Enhancing elastic energy focusing in multimode strain regions via Bayesian optimization of gradient-index phononic crystals for energy harvesting

Acoustic waves in a phononic crystal (PnC) showed properties of band gaps and anisotropic propagation and promised many applications. By arranging the filling fraction of PnCs gradually in space, a gradient-index (GRIN) PnC was proposed to bend the wave propagation. GRIN PnCs were reported and applied as an acoustic lens to focus acoustic waves. Theoretically, this kind of lens has a hyperbolic secant refractive index profile along the transverse direction. In this paper, a two-dimensional GRIN PnC for surface acoustic wave (SAW) was studied. The anisotropy of SAW in PnCs was analyzed and trajectories of a SAW beam were estimated. A 16-layers GRIN tungsten/silicon PnC lens was designed. FEM simulation showed that a 150-MHz SAW beam was focused in the GRIN PnC. The GRIN PnC could be applied as a beam aperture modifier or a beamwidth compressor.

The aim of this study is to realize an achromatic acoustic gradient-index (GRIN) phononic crystal (PC) lens system with a spatially invariant focal length over a broad operating frequency range. To this end, we propose an approach of introducing thin achromatic coating layers that can be easily assembled into the front and rear regions of the acoustic GRIN PC lens. A systematic design method based on topology optimization (TO) is developed to inversely design the achromatic coating components. The topology-optimized achromatic coating components are fabricated using 3D printing and coupled with the acoustic GRIN PC lens for acoustic characterization. Both numerical simulation and experimental characterization demonstrate the achromatic focusing capabilities of the GRIN PC lens with the designed achromatic coating layers in a wide range of frequencies (2.5 kHz–5.5 kHz). The proposed concept of applying achromatic coating layers along with the TO-based design method is expected to provide remarkable versatility to design GRIN PC lens-based applications such as energy harvesting, acoustic imaging, and acoustic wireless power transfer in broadband operation.

Gradient-index (GRIN) refers to a system where the refractive index changes spatially within a specific region. GRIN phononic crystals are capable of not only amplifying the magnitude of wave energies but also controlling the directional nature of the wave propagation, thus offering substantial benefits with regard to energy harvesting (EH) improvements. Here, we propose a systematic design method for GRIN phononic crystals which combine the two-dimensional Reissner–Mindlin plate model and a genetic algorithm for optimization. This design process allows us to design a GRIN phononic crystal with any arbitrary refractive index profile or complex shape of the unit cells. The experimentally verified focusing capability of the GRIN phononic crystals led to the realization of piezoelectric energy harvesting with a maximum areal power density value of up to 240.4 mW/m2, considerably outperforming the existing non-GRIN-based EH systems without direction controllability.

We report on the subwavelength focusing of Rayleigh waves using gradient-index (GRIN) phononic crystals (PCs) made of air holes scatters in a thick silicon substrate. The subwavelength focusing is demonstrated both in the inner and in the silicon substrate behind the GRIN PCs by using a non-contact experimental technique. In both situations, the focal zone was observed at the position, which is in very good agreement with our theoretical predictions, at a frequency in the sound cone free of radiation into the substrate.

Machine learning-enabled development of high performance gradient-index phononic crystals for energy focusing and harvesting

The design, fabrication, and analysis of omnidirectional gradient-index (GRIN) phononic crystals (PnCs) for acoustic wave focusing and energy harvesting have been demonstrated both numerically and experimentally. Despite that omnidirectional functionality is a key factor to alleviate the directivity dependence issues, the concept has not yet been incorporated into acoustic energy harvesting. In this work, a symmetrical GRIN PnC structure consisting of cylinders with variation in filling fractions has been presented to tailor the spatial acoustic refractive index, thus enforcing the acoustic waves in any direction toward the targeted center area for focusing purposes. Both a numerical simulation and experimental validation confirm substantial sound energy amplification of the designed GRIN PnC over a broad frequency range from 250 Hz to 1 kHz. Notably, the maximum sound amplification occurs at the hybrid resonant frequency of the GRIN PnC structure and the acoustic duct system used to generate incident plane waves. Numerical simulation reveals that the cavity resonance and the refraction of the GRIN PnC mainly contribute to enhanced sound amplification in addition to the reflection from the acoustic duct. The GRIN PnC structure coupled with the acoustic duct system leads to enhanced harvesting output performance when integrated with a piezoelectric energy harvesting device.

We explore the enhancement of structure-borne elastic wave energy harvesting, both numerically and experimentally, by exploiting a Gradient-Index Phononic Crystal Lens (GRIN-PCL) structure. The proposed GRIN-PCL is formed by an array of blind holes with different diameters on an aluminum plate, where the blind hole distribution is tailored to obtain a hyperbolic secant gradient profile of refractive index guided by finite-element simulations of the lowest asymmetric mode Lamb wave band diagrams. Under plane wave excitation from a line source, experimentally measured wave field validates the numerical simulation of wave focusing within the GRIN-PCL domain. A piezoelectric energy harvester disk located at the first focus of the GRIN-PCL yields an order of magnitude larger power output as compared to the baseline case of energy harvesting without the GRIN-PCL on the uniform plate counterpart.

Gradient-index phononic crystal and Helmholtz resonator coupled structure for high-performance acoustic energy harvesting

Using phononic crystals (PnCs) to enhance the electrical performance of piezoelectric energy harvesting (PEH) devices is an effective strategy for enabling self-powered operation in low-power electronic systems. Building on prior studies of PnCs with incomplete line defects, this study proposes a PnC with decoupled double incomplete line defects. In the upper (y-direction) subsystem, the defect was extended stepwise from the second to the sixth supercell layer, while the other subsystem was kept fixed, yielding five supercells. Their dispersion relations, elastic wave localization, and energy harvesting characteristics were systematically examined. All supercells exhibited effective decoupling between the two subsystems. As the size of defects in the upper subsystem increased, the total system's electrical performance first increased and then decreased. Specifically, when the defect extended to the fourth layer, the total system reached its optimum, yielding 17.58 mW of output electric power and representing a 349-fold improvement compared with conventional materials. Furthermore, because incomplete line defects induce waveguide-localized coupling modes, an efficient, tunable, relatively broad energy harvesting bandwidth of elastic waves was achieved by adjusting the subsystem's defect size. Therefore, a practical route is provided to optimize PEH electrical output and tune the operating frequency range through multi-defect PnC designs.

Phononic crystals and acoustic metamaterials are periodic structures whose effective properties can be tailored at will to achieve extreme control on wave propagation. Their refractive index is obtained from the homogenization of the infinite periodic system, but it is possible to locally change the properties of a finite crystal in such a way that it results in an effective gradient of the refractive index. In such case the propagation of waves can be accurately described by means of ray theory, and different refractive devices can be designed in the framework of wave propagation in inhomogeneous media. In this paper we review the different devices that have been studied for the control of both bulk and guided acoustic waves based on graded phononic crystals.

Wireless sensor networks that enable advanced internet of things (IoT) applications have experienced significant development. However, low-power electronics are limited by battery lifetime. Energy harvesting presents a solution for self-powered technologies. Vibration-based energy harvesting technology is one of the effective approaches to convert ambient mechanical energy into electrical energy. Various dynamic oscillating systems have been proposed to investigate the effectiveness of energizing low-power electronic sensor devices for supporting various IoT applications across engineering disciplines. Phononic crystal structures have been implemented in vibrational energy harvesters due to their unique bandgap and wave propagation properties. This work proposes a Rubik’s cube-inspired defective-state locally resonant three-dimensional (3D) phononic crystal with a 5 × 5 × 5 perfect supercell that contains 3D piezoelectric energy harvesting units. The advantage of defect-induced energy localization is utilized to harness vibrational energy. The 3D piezoelectric energy harvesting units are constructed by the buckling-driven assembling principle. Adapting to the low-frequency and broadband characteristics of ambient vibration sources, soft silicone gel is used to encapsulate the buckled 3D piezoelectric units, which are embedded in the 3D cubic phononic crystal to assemble an entire system. The energy harvesting performance of various defective layouts and their defect modes is discussed. The results demonstrate that the harvester functions well under multidirectional, multimodal, and low-frequency conditions. The proposed methodology also offers a new perspective on vibrational energy harvesters for defective phononic crystals with superior working performance.

In recent years, metamaterial/ phononic crystal (PnC) based energy harvesters are gaining interest due to their excellent elastic wave manipulation and energy trapping capabilities. Here, we propose a novel PnC comprising of Tungsten Carbide (WC) spheres embedded in epoxy resin matrix. The sphere-epoxy composite is encapsulated by Aluminum (Al) holey structure and the device is sandwiched between two Al plates. Numerical analysis of band structure reveals a wide phononic band gap (BG) from 50.65 kHz to 71.12 kHz. These BGs can be engineered by varying geometric parameters of the unit cell viz., the radius of the sphere and thickness of Al plates. A point defect is introduced by removing the central sphere of the 5 × 5 PnC to facilitate the robust localization of evanescent wave defect modes within the bandgap. Moreover, it is observed that, by altering the radius of the defect sphere, the number of defect modes and their shift can be reconfigured. A PnC based energy harvester is implemented by attaching a piezoelectric disk (PZT-5H) onto the defect PnC just above the defect site. This arrangement of PZT disk converts the highly resonant mechanical defect mode into electrical energy, thereby allowing vibration energy harvesting. Finally, we show that the power enhancement can be achieved by ∼12 times with the proposed PnC compared to the bare Al block.

In this letter, we numerically demonstrate focusing of the lowest antisymmetric Lamb wave in a gradient-index phononic crystal (PC) silicon plate and its application as a beam-width compressor for compressing Lamb wave into a stubbed phononic tungsten/silicon plate waveguide. The results show that beam width of the lowest antisymmetric Lamb wave in the PC thin plate can be compressed efficiently and fitted into tungsten/silicon PC plate waveguide over a wide range of frequency.

Phononic crystals (PnCs) have been shown to manipulate and amplify elastic waves. Using this characteristic of PnCs to assist energy harvesting has a remarkable effect. Generally, a defect occurs when a unit cell in a PnC is replaced by another cell with different geometric or material properties; then the output electric power of piezoelectric energy harvesting (PEH) devices will be significantly enhanced. In this study, a cross-hole-type PnC-assisted PEH device with a large defect is presented by replacing several adjacent cells with other cells. It is found that multiple peak voltages can be created within the bandgap and multimodal energy harvesting can be performed. Compared with the defect mode composed of a small defect, energy localization and amplification of the proposed PnC leads to substantial enhancement of harvesting power after tailoring the geometric parameters of a PEH device. This work will help in designing PnC-assisted PEH devices in a reasonable way.

Several previous studies have been dedicated to incorporating double defect modes of a phononic crystal (PnC) into piezoelectric energy harvesting (PEH) systems to broaden the bandwidth. However, these prior studies are limited to examining an identical configuration of the double defects. Therefore, this paper aims to propose a new design concept for PnCs that examines differently configured double defects for broadband elastic wave energy localization and harvesting. For example, a square-pillar-type unit cell is considered and a defect is considered to be a structure where one piezoelectric patch is bonded to a host square lattice in the absence of a pillar. When the double defects introduced in a PnC are sufficiently distant from each other to implement decoupling behaviors, each defect oscillates like a single independent defect. Here, by differentiating the geometric dimensions of two piezoelectric patches, the defects’ dissimilar equivalent inertia and stiffness contribute to individually manipulating defect bands that correspond to each defect. Hence, with adequately designed piezoelectric patches that consider both the piezoelectric effects on shift patterns of defect bands and the characteristics for the output electric power obtained from a single-defect case, we can successfully localize and harvest the elastic wave energy transferred in broadband frequencies.