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

[+] Author and Article Information
Matthew D. Fronk

771 Ferst Drive NW Atlanta, GA 30332-0405 mfronk3@gatech.edu

Sameh Tawfick

1206 W. Green St. Urbana, IL 61801 tawfick@illinois.edu

Chiara Daraio

1200 E California Blvd. MC 104-44 Pasadena, CA 91125 daraio@caltech.edu

Shuangbao Li

2898 Jinbei Road, Dongli District Tianjin, China 300300 China shuangbaoli@yeah.net

Alexander F. Vakakis

1206 West Green Street Department of Mechanical Science and Engineering Urbana, IL 61801 avakakis@illinois.edu

Michael J. Leamy

771 Ferst Drive N.W. Atlanta, GA 30332-0405 mjleamy@gmail.com

1Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the Journal of Vibration and Acoustics. Manuscript received January 23, 2018; final manuscript received April 29, 2019; published online xx xx, xxxx. Assoc. Editor: Mahmoud Hussein.

ASME doi:10.1115/1.4043783 History: Received January 23, 2018; Accepted April 30, 2019


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. Non-reciprocity violates this property and can be introduced to systems if time-reversal symmetry and/or parity symmetry is lost. While many studies have induced non-reciprocity 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.

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