Acoustic non-reciprocity in passive nonlinear waveguides with configurational asymmetry

Wang, Chongan

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https://hdl.handle.net/2142/116236 Copy

Description

Title

Acoustic non-reciprocity in passive nonlinear waveguides with configurational asymmetry

Author(s)

Wang, Chongan

Issue Date

2022-07-15

Director of Research (if dissertation) or Advisor (if thesis)

• Vakakis, Alexander
• Tawfick, Sameh

Doctoral Committee Chair(s)

Vakakis, Alexander

Committee Member(s)

• Bergman, Lawrence
• Matlack, Kathyrn
• Elbanna, Ahmed

Department of Study

Mechanical Sci & Engineering

Discipline

Theoretical & Applied Mechans

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Acoustic Nonreciprocity
• Nonlinear acoustics
• Passive control of acoustics

Abstract

Reciprocity is a fundamental feature in linear time-invariant acoustics, stating the responses are invariant by switching the locations of excitation and measurement. Breaking acoustic reciprocity enables a broad class of unconventional acoustic features. Non-reciprocal acoustics can be achieved either actively or passively, and the key to passive non-reciprocity is nonlinearity and asymmetry. In non-reciprocal systems, the responses are qualitatively different with identical excitation applied on different locations. This is achieved due to the break of spatial symmetry and nonlinear features such as nonlinear resonances, bifurcations, harmonic generation etc. In the dissertation, we study various classes of passive non-reciprocal systems. These non-reciprocal systems are predictively designed by analytical, numerical and machine learning methods. In the first part of the dissertation, we consider a semi-infinite asymmetric lattice network of two nonlinear lattices with weak linear inter-lattice coupling. We study its capacity for passive wave redirection and non-reciprocity subject to an impulse applied on one lattice. By breaking the symmetry and varying the grounding stiffnesses, the energy is irreversibly redirected， and the wave redirection is induced by Landau-Zener Tunneling (LZT) effect. Moreover, this wave redirection is realized only in a specific range of impulse intensity (energy), otherwise motion localization occurs. Through a set of reduced order models we provide guidance for selecting system parameters of the lattice network supporting robust breather redirection despite the presence of dissipation. We also study the acoustic non-reciprocity and formulate a quantitative measure based on measured time-series responses at the four free boundaries of the finite network. These results pave the way for conceiving practical nonlinear lattice networks with inherent capacities for passive wave redirection and acoustic non-reciprocity that are tunable (self-adaptive) to the applied impulsive excitations. In the second part, we propose a two-dimensional granular-solid hybrid system with contact nonlinearity, scale hierarchy and asymmetry. Specifically, we consider a left, larger-scale and a right, smaller-scale granular media composed of two-dimensional (2D), initially uncompressed, hexagonally packed granules. These two granular media interface with an intermediate linearly elastic solid. Identical half-sine shock excitation is applied on either side (large or small granules) of the system. The nonlinear acoustics are computationally studied accounting for the combined effects of Hertzian, frictional and rotational interactions in the granular media, as well as the highly discontinuous interfacial effects. To this end, an interpolation-iteration computational algorithm is developed, and the approximated eigenvalues are monitored at each time instant to ensure the robustness of the algorithm. Depending on the location and intensity of the applied shock, either (slow) low-frequency vibrations or (fast) high-frequency acoustics are excited in the intermediate elastic medium. The non-reciprocal interfacial acoustics studied here apply to a broad class of asymmetric hybrid (discrete-continuum) nonlinear systems, and can inform predictive designs of highly effective granular shock protectors or granular acoustic diodes. In the third part, we propose a new, simple, and highly effective passive phononic waveguide with controllable global non-reciprocity by means of local nonlinear and asymmetric elements. The nonlinearity and asymmetry in the waveguide are realized by means of a local nonlinear gate involving two linear oscillators with detuned stiffnesses coupled with a cubic nonlinear stiffness. By applying a harmonic excitation, a propagating wave is excited and transmitted across the nonlinear gate. The objectives of this work are to study the effects of local nonlinearity and asymmetry on the global non-reciprocal acoustics and to optimize the non-reciprocal performance of the waveguide. To this end, we employ analytical and machine learning approaches to study the non-reciprocal acoustics. Bifurcations inducing non-reciprocal acoustics are predicted by the analysis. In addition to the analytical methods, we also train a machine learning simulator that drastically saves the simulation time and allows the optimization of non-reciprocal performances. Combining the analytical and machine learning results we find robust parameter ranges with strong non-reciprocity thus guiding the design. The efficacy of the analytical and machine learning approaches is demonstrated and their capacity goes beyond the study of this waveguide. The final part of the presented work is concerned with frequency conversion through a nonlinear gate in a two-dimensional waveguide supporting an acoustic frequency pass-band and an optical frequency pass-band. A harmonic excitation is applied on one side of the waveguide, initiating a propagating wave at the excited frequency in the acoustic band. As the wave transmits across the gate, the frequency is converted from the acoustic band to the optical band. We show that the local nonlinear 1:3 resonance at the gate dominates the global frequency conversion. We also show that the nonlinear resonance can be predictively designed. Moreover, the frequency conversion due to the local 1:3 resonance is non-reciprocal and tunable with energy. With identical excitation from the opposite side, the energy cannot transmit across the gate due to the impedance mismatch. The results presented in this dissertation reveal how non-reciprocity in design is related to nonlinearity and configurational asymmetry. These results guide the predictive design of acoustic systems with preferred non-reciprocal features. The analytical, numerical and machine learning tools can also be applied to study broader classes of nonlinear dynamical and acoustic problems than acoustic non-reciprocity.

Graduation Semester

2022-08

Type of Resource

Thesis

Copyright and License Information

Copyright 2022 Chongan Wang

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