AEH with phononic crystals and metamaterials

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Acoustic metasurfaces for reflected wave manipulations

As a kind of scalar wave, sound waves can be guided freely in artificial structures without cut-off frequencies, which enables the sound path control and the phase manipulation of acoustic waves by introducing labyrinthine designs[47, 61, 71– 73]. For the reflected wave manipulation, as elucidated in Fig. 1.7, the reflected waves can be tailored by modulating the phase distribution in the interface boundary. Figure 1.9 demonstrates an exemplary metasurface for reflected acoustic wave focusing with generalized Snell’s law, where both theoretical and experimental results are provided[74]. To achieve the focusing at the position (fx, fy), the phase profile along the boundary should be theoretically designed a Fig. 1.9(b) to realize the wavefront shown as an arc in Fig. 1.9 (a). The analytical result in Fig. 1.9(c) achieved by the theoretical boundary design shows good reflected wave focusing.
For the experimental part, eight labyrinthine elements in Fig. 1.9(d) with various sound paths and the resulting full 0 – 2π phase shifts were applied to construct the acoustic metasurface and implement the theoretical phase profile in the boundary for the previously designed reflected wave focusing. With an acoustic field scanning platform in Fig. 1.9(d), the experimental focusing result was obtained in Fig. 1.9(e), and both theoretical and experimental results reach a good consensus. In addition to the reflected wave focusing illustrated in Fig. 1.9, negative reflection[75], retroreflection[76], acoustic surface wave conversion[77], arbitrary reflective beam forming[74], reflected acoustic lensing[77], sound reflective diffusion[56, 78] can also be achieved by various reflective acoustic metasurfaces.
According to the aforementioned generalized Snell’s law, for any predefined incident angle, the reflected angle can be arbitrarily assigned through modulating the phase along the reflective interface.

Acoustic metasurfaces for transmissive wave manipulations

As another major branch of wavefront engineering, wave manipulations in transmissive field realized by acoustic metasurfaces share almost all the parallel applications, such as beam steering, beam forming, focusing, lensing, propagating to surface wave conversion, etc., which are previously introduced in reflective field. Similar to the reflective cases, delicate phase modulation along the interface in Fig. 1.7 remains to be essential in achieving transmissive wave steering. However, impedance matching of the transmissive metasurfaces with the ambient media, not necessarily required in reflective situations, should be carefully considered to ensure sufficient transmission of acoustic energy for effective application potential in practice. Therefore, in addition to the capability of phase shifting for desired wavefront tailoring, the candidate elements to construct the transmissive metasurfaces should also take into account the impedance matching. Because of straightforward manner, the coiling-up-space concept to tune the length of sound path and the relative phase still prevails in the design of non-resonating elements for individual transmitted phase shift[35, 82, 83]. Labyrinthine elements proved promising candidates in achieving phase gradient in the interface through elongating the wave propagation length with their rigid coiled channels, demonstrating low acoustic absorption over a wide range of frequency[38]. Nevertheless, the impedance of typical labyrinthine elements cannot well match that of the surrounding medium, e.g., the air. In order to manage the impedance matching, delicately processed coiling-up-space structures, such as tapered labyrinthine element[84], horn-like coiling-up-space elements[69, 70], spatially varied coiling-slit elements[85], filled-up space coiling designs[47], space coiling structure with impedance matching layers[86], etc., have been extensively proposed.
Tapered structural designs have been broadly used in conventional musical instruments and loudspeakers to improve impedance matching and bandwidth through their gradually varying cross-section area. Labyrinthine elements illustrated in Fig1.12 (a) are tapered as spiral geometries to achieve desirable transmissive phase shifts with 2π range and sufficient impedance matching, simultaneously. With designing the phase gradient along the interface according to the generalized Snell’s law (Eq.1.2), various kinds of predefined transmitted wave controls can be theoretically accomplished. Subsequently, the theoretical phase distributions for various wave manipulations can be discretized and further implemented by an array of elements with individual phase shits, i.e., acoustic transmissive metasurfaces. An exemplary metasurface composed of these tapered labyrinthine elements for typical negative refraction is provided in Fig. 1.12(a)[82]. With the predefined phase design and these tapered elements, focusing, propagating to evanescent wave conversion, and other wave steering applications can be also realized[82].

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AEH with phononic crystals and metamaterials

Phononic crystals and acoustic metamaterials have demonstrated tremendous potentials in AEH, due to their innovative mechanisms and unconventional wave localization behaviors. As an important application of phononic crystals and metamaterials, the defect mode in the band gaps can be effectively and efficiently applied for wave focusing or localization, and the subsequent AEH[125, 126]. To be more specific, the resonators (meta-atoms) the PCs or AMMs are adjusted to achieve the band gaps with bandwidth as broad as possible, and then several resonators are removed from the PCs or AMMs to create cavity or line defect to induce defect mode. The waves are localized or confined in the defect cavity or line with the acoustic incidence at the defect mode, and the confined acoustic energy is then converted into electricity through piezoelectric method. As illustrated in Fig. 1.16(a), a point is created by removing a rod of a perfect sonic crystal, and the defect mode can be observed in the band structure of the defected sonic crystal[125]. Through the airborne analysis, the sound transmission level evolution towards frequency is plotted in Fig. 1.16(b), and a high sound transmission is acquired at the defect mode frequency.

Implementation of the planar AMM

Band gaps of the periodic structures could be applied for wave guiding and confinement through introducing defect modes inside. Defect mode in the band gap can be created by breaking the periodicity of the perfect structures. At the defect mode frequency, the propagating waves are localized in the defect region, which leads to the strain energy confinement. The defect mode in a larger band gap contributes to a stronger energy confinement effect. According to the theoretical analyses in Sec. 2.2, the STL and band structure of the periodic plate metamaterial can be acquired. Through adjusting the mass and the dynamic stiffness of the resonators, and the fluid loading and plate stiffness, the band structure can be modified or optimized for wider band gap and larger quality factor of the defect mode.

Space coiling elements

Metasurfaces made up of a variety of unit cells, such as Helmholtz resonators [87] and labyrinthine chambers [82], have demonstrated extraordinary wavefront shaping capabilities. In this chapter, different labyrinthine unit cells are utilized as candidates to manipulate the phase of reflected waves by coiling up space.
The shifted phase of the reflected waves controlled by each unit is crucial to achieve desired reflected field. A sample labyrinthine unit (length lx and width ly) of the case (m, n) = (3, 2) is illustrated in Fig. 3.1, with m and n referring to the number of the identical bars (length l and width w) in upper and lower boundaries, respectively. The identical and parallel bars, arrayed with equal space d in the upper and lower boundaries of a unit, construct a zigzag channel to realize space coiling for effective sound path control, and the left end of the unit is set as hard boundary.

Table of contents :

1 State of the art 
1.1 Metamaterials and metasurfaces
1.1.1 Phononic crystals and acoustic metamaterials
1.1.2 Acoustic metasurfaces
1.2 Acoustic energy harvesting (AEH)
1.2.1 AEH with resonators
1.2.2 AEH with phononic crystals and metamaterials
2 AEH with planar acoustic metamaterials 
2.1 Introduction
2.2 Theoretical modeling and analysis
2.3 Implementation of the planar AMM
2.4 Electrical model
2.5 Discussion and conclusion
3 Multilateral metasurfaces for AEH 61
3.1 Introduction
3.2 Space coiling elements
3.3 Acoustic confinement results
3.3.1 Two-sided metasurface
3.3.2 Three-sided metasurface
3.3.3 Enclosed metasurface
3.3.4 Summarized focusing results
3.4 Thermovicous effects
3.5 Time domain analysis of two-sided metasurface
3.6 Metasurface AEH system and outputs
3.6.1 Acoustic energy harvesting system
3.6.2 Acoustic energy harvesting outputs
3.7 Summary and conclusions
4 Three-dimensional metasurfaces for energy confinement 
4.1 Introduction
4.2 Method and Design
4.3 Results and Discussion
4.3.1 Ultrathin metasurface constructed by Helmholtz-like elements
4.3.2 Comparison of two acoustic metasurface designs
4.3.3 Thermoviscous effects
4.4 Summary and outlook
General conclusion and perspective
Acoustic energy harvesting with a planar AMM
Acoustic energy harvesting with metasurfaces
Bibliography 

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