Acoustic nonreciprocity in a lattice incorporating nonlinearity, asymmetry, and internal scale hierarchy: Experimental study

Abstract

In linear time-invariant systems acoustic reciprocity holds by the Onsager-Casimir principle of microscopic reversibility, and it can be broken only by odd external biases, nonlinearities, or time-dependent properties. Recently it was shown that one-dimensional lattices composed of a finite number of identical nonlinear cells with internal scale hierarchy and asymmetry exhibit nonreciprocity both locally and globally. Considering a single cell composed of a large scale nonlinearly coupled to a small scale, local dynamic nonreciprocity corresponds to vibration energy transfer from the large to the small scale, but absence of energy transfer (and localization) from the small to the large scale. This has been recently proven both theoretically and experimentally. Then, considering the entire lattice, global acoustic nonreciprocity has been recently proven theoretically, corresponding to preferential energy transfer within the lattice under transient excitation applied at one of its boundaries, and absence of similar energy transfer (and localization) when the excitation is applied at its other boundary. This work provides experimental validation of the global acoustic nonreciprocity with a one-dimensional asymmetric lattice composed of three cells, with each cell incorporating nonlinearly coupled large and small scales. Due to the intentional asymmetry of the lattice, low impulsive excitations applied to one of its boundaries result in wave transmission through the lattice, whereas when the same excitations are applied to the other end, they lead in energy localization at the boundary and absence of wave transmission. This global nonreciprocity depends critically on energy (i.e., the intensity of the applied impulses), and reduced-order models recover the nonreciprocal acoustics and clarify the nonlinear mechanism generating nonreciprocity in this system.

Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions

“…Topological states have been successfully observed in several platforms [13][14][15][16][17][18][19][20][21], and have been pursued to achieve robust, diffraction-free wave motion. Additional functionalities have been explored in the context of topological pumping [22][23][24][25][26], quasi-periodicity [27][28][29], and non-reciprocal wave propagation in active [30][31][32][33][34][35][36] or passive non-linear [37][38][39][40] systems. These works and the references therein illustrate a wealth of strategies for the manipulation of elastic and acoustic waves, and suggest intriguing possibilities for technological applications in acoustic devices, sensing, energy harvesting, among others.…”

Non-Reciprocal Wave Transmission in a Bilinear Spring-Mass System

“…Assuming that the stiffness of the bilinear spring is greater in compression than in tension, we set ∆ j,c > ∆ j,t = 0 and ∆ j,c changes linearly over location according to Eqs. (8) and (9) . Figures 14(a) and 14(b) depict the displacement fields along the test chain at four different moments for the stiffness modulations of Fig.…”

“…The same incident wave traveling in opposite directions should result in the same transmitted wave. Recent advances have shown that the principle of reciprocity can be violated under special conditions in electromagnetism [1], acoustics [2,3,4,5,6,7,8,9,10] and other physical systems supporting wave propagation [11]. The ability to violate reciprocity in a controlled and passive manner opens the possibility of extreme wave dynamics and control mechanisms such as one-way propagation, acoustic diodes, etc, and provide revolutionary solutions to existing problems and useful tools for promising applications.…”

Nonreciprocal wave phenomena in spring-mass chains with effective stiffness modulation induced by geometric nonlinearity

“…One way to realize acoustic non-reciprocity is by applying a bias that is oddly-symmetric upon time reversal, which has been achieved in moving media [6,7], gyroscopic phononic crystals [8,9], and piezophononic media [10], for example, and effectively establishes 'up-stream' and 'down-stream' directions for propagating waves. Another means to break reciprocity is nonlinearity, which has been used to create one-way sound propagation via harmonic generation [11][12][13]. A third mechanism, which is the subject of the present study, is spatiotemporal modulation of material properties [14][15][16][17][18][19][20].…”