Page 38 - 2016Fall

Acoustic Metamaterials
Figure 5. The use of nonlinear effects is an emerging area of
acoustic metamaterial research. One possibility is to control
the linear acoustic response by imposing a state of prepressur-
pressure-volume change (solid black line). Boxes: Approxi- mate linear responses about two different reference configura- tions. The configurations are (1) zero pressure, zero volume change (gray box) and (2) a state of prepressurization (blue box). Pressure perturbations associated with acoustic waves are well approximated by the gray tangent lines. Nonlinear ef- fects become important at much lower acoustic pressure am- plitudes for the prepressurization configuration as indicated by the vertical extent of the blue box relative to that of the gray box.
al., 2015), active elements (Popa and Cummer, 2014), and granular media. A simulation of a “sound bullet” generated by granular chains can be seen at http://bit.do/soundb. In all but the granular media, the structures studied can produce equations of state with multiple stable configurations, analo- gous to phase transformation in solids. This is of interest to reconfigurable AMMs discussed later.
Nonreciprocal Materials
One of the most fundamental ideas in acoustics is that wave propagation is reciprocal in the sense that transmission from a source to observer is identical if they are interchanged. However, it is also known that reciprocity may not hold in specific situations, for instance, in the presence of a moving fluid. Considerable recent effort has been focused on devel- oping nonreciprocal AMM devices because of the exciting potentials, such as the ability to hear but not be heard, sen- sors that can transmit and receive at the same time, or sen- sors that have different transmit and receive patterns. The first such device exploited material nonlinearity to generate nonreciprocal acoustic wave behavior (Liang et al., 2009). Other nonreciprocal acoustical systems followed, including a linear device that employed momentum field biasing via fluid motion in a resonant cavity (Fleury et al., 2014) and another that modulated the material properties using elec- trically active components (Popa and Cummer, 2014).
ization (p ). The idea is based on the schematic nonlinear pre
Equation 1 Article #3 Haberman/NorrisSo how does one generate nonreciprocal behavior? As with
the cases of negative dynamic density and compressibility, one must take a closer look at the fundamentals; it is essen- tial to understand what physical principles underpin acous- tic reciprocity. A brief description is provided here, but the reader is referred to the recent Acoustics Today article on this topic (Fleury et al., 2015) for detailed explanations.
Reciprocity can be formulated for most systems support-
Material nonlinearity like that in Figure 5 can be produced by subwavelength, microscale geometric nonlinear mecha- nisms, much in the same way that the dynamic linear mi- crostructure leads to effective negative material parameters. The result is a nonlinear effective equation of state
𝐶𝐶 𝑝𝑝= 𝑥𝑥 + 𝑥𝑥 + 𝑥𝑥 +...with𝑥𝑥=𝜌𝜌′/𝜌𝜌 !!!!!!! !
!!
(1)
where p is the acoustic pressure, C0 and ρ0 are ambient com- pressibility and density, respectively, ρ' is the density per- turbation from ambient, and B/A and C/A are the effective parameters of nonlinearity. This results in strong nonlinear effects, including generation of higher harmonics, which can be used to improve imaging resolution and even to produce nonreciprocal wave propagation as discussed next.
Elevated material nonlinearity has been achieved using sev- eral mechanisms, including buckled structures (Klatt and Haberman, 2013), patterned holes in soft media (Shim et
ing wave propagation (acoustic, electromagnetic, elastody- namic) using the Onsager-Casimir principle of microscopic reversibility. Consider a linear time-invariant medium, pos- sibly inhomogeneous, in which time-harmonic waves are excited at source point A and detected at B. The Onsager- Casimir principle implies tAB(ω,η,B) = tBA(ω,η,−B) where tAB and tBA are the transmission coefficients for waves propagat- ing from A to B and B to A, respectively, ω is the frequency, η is the material loss factor, and B is a set of parameters that influence propagation. The proper selection of B, therefore, allows one to break microscopic reversibility and thus pro- duce linear materials that support nonreciprocal acoustic
36 | Acoustics Today | Fall 2016