Acoustic Non-Reciprocity in Lattices With Nonlinearity, Internal Hierarchy, and Asymmetry: Computational Study
Acoustic Non-Reciprocity in Lattices With Nonlinearity, Internal Hierarchy, and Asymmetry: Computational Study
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DOI：
10.1115/1.4043783
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发表时间：
2019-10-01
影响因子：
1.7
通讯作者：
Leamy, Michael J.
中科院分区：
文献类型：
--
作者：
Fronk, Matthew D.;Tawfick, Sameh;Leamy, Michael J.
互易性是线性时不变系统的一个属性，在交换源和接收器后，从源到接收器的能量传输不会改变。非互易性违反了这一性质，并且如果时间反转对称性和/或奇偶对称性丢失，则可以将非互易性引入到系统中。虽然许多研究通过主动手段（即奇对称外部偏差或系统属性的时间变化）诱导非互易性，但对被动破坏互易性的声学结构的关注却少得多。这项研究提出了一种具有强刚度非线性、内部尺度层次和打破声学互易性的不对称性的晶格结构。从宏观上看，该结构表现出周期性，但其晶胞设计存在不对称性。在实验验证的支持下，对两尺度晶胞的理论研究表明，互易性在局部被破坏，即在晶格的单个晶胞内。在这项工作中，通过研究晶胞周期性排列中的波传播，从理论上分析了整个晶格结构中互易性的全局破缺。在窄带和宽带激励下，该结构表现出高度不对称的波传播，因此声学互易性的全局破坏。解释不同脉冲幅度以及不同谐波强迫幅度和频率/波数的数值结果提供了强有力的证据，证明瞬态共振捕获是周期性结构中互易性全局破坏背后的驱动力。在配套工作中，本文提出的一些理论结果通过脉冲激励下由两尺度晶胞组成的晶格进行了实验验证。
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.