude and frequency/wavenumber, provides strong evidence that transient resonant capture is the driving force behind the global breaking of reciprocity in the periodic structure. In a companion work, some of the theoretical results presented herein are experimentally validated with a lattice composed of two-scale unit cells under impulsive excitation.",
keywords = "Hierarchical materials, Nonlinear wave propagation, Nonreciprocity, Periodic structures",
author = "Fronk, {Matthew D.} and Tawfick, {Sameh H} and Chiara Daraio and Shuangbao Li and Vakakis, {Alexander F} and Leamy, {Michael J.}",
year = "2019",
month = "10",
day = "1",
doi = "10.1115/1.4043783",
language = "English (US)",
volume = "141",
journal = "Journal of Vibration and Acoustics, Transactions of the ASME",
issn = "1048-9002",
publisher = "American Society of Mechanical Engineers(ASME)",
number = "5",

}

TY - JOUR

T1 - Acoustic non-reciprocity in lattices with nonlinearity, internal hierarchy, and asymmetry

T2 - Computational study

AU - Fronk, Matthew D.

AU - Tawfick, Sameh H

AU - Daraio, Chiara

AU - Li, Shuangbao

AU - Vakakis, Alexander F

AU - Leamy, Michael J.

PY - 2019/10/1

Y1 - 2019/10/1

N2 - Reciprocity is a property of linear, time-invariant systems whereby the energy transmission from a source to a receiver is unchanged after exchanging the source and receiver. Nonreciprocity violates this property and can be introduced to systems if time-reversal symmetry and/or parity symmetry is lost. While many studies have induced nonreciprocity by active means, i.e., odd-symmetric external biases or time variation of system properties, considerably less attention has been given to acoustical structures that passively break reciprocity. This study presents a lattice structure with strong stiffness nonlinearities, internal scale hierarchy, and asymmetry that breaks acoustic reciprocity. Macroscopically, the structure exhibits periodicity yet asymmetry exists in its unit cell design. A theoretical study, supported by experimental validation, of a two-scale unit cell has revealed that reciprocity is broken locally, i.e., within a single unit cell of the lattice. In this work, global breaking of reciprocity in the entire lattice structure is theoretically analyzed by studying wave propagation in the periodic arrangement of unit cells. Under both narrowband and broadband excitation, the structure exhibits highly asymmetrical wave propagation, and hence a global breaking of acoustic reciprocity. Interpreting the numerical results for varying impulse amplitude, as well as varying harmonic forcing amplitude and frequency/wavenumber, provides strong evidence that transient resonant capture is the driving force behind the global breaking of reciprocity in the periodic structure. In a companion work, some of the theoretical results presented herein are experimentally validated with a lattice composed of two-scale unit cells under impulsive excitation.

AB - Reciprocity is a property of linear, time-invariant systems whereby the energy transmission from a source to a receiver is unchanged after exchanging the source and receiver. Nonreciprocity violates this property and can be introduced to systems if time-reversal symmetry and/or parity symmetry is lost. While many studies have induced nonreciprocity by active means, i.e., odd-symmetric external biases or time variation of system properties, considerably less attention has been given to acoustical structures that passively break reciprocity. This study presents a lattice structure with strong stiffness nonlinearities, internal scale hierarchy, and asymmetry that breaks acoustic reciprocity. Macroscopically, the structure exhibits periodicity yet asymmetry exists in its unit cell design. A theoretical study, supported by experimental validation, of a two-scale unit cell has revealed that reciprocity is broken locally, i.e., within a single unit cell of the lattice. In this work, global breaking of reciprocity in the entire lattice structure is theoretically analyzed by studying wave propagation in the periodic arrangement of unit cells. Under both narrowband and broadband excitation, the structure exhibits highly asymmetrical wave propagation, and hence a global breaking of acoustic reciprocity. Interpreting the numerical results for varying impulse amplitude, as well as varying harmonic forcing amplitude and frequency/wavenumber, provides strong evidence that transient resonant capture is the driving force behind the global breaking of reciprocity in the periodic structure. In a companion work, some of the theoretical results presented herein are experimentally validated with a lattice composed of two-scale unit cells under impulsive excitation.

KW - Hierarchical materials

KW - Nonlinear wave propagation

KW - Nonreciprocity

KW - Periodic structures

UR - http://www.scopus.com/inward/record.url?scp=85067341214&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85067341214&partnerID=8YFLogxK

U2 - 10.1115/1.4043783

DO - 10.1115/1.4043783

M3 - Article

AN - SCOPUS:85067341214

VL - 141

JO - Journal of Vibration and Acoustics, Transactions of the ASME

JF - Journal of Vibration and Acoustics, Transactions of the ASME

SN - 1048-9002

IS - 5

M1 - 051011

ER -