Abstract
We study a one-dimensional nonlinear periodic structure which contains two different spring stiffness and an identical mass in each period. The linear dispersion relationship we obtain indicates that our periodic structure has obvious advantages compared to other kinds of periodic structures (i.e. those with the same spring stiffness but two different mass), including its increased flexibility for manipulating the band gap. Theoretically, the optical cutoff frequency remains unchanged while the acoustic cutoff frequency shifts to a lower or higher frequency. A numerical simulation verifies the dispersion relationship and the effect of the amplitude-dependent signal filter. Based upon this, we design a device which contains both a linear periodic structure and a nonlinear periodic structure. When incident waves with the same, large amplitude pass through it from opposite directions, the output amplitude of the forward input is one order magnitude larger than that of the reverse input. Our devised, non-reciprocal device can potentially act as an acoustic diode (AD) without an electrical circuit and frequency shifting. Our result represents a significant step forwards in the research of non-reciprocal wave manipulation.
Highlights
The concept of the “acoustic diode” (AD) was proposed several decades ago.[1,2] Recently, nonlinear optical isolators have become a hot topic for a broad range of interests,[3,4,5] and the pioneering applications of ADs have attracted a lot of attention which may offer the potential to revolutionize existing acoustic techniques in different important fields
Daraio et al demonstrated experimentally that one-dimensional nonlinear phononic crystals form in chains of viscoelastic polyterafluomethylene (PTFE), as well as elastic beads, and they exhibit significant wave speed induced by varying the induced preload.[8]
Let us consider an infinite mass-spring system which has the same spring stiffness (K) and two kinds of masses (M1, M2) arranged periodically. In this set-up, there exists both a band gap in which waves propagate with exponential decay, and “propagation zone” waves with admissible frequencies that propagate without any decay.[24,25,26]
Summary
The concept of the “acoustic diode” (AD) was proposed several decades ago.[1,2] Recently, nonlinear optical isolators have become a hot topic for a broad range of interests,[3,4,5] and the pioneering applications of ADs have attracted a lot of attention which may offer the potential to revolutionize existing acoustic techniques in different important fields. Theocharis used a combination of frequency filtering and asymmetrically excited bifurcations to obtain rectification ratios greater than 104.13 Aluand colleagues realized acoustic isolation by using external fluid flows to break space-time symmetry.[14] Popa et al proposed an active acoustic metamaterial with a compact structure to achieve unidirectional transmission.[15] Gu et al designed a broadband AD, which was close to the desired features of a perfect AD, by using an acoustic nonlinear material, a nonlinear electric circuit and a lossy material design.[16] In 2015, Devaux investigated the experimental characteristics of nonreciprocal elastic wave transmission in a single-mode elastic waveguide which was obtained by coupling a selection layer with a conversion layer.[17] The emergence of nonlinear ADs has been investigated by considerable efforts dedicated to the pursuit of linear acoustic one-way devices,[18,19,20,21] which cannot be regarded as practical ADs since the reciprocity principle still holds in such systems due to their linear nature.[22] In 2015, Xu Guo designed a AD model based on a monatomic chain.[23] In this article, we calculate the dispersion relationship of a one-dimensional periodic system with linear springs and predict an amplitudedependent dispersion relationship with nonlinear springs. A Finite Element Method (FEM) simulation (Abaqus software) is used to verify the results, which are fit well with the theoretical dispersion relationship
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
