Two-dimensional octagonal phononic crystals for highly dense piezoelectric energy harvesting

Two-dimensional octagonal phononic crystals for highly dense piezoelectric energy harvesting

Author’s Accepted Manuscript Two-dimensional octagonal phononic crystals for highly dense piezoelectric energy harvesting Choon-Su Park, Yong Chang Sh...

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Author’s Accepted Manuscript Two-dimensional octagonal phononic crystals for highly dense piezoelectric energy harvesting Choon-Su Park, Yong Chang Shin, Soo-Ho Jo, Heonjun Yoon, Wonjae Choi, Byeng D. Youn, Miso Kim www.elsevier.com/locate/nanoenergy

PII: DOI: Reference:

S2211-2855(18)30930-3 https://doi.org/10.1016/j.nanoen.2018.12.026 NANOEN3274

To appear in: Nano Energy Received date: 14 October 2018 Revised date: 6 December 2018 Accepted date: 9 December 2018 Cite this article as: Choon-Su Park, Yong Chang Shin, Soo-Ho Jo, Heonjun Yoon, Wonjae Choi, Byeng D. Youn and Miso Kim, Two-dimensional octagonal phononic crystals for highly dense piezoelectric energy harvesting, Nano Energy, https://doi.org/10.1016/j.nanoen.2018.12.026 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Two-dimensional octagonal phononic crystals for highly dense piezoelectric energy harvesting

Choon-Su Parka1, Yong Chang Shinb1, Soo-Ho Job, Heonjun Yoonb, Wonjae Choia, Byeng D. Younb,c,d*, Miso Kima* a

Center for Safety Measurement, Korea Research Institute of Standards and Science (KRISS), Daejeon 34113, Republic of Korea b Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul 08826, Republic of Korea c Institute of Advanced Machines and Design, Seoul National University, Seoul 08826, Republic of Korea d OnePredict Inc., Seoul 08826, Republic of Korea [email protected] [email protected] * Corresponding author:

Abstract Piezoelectric energy harvesting at multi-scales has received considerable attention as an attractive powering technology which enables sustainable self-powered operation of small electronics such as wireless sensors. Self-powered wireless sensors for structural health monitoring, biomedical and wearable applications would be great potential applications with high market demand. A key challenge has been insufficient power generation for practical applications, which necessitates a new paradigm in the design of energy harvesting systems. In this work, drastic enhancement of harvesting performance along with energy focusing is demonstrated both analytically and experimentally by introducing metamaterial-based energy harvesting (MEH) systems. Metamaterials, artificially engineered structures, exhibit unique properties including band gap and negative refractive index and thus enable us to manipulate mechanical wave propagations. Wave guide and localization toward a desired position can lead to amplification of harvestable input mechanical energy. In this work, systematic design of twodimensional octagonal phononic crystals (PnCs) through geometric and band gap optimization process is proposed and followed by experimental demonstration. Energy confinement and

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These authors contributed equally to this work as the first authors 1

localization at the defect of proposed PnCs leads to successful enhancement of harvesting power up to 22.8 times compare to the case without the presence of metamaterial. Graphical Abstract:

Keywords: metamaterial; energy harvesting; piezoelectricity; phononic crystals; elastic waves

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1. Introduction

Energy harvesting is a technology where ambient energy, otherwise wasted, is converted into useful electrical energy. The demand for energy harvesting as sustainable self-powering technology has been fueled by the rapidly growing markets of low-power electronics such as wireless sensors. Harvesting wireless sensors is a key technology especially for Internet of Things (IoT) ranging from structural health monitoring of infrastructures to wearable and biomedical applications. Depending on harvesting sources and conversion mechanisms, a wide range of technology has been actively researched including wind, solar, thermal, and mechanical energy harvesting. The power level that can be generated from each source ranges from megawatts to micro-, nano-, even pico-watts. This suggests that each technology offers a different powering solution depending on the required power level of target applications. Conversion of mechanical energy source into electrical power is capable of providing micro- to milli-watts of power, potentially satisfying the power level of sensors for both industry and everyday life applications. There are abundant mechanical sources available in nature including sound, vibration, ultrasonic waves and human-based kinetic energies (Fig. 1a). These sources can be converted into useful electrical energy via piezoelectric materials and devices that are advantageous due to its high efficiency and direct conversion mechanism. Although mechanical energy harvesting using piezoelectricity is a very attractive technology, insufficient power generation still remains as an issue to overcome in order to realize a self-powered system for practical use. To date, development of high efficient piezoelectric materials, devices, and electrical circuits have been the key research approaches in order to enhance harvesting performance [1-22]. Optimal device 3

designs allow efficient mechanical-to-mechanical energy coupling by allowing absorption of mechanical energy into the harvesting device as much as possible. High performance piezoelectric materials along with proper selection of electrode and structural materials increase conversion efficiency of mechanical-to-electrical energy while circuit design with high efficiency reduces loss in the process of generated electrical power management and transfer to the target applications. Recently, a new paradigm concept, that is, enhancement of metamaterialbased energy harvesting has intrigued scientists as well as engineers. Metamaterial-based energy harvesting (MEH) is a concept where input mechanical energy is controlled and manipulated to localize and focus at the desired harvesting position before any conversion process is involved (Fig. 1b). Thus, it is a way of active energy harvesting in that we amplify the input mechanical energy by actively controlling it rather than passively harvesting and converting the given energy from the environment. Elastic/acoustic/mechanical metamaterials are artificially engineered structures which exhibit exotic properties such as effective negative dynamic modulus and density. The prefix meta means “beyond” while materials in metamaterials mean the material properties. By definition, metamaterials enable realization of material properties that do not normally exist in nature. The concept was theoretically proposed in 1968 by Veslago [23] for electromagnetic regime while design of metamaterials and experimental realization of microwave cloaking were followed much later in 1999 and 2006 by Pendry [24] and Smith et al. [25]. Acoustic and elastic metamaterials followed later from the year of 2000 when Liu et al. [26] showed a total reflection of sound by having negative effective bulk modulus in sonic crystals. In conventional materials, mass density and modulus have positive values. In metamaterials, either or both of these values can exhibit negative values within a certain range of frequencies, so called, negative effective 4

dynamic modulus, mass density, and Poisson’s ratio [27-30]. Modulus and mass density are the key parameters that determine the wave propagation, particularly, the wave velocity. By having negative values of modulus and mass density, unusual phenomenon of negative refraction and band gap can occur via metamaterials [31, 32]. Thus, careful design of metamaterials provides a way of controlling acoustic and elastic wave propagation along desired paths, which opens up a substantial possibility of potential applications including sound and vibration insulation [33-35], acoustic and elastic superlens [36-38], ultrasonic wave collimators, [39] and energy harvesting [40]. In energy harvesting, metamaterials can be utilized to guide and focus acoustic, elastic, vibration energies towards the desired position in order to amplify input mechanical energy that goes into the energy harvesting systems for conversion. There are two kinds of metamaterials that can be used for energy focusing and harvesting. Metamaterials are artificially engineered periodic (not necessarily) arrangement of building blocks, so called, unit cells. One kind is phononic crystals (PnCs) where the wavelength of interest is similar to the size of the unit cell. In phononic crystals, multiple scattering of unit cells, Bragg scattering, results in phononic band gaps which prohibit wave propagation within the designed frequency range [41]. The other kind is locally resonant structures [26, 42], sometimes regarded as acoustic/elastic metamaterials in a narrow meaning. In such structures, the principle is local resonance of constituent units and the size of unit cell is usually much smaller than the wavelength. Note that the term, metamaterial, is used to cover both phononic crystals and locally resonant structures in this paper. Several research efforts on metamaterial-based enhancement of energy harvesting have been reported. Periodic structures have been proposed to confine and harvest mechanical vibration energies, including hexagonal honeycomb structures with piezoelectric cantilevers [43], one-dimensional 5

phononic piezoelectric cantilever beams [44], a phononic crystal consisting of two-dimensional periodic cylinders with a defect state [45], and mechanical metamaterials with auxiliary structures for low frequency band gaps [46]. Acoustic focusing and energy confinement in the defect of a phononic crystal has been of interest as well. For instance, curved PVDF films were located in the cavity of two-dimensional PMMA cylinder arrangement and shown to exhibit enhanced power performance compared to the case without PnCs [47, 48]. Combination of sonic crystal and Helmholtz resonators with enhanced acoustic wave localization and harvesting were also reported [49-51]. Qi et al. proposed a planar metamaterial for both acoustic energy harvesting and low frequency sound insulation based on the numerical simulation study [52]. Pertaining to elastic wave energy harvesting, acoustic mirrors [53-55] and funnels [54] as well as a point defect in two-dimensional PnCs [54] were demonstrated to focus, guide, and localize the incoming elastic waves, respectively. These structures consisted of cylinder stubs attached to the host plate and provided a platform for improved energy harvesting performance by an order of magnitude compared to case of bare plate. Some of optical lens concepts such as gradient index (GRIN) phononic crystals and phononic crystal Luneburg lens were also introduced to vary refractive index of the structure so as to adjust the direction of the wave propagation for the purpose of omnidirectional elastic wave focusing and energy harvesting [56, 57]. These prior works definitely open up a way to explore the potential of integrating metamaterials into energy harvesting systems. Despite intriguing concepts, there are several issues to tackle for further improvement of MEH performance. First, more systematic design approach including not only unit cell baseline design but also size optimization is strongly required along with thorough experimental demonstration. In particular, most PnC designs in the previous work feature a periodic circular or cylinder-type structure with bulk stubs, the simplest 6

designs that can be drawn from intuition. Moreover, in many cases, such MEH research focused only on the theoretical studies with little experimental support. Second, the absolute magnitude of power level generated from previous MEH systems remains in the sub-micro or microwatt level although the amplification ratio is reported quite high: the amplification ratio is the ratio of power obtained (or voltage performance) with metamaterial to power output obtained without metamaterial. For practical applications, sufficient power output should be achieved with high amplification through metamaterials. In this work, drastic enhancement of MEH will be presented from design, analysis towards experimental demonstration. Here, we propose an optimized design of two-dimensional octagonal phononic crystals with a single defect as metamaterial for highly dense elastic energy harvesting. Systematic design through size optimization is performed to maximize the band gap and followed by theoretical analysis and experimental verification. Substantial enhancement of energy harvesting capability via metamaterials, more than 20 times of output power amplification at the level of micro-watts, is demonstrated and thoroughly investigated both numerically and experimentally.

2. Simulation and experimental methods

2.1 Unit cell design for band gap

The first step is band gap design for PnCs, which requires the design optimization of a unit cell of PnC structures to maximize band gaps in the dispersion relations. The band gap maximization is performed to ensure a robust wave manipulation performance against uncertain factors such as manufacturing tolerances in reality. The proposed unit cell design is a square 7

plate with an octangular hole inside, which is graphically shown in Fig. 2a. The architecture of four unit cells is also demonstrated in Fig. 2b. Since the periodicity of the PnC is comparable to wavelengths, the geometry of the unit cell strongly affects the band structure. The octagonal hole is specially devised to incorporate various hole shapes, thereby enlarging a design space in size optimization. Depending on the values of the design variables (a, b, and c), the octagonal hole can be seen as square-like, 45°-rotated square-like, and circle-like shape as shown in Fig. S3. With the geometric design variables, the band gap width is defined as the objective function to be maximized, subjected to a target frequency of 50 kHz. The design variables are the unit cell size (i.e. periodicity), distance between edges of unit cell and octagon, and the side length of octagon. These are denoted as a, b, and c, respectively, as shown in Fig. 2a. The initial values of a, b, and c are set to be 33.8 mm, 2.00 mm, 4.00 mm so as to target 50 kHz as band gap center frequency for fast convergence of iterative optimization process. The range of each variable is set to be 33 ≤ a ≤ 35, 2 ≤ b ≤ 3, 2 ≤ c ≤ 11 (mm). Thus the optimization problem is formulated as follows:

Maximize Band Gap Width subject to |Center Frequency – 50 kHz| - 0.1 < 0 where 33 ≤ a ≤ 35, 2 ≤ b ≤ 3, 2 ≤ c ≤ 11 (mm)

In order to achieve a dispersion relation, a finite element model is developed to analyze the unit cell using the commercially-available software, COMSOL MULTIPHYSICS version 5.3. By applying Floquet-Bloch periodic boundary conditions to the four edges of the unit cell and

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solving the eigenvalue problem, the dispersion relation can be derived, which reveals wave propagation characteristics. It is required to select the proper material and thickness of the plate exhibiting the band gap at the target frequency of 50 kHz. For instance, it is known that the thinner plate is and the denser/stiffer material is, the lower band gap forms [58, 59]. Of course, as long as the obtained band gap is suitable for the target frequency, any material can be used for the PnC. Owing to easy fabrication and low cost, the material used here is aluminum and assumed to have material properties of elastic modulus of 70 GPa, mass density of 2700 kg/m3, and Poisson’s ratio of 0.33. Parametric analysis is also performed to investigate the effect of each design variable, a, b, and c, on the band gap formation. Size optimization provides the optimal values of a, b, and c. However, optimal values are not the final values. In order to consider manufacturing tolerances, band gap sensitivity analysis is also carried out when the design variables differ in +/- 0.2 mm based on the commonly used criterion. Then, the final values for geometric design variable are achieved to offer the largest band gap in the given PnC supercell structure.

2.2 Analysis of harmonic wave propagation

Simulation is performed to analyze harmonic wave propagation behaviors both in the propagation band (pass band) and in the band gap (stop band). A supercell consisting of 5 x 7 octangular unit cells is set to place within the boundary of perfect matching layers (omitted for brevity in Figures), which is illustrated in Figs. 2d and 2e. The input harmonic signal is flexural elastic waves, more specifically, asymmetric Lamb waves (A0 mode) with amplitude of 10 nm. In the phononic band gap, the input elastic waves are not allowed to propagate any further 9

beyond PnC supercell structures, suggesting that the energy is all reflected back while leaving only evanescent waves inside the PnC supercell structures due to displacement continuity. Here, if a defect is introduced by eliminating one unit cell at a designated region inside the supercell, it is possible to localize this evanescent wave energy at the region. In our supercell structure, a single defect is placed at the 4th row, 2nd column from left to right direction in Fig. 2f. Note that the direction of incident plane waves is from left to right in this simulation. Finally, the displacement field inside the PnC supercell structure with the defect confirms the energy localization at the designated region.

2.3 Fabrication of meta-plate

We employed two kinds of aluminum plates with thickness of 2mm as platform for elastic wave generation, propagation, localization and harvesting. One is named meta-plate where designed phononic crystal supercell 5 x 7 was located in the center. The other is bare plate of aluminum with the same size as meta-plate but without any PnC structure inside for comparison purpose. The size of each Al plates was 1800 mm x 900 mm. Note that we tried to use plates with the largest size from the commercial production of Al plates as much as possible in order to clearly observe wave propagations near the defect without unwanted reflections from the boundaries. In other words, the most parts of the plate other than the supercell are used for only experiment purpose to avoid the effects of the reflected waves from the boundaries. The measured thickness of 2T-Al was 2.13 mm. One side of the plates was polished to some extent in order to reduce the surface roughness effect on the measurement of elastic wave propagation such as unwanted laser-light scattering of interferometry. Laser cutting was utilized to fabricate 10

the designed octangular PnC supercell 5 x 7 in the center of meta-plate. Fig. 3b includes the image of the meta-plate fabricated along with the enlarged image of the PnC supercell.

2.4 Characterization of MEH systems

Fig. 3 presents the experimental setup along with a fabricated meta-plate prototype. The experimental setup consists of three parts, each of which is for elastic wave generation, visualization of elastic wave propagation, and characterization of energy harvesting performance, respectively. The experimental configuration for flexural wave generation includes piezoelectric transducers, function generators (Keysight 33512B), and power amplifier (AE Techron 7224). Disc-type lead zirconate titanate (PZT) transducers having a resonant frequency of 50 kHz are custom-made by Ceracomp Co. Ltd., which were directly attached to the Al plate for high signalto-noise ratio. It is important to locate the transducers with a sufficient distance from the measured area (typically 10~20 times of wavelength), as a rule of thumb for plane wave generation from a point source. Tone-burst signals at 50 kHz were generated by the function generator and fed to the PZT transducers through the power amplifier. Visualization of elastic wave propagation is possible using scanning laser doppler vibrometer (LDV, Polytec, PSV-400, OFV-5000). We scanned three areas: an area before metamaterial (14.5 cm x 11.7 cm), an area at the defect inside metamaterial (3.2 cm x 3.2 cm), and an area behind metamaterial (14.5 cm x 11.7 cm) with tone-burst signals with three cycles at 50 kHz. Each scan allows observation of plane wave generation before entering metamaterial, energy localization at the defect, and band gap effect after passing metamaterial, respectively. For energy harvesting performance characterization, piezoelectric device, harvesting circuits, and data acquisition system are 11

required. PZT ceramic disc (SMD10T2R111WL, STEMiNC) with electrodes is chosen as an energy harvesting device. The diameter of the harvesting device is 10 mm while the thickness is 2 mm. The disc is attached at the center of the defect. The piezoelectric disc is connected to electrical circuit with pure electrical resistors so that the output performances such as voltage and power are measured and calculated across various electrical impedance conditions. Oscilloscope is used as data acquisition system to obtain electrical output voltage in the time-domain. Power output is then calculated using Ohm’s law. Mechanical displacement of the harvesting device is also measured using LDV. Harvesting performance is characterized under the tone-burst signals with 40 cycles at 50 kHz.

3. Results and Discussions

3.1 Unit cell design of 2-D octagonal phononic crystals

Size optimization for band gap maximization provides the unit cell design with optimal geometric values, which are summarized in Table 1. The optimum values for a, b, and c are 33.51 mm, 2.00 mm, and 5.00 mm, respectively. Since decimal numbers are not realistically practical from a manufacturing perspective, the final values are again obtained without decimal points and listed in the last column of Table 1. The final values feature an octangular unit cell with a size of 34 mm with octangular side length of 6 mm and the width of 2 mm. The designed unit cell of these values results in the formation of band gap from 46.93 kHz to 52.68 kHz with a center frequency of 49.80 kHz, which is quite close to the targeted 50 kHz. This is apparently observed in the band structure, which is illustrated in Fig. 2c. This means that elastic waves are 12

forbidden to propagate along all directions within the band gap from 46.93 kHz to 52.68 kHz in the designed PnC supercell structure. Interestingly, each design variable is found to affect the property of band gap differently. Observation of the parametric study results in Table 2 and Fig. S1 leads to the following conclusions: i) unit cell size, a, determines where band gap frequencies appear, ii) width, b, affects band gap size, and iii) both band gap frequency and size depend on octangular side length, c. Sensitivity analysis results can also be found in Table S1 where manufacturing tolerance is taken into account. It is seen that the center frequency of band gap is always found close to the targeted frequency of 50 kHz even when there is a variation of 0.2 mm in a, b, and c as dimension and fabrication tolerance. Hence, we claim that our unit cell design satisfies manufacturing tolerance while exhibiting desired band gap performances. The optimized octagonal unit cell could form a larger phononic band gap than the circular one. In addition, the lattice constant of the optimized octagonal unit cell is smaller than that of the circular one, which is more beneficial to a compact design. For comparison purposes, similar size optimization that targets a center frequency of 50 kHz is also performed on the unit cell with a circular hole inside. In this case, the unit cell size is obtained as 36 mm with a hole radius of 17 mm, which is bigger than the proposed octangular unit cell size. The band structure of the circular hole-type unit cell is presented in Fig. S2 where the band gap ranges from 49.64 kHz to 53.6 kHz, offering smaller size band gap of 3.96 kHz compared to our octangular design.

3.2 Band gap effects and energy localization at the defect

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To validate the band gap effect of our designed PnC supercell structure, harmonic analysis has been carried out. The simulation results of elastic wave propagation at 40 kHz and 50 kHz in Figs. 2d and 2e clearly show distinct difference in the wave propagation behaviors of propagation band and stop band (i.e. band gap). When the incident plane waves enter from the left to right toward the PnC supercell structure, the waves are seen to propagate further even after they pass through the PnC supercell structure at 40 kHz in Fig. 2d. In contrast, it is clearly seen that the waves are forbidden to propagate when passing through the PnC supercell structures at 50 kHz in Fig. 2e. Accordingly, the designed unit cell is numerically proven to exhibit band gap capability at the desired frequency. Although larger supercell (more than 2 layers) is still required to guarantee the band gap effect due to periodicity, closer observation also suggests that the amplitude of waves is greatly attenuated after the second columns in Fig. 2e. This implies that most of elastic energy can be effectively confined around this layer, potentially offering a great candidate place for defect formation and thus energy localization. Introducing a point defect in a PnC enables tailoring of dispersion properties in a band structure. A point defect is formed in the middle of the second column by removing an octangular hole, as illustrated in Fig. 2f. The defect mode is generated inside the bang dap, the area shadowed in yellow color in Fig. 2c. PnCs containing such a point defect can provide remarkable features such as wave localization [41]. Substantial amplification of amplitude inside the defect is apparently observed in the harmonic analysis result (Fig. 2f). Here, originating from elastic incidence with amplitude 10 nm at 50 kHz, the maximum amplitude up to 61.5 nm is achieved. This confirms elastic wave energy localization in the point defect of the designed PnCs. It is worth pointing out that one defect imposed in the PnC supercell structure would result in the formation of several defect bands within the band gap and corresponding mode shapes. In 14

elastic waves, defect mode shapes would be more complex due to the effect of Poisson’s ratio, compared to acoustic waves. This study focuses the monopole mode shape, which is beneficial to energy harvesting application. Fig. 2f is the monopole mode shape corresponding to the defect near the band gap center frequency.

3.3 Elastic wave generation and propagation

We experimentally visualize elastic wave propagation before, inside, and behind a PnC in a meta-plate. Fig. 4 contains snapshots of displacement amplitude field scanned as a function of time: (a) wave propagation before meta, (b) wave propagation at the defect, (c) wave propagation behind meta. Note that the term meta equivalently refers to PnC in Fig.4. Yellow lines shown in Fig. 4a provide beautiful evidence that plane waves are successfully generated. It is general that plane waves are assumed in theoretical analysis for simplicity. However, realizing plane wave generation experimentally is often known to be painful (e.g. requirement of an array of numerous transducers). It is, therefore, worth noting that the rule of thumb – i.e. positioning point transducers with a sufficient distance from the measurement area of interest – works well in this work. One or two PZT transducers that are closely aligned are employed depending on the test (see Fig. 3b). Fig. 4b presents the change of mode shape at the defect with time. It is observed that a circular area with a dimeter that is about one third of the scanned square side length moves upward and downward in z-direction in turn as time. Larger circle with a diameter similar to the scanned square side length behave similarly to the smaller circle but in opposite direction. The overall mode at the defect changes with time in a doughnut shape. Importantly, the magnitude of displacement amplitude that is much more amplified than that of incident waves, indicating wave 15

energy localization at the defect. (For clearer view on the wave propagation behavior, the videos of all three cases are available in Supplementary data.) Fig. 4c experimentally supports band gap effect of our designed PnC. Little displacement amplitude is observed after waves pass through meta, which confirms that band gap effectively works and blocks wave propagation at the desired frequency. Small amplitude elastic waves are observed to propagate after a while in this scanned area and these are the reflected waves from the boundary of the Al specimen. Note that this is why it is important to fabricate large size Al plate as a host plate as addressed in Section 2.3.

3.4 Energy harvesting performance

Harvesting performance using metamaterial is of our utmost interest. The measured voltages in open-circuit conditions without meta (bare plate) and with meta are plotted as a function of time in Figs. 5a and 5b, respectively. Careful attention is paid to locate energy harvesting devices as well as PZT transducers exactly in the same positions in bare plate and meta-plate for fair comparison. First, we can see that it takes about 0.34-0.35 msec that waves generated from transducers reach the defect center of PnC (or equivalent position in case of bare plate), similarly in both cases. Second, it is observed that the output voltage varies with time in terms of the magnitude. We attribute this phenomenon to constructive and destructive interference of several waves including incident input waves, subsequent input waves, and reflected waves from the specimen boundaries. Furthermore, such interference is a consequence of more complicated interaction (i.e. multiple scattering) among elastic waves and the constituent unit cells and defects. As a result, an increase in voltage up to 4.55 V at 1.13 msec is observed and then 16

followed by a decrease down to voltage of 1.79 V at 1.83 msec in meta-plate (Fig. 5b). The maximum value corresponds to the point where constructive interference of waves is dominant over destructive interference waves while the minimum is the opposite case. As voltage behavior in time domain in bare plate and meta-plate is not the same, the time when maximum voltage occurs differ as well. The maximum harvesting voltage of 0.97 V appears at 2.82 msec in bare plate. In meta-plate, much more amplified voltage up to 4.55 V is achieved at 1.13 msec. However, from a viewpoint of harvesting performance, the maximum output values in a given time domain are the subject of primary interest regardless of the time they appear. Hence, we focus on maximum values that are obtained from each measurement for comparison. Comparison between the maximum voltages in bare plate and meta-plate reveals that harvesting voltage can be amplified by about 4.7 times using our designed PnC plate. Fig. 5c shows output voltages across various electrical resistances in bare plate and meta-plate. These voltage values are obtained from the maximum values in time-domain results like Figs. 5a and 5b. In both cases, voltage tends to increase with increasing resistance and becomes saturated at its maximum values, corresponding to open-circuit voltages of 0.97 V and 4.55 V, respectively for bare plate and meta-plate cases. Quite a steep increase in the output voltage with increasing resistances is interestingly seen. This implies that the electrical impedance matching conditions of elastic wave energy harvesting using piezoelectricity take place at low resistance values when compared to vibration energy harvesting [17]. Amplification ratio can be defined as the ratio of output performance with metamaterial to the performance without metamaterial under the same electrical conditions. The amplification ratio of voltage is then calculated as 4.69 for open-circuit conditions while amplification ratio of 4.55 is obtained on average from the result of Fig. 5c.

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From measured voltage, output power is calculated and plotted as a function of electrical resistance in Fig. 5d. The relation of power with electrical resistance here follows the typical trend of mechanical energy harvesting power performance using piezoelectricity [13]. Power increase and then decrease with increasing resistance and there exists a maximum power at optimal electrical resistance. We achieve 1.59 mW at optimal resistance of 4.99 kΩ from a PZT disc as a harvesting device integrated into meta-plate while the optimal power of 84.7 µW at 4.99 kΩ is obtained in bare plate case. Two aspects should be strongly emphasized here: amplification ratio and absolute magnitude of generated power. It is evidently proven that our systematic design-based metamaterial contributes to drastic enhancement of harvesting power performance with an amplification ratio of up to 22.8 (20.6 on average). This amplification ratio is the largest number ever reported in terms of elastic wave harvesting using PnCs. Moreover, the level of power generated out of this metamaterial energy harvesting system is in the level of mW. Considering that the power level reported in the existing work on elastic energy harvesting is normally of the order of 10s of µWs or less, our power level indicates a significant improvement in the relevant research and offers great potential for practical applications. It is noteworthy that the harvesting device employed here is just a commercially available PZT disc, which is not optimized at all in terms of either material properties or geometric parameters. This suggests further room for performance enhancement of MEH systems. The output current is also an important performance metric of energy harvesting. Based on the measured values of voltage and power in Figs. 5c and 5d, we calculated the corresponding output current. The output current across various electrical resistances is plotted and shown in Fig. S4. The maximum current in meta-plate is 564.6 µA at 4.99 kΩ while 130.03 µA is obtained in bare plate, resulting in the amplification ratio of 4.33 in terms of current. 18

We have subsequently investigated the mechanical behavior of our MEH system. The mechanical displacement amplitudes in time domain are measured at the center of the PnC defect before and after attachment of a piezoelectric harvesting device onto the host aluminum plate. Figs. 6a and b present the resulting mechanical displacement of the Al meta-plate only and the Al meta-plate with an energy harvesting device. Attachment of a PZT disc to the Al host plate causes reduction in the magnitude of mechanical displacement in both meta-plate (Figs. 6a and b) and bare plate (Figs. 6d and e). This can be explained in terms of mass and elastic modulus. Before attaching the energy harvesting device, the moving object is just the plate. When the harvesting device is attached, then the moving system consists of plate and the ceramic disc, meaning a system with larger mass. Therefore, smaller mechanical displacement is expected with larger mass under the same given force, which is consistent with the observation result. Additionally, the modulus of PZT ceramic is larger than that of Al plate, leading to the increased effective modulus of the entire system containing the PZT disc. Under the same force, then, less mechanical displacement is expected with larger modulus according to Hooke’s law (i.e. force = modulus x mechanical displacement) as well. Comparison between Figs. 6a and 6d (or between Figs. 6b and 6e) confirms large amplification effect of metamaterial regardless of whether harvesting disc is integrated or not. This result is consistent with the result of wave propagation visualization described in Section 3.3 except that the results in Fig. 6 are obtained under open-circuit conditions. Another interesting aspect should be addressed regarding the effect of metamaterial on the wave velocity. In Figs. 6a and 6d (or between Figs. 6b and 6e), the signals in the meta-plate are found to reach the measurement point later than those in the bare plate. Slow wave physics in metamaterials is a commonly known phenomenon [60]. The observation made here that waves become slower 19

when passing through the metamaterial provides another evidence of our designed metamaterial functionality for wave manipulation. Mechanical displacement in frequency domain is presented in Figs. 6c and 6f. These are obtained by performing fast Fourier transform (FFT) on the time-domain data in Figs. 6a, 6b, 6d, and 6e. The FFT results in Figs. 6c and 6f confirms that the center frequency of 50 kHz is well maintained after attachment of a PZT disc as well as before the attachment for both meta-plate and bare plate. Hence, we regard that integration of an energy harvesting device into the host system with PnCs hardly affects frequency component of propagating waves.

4. Conclusion

To summarize, using PnC with a single defect, we successfully realized drastic enhancement of piezoelectric energy harvesting both numerically and experimentally. Our objective in this work is to investigate the effect of metamaterials on elastic energy focusing and harvesting with a particular focus on defected phononic crystal. With this purpose in mind, we propose a twodimensional phononic crystal with octagon-shaped unit cells systematically designed through optimization process. Time harmonic analysis is followed not only to investigate band gap effect and wave propagation but also confirm energy localized at the defect in the designed PnC. Most importantly, we experimentally visualize elastic wave propagation and evaluate harvesting performance with and without metamaterial. More than 20 times of power enhancement with designed metamaterial is successfully achieved in comparison with bare plate while generating substantial power generation of 1.59 mW out of elastic wave energies in aluminum plate. Metamaterial-based energy harvesting based on systematic design optimization open up a drastic 20

enhancement solution of energy harvesting performance to develop self-powered wireless sensor network systems in structural health monitoring applications for infrastructures. For instance, when a transformer or a rotating machinery operate, elastic waves at an ultrasound frequency regime (hundreds of kHz) would be induced; this could be suitable for the working frequency of the phononic metastructure [61-63]. Further investigation on optimization of piezoelectric materials and devices as well as development of metamaterials for broadband and omnidirectional energy harvesting would contribute to facilitating realization of MEH systems for practical applications.

Acknowledgements This research was supported by the National Research Council of Science & Technology (NST) grant by the Korea government (MSIP) (No. CAP-17-04-KRISS).

Appendix A. Supplementary material Supplementary data associated with this article can be found in the online version at .

Supplementary Video Information Experimental visualization of elastic wave propagation: videos of elastic wave propagation in the areas (video 1) before meta, (video 2) at the defect, and (video 3) behind meta as a function of time. The actual scanned areas of (video 1) before meta, (video 2) at the defect, and (video 3) behind meta are 14.5 cm x 11.7 cm, 3.2 cm x 3.2 cm, and 14.5 cm x 11.7 cm, respectively.

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Fig. 1. (a) Frequency levels of various mechanical sources available in nature. (b) Schematic of an energy harvesting process: amplification of input mechanical energy using metamaterials, conversion of mechanical energy into electrical energy via harvesting devices, and power management through circuit for target applications.

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Fig. 2. (a) Proposed design of a unit cell for two-dimensional octagonal phononic crystals. (b) Architecture of a 2 x 2 supercell consisting of four unit cells. (c) Band structure of the proposed unit cell showing dispersion relations. Simulation results of wave propagation behavior in 5 x 7 PnC supercell structures: displacement field distribution (c) at 40 kHz in the propagation band and (e) at 50 kHz in the band gap. (f) Simulation result of energy localization at the defect of the PnC supercell structure.

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Fig. 3. (a) Schematic of an experimental setup for elastic wave generation, visualization of elastic wave propagation and energy harvesting performance characterization. (b) Photograph of a characterization system for MEH along with the fabricated Al meta-plate specimen.

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Fig. 4. Experimental visualization of elastic wave propagation: snapshots of elastic wave propagation in the areas (a) before meta, (b) at the defect, and (c) behind meta as a function of time. Note the term meta equivalently refers to the 5 x 7 PnC structure shown in the left side of this figure. The actual scanned areas of (a) before meta, (b) at the defect, and (c) behind meta are 13.0 cm x 10.2 cm, 3.2 cm x 3.2 cm, and 13.0 cm x 10.2 cm, respectively.

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Fig. 5. Experimental results of electrical energy harvesting performance: output voltages as a function of time (a) in bare plate and (b) in meta-plate, (c) output voltage versus electrical resistance in bare plate and meta-plate, and (d) output power versus electrical resistance in bare plate and meta-plate.

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Fig. 6. Experimental results of mechanical displacement at the center of the defect in PnC structures in time domains: (a) Al meta- plate only, (b) Al meta-plate with an EH device, (d) Al bare plate only, and (d) Al bare plate with an EH device. Fast Fourier transform results of mechanical displacement: (c) for Al meta-plates with and without an EH device and (f) for Al bare plates with and without an EH device.

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Table 1. Design variables: initial values, optimum values from size optimization, and final values based on the consideration of manufacturing tolerance. Design Variables

Initial

Optimum

Manufacturing

a [mm]

33.80

33.51

34.00

b [mm]

2.00

2.00

2.00

c [mm]

4.00

5.00

6.00

Center Freq. [kHz]

50.04

50.04

49.80

Band gap size [kHz]

1.62

5.94

5.74

Table 2. Band gap size and range for different design variable values a [mm]

b [mm]

c [mm]

Band gap size [kHz]

Band gap range [kHz]

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1.7

5.95

6.97

49.47 – 56.44

34

1.7

5.95

6.61

46.82 – 53.43

35

1.7

5.95

6.27

44.39 – 50.67

34

1.5

6

7.29

46.82 – 54.11

34

2

6

5.74

46.93 – 52.68

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Choon-Su Park is a principal research scientist in Korea Research Institute of Standards and Science (KRISS), and also serves as an associate professor in School of Science of Measurement at University of Science and Technology (UST) in Korea. He received his Ph.D. degree from Korea Advanced Institute of Science and Technology (KAIST) in Department of Mechanical Engineering in 2010. His current research interests include wave control with meta-structures for energy harvesting and wave visualization in various wave fields such as non-linear ultrasound inspection, acoustic holography, air-borne ultrasound imaging, high-resolution underwater camera, structural health monitoring for long range pipeline, and so on.

Yong Chang Shin is a Ph.D. Candidate in the Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul, Republic of Korea. He received the B.S. degree from Hanyang University, Seoul, Republic of Korea, in 2014. His current research topics include piezoelectric vibration energy harvesing and elastic metamaterials. He was the recipeint of Bronze Prize from KSME-SEMES Open Innovation Challenge (2016); Best Paper Award from the KSME (2018).

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Soo-Ho Jo is currently pursuing the Ph.D. degree in Mechanical and Aerospace Engineering, Seoul National University, Seoul, Republic of Korea. He received the B.S. degree from Seoul National University, Seoul, Republic of Korea, in 2016. His current research topics include piezoelectric vibration energy harvesting and elastic metamaterials. He was the recipient of Bronze Prize from KSME-SEMES Open Innovation Challenge (2016); Best Paper Award from the KSME (2018); and the 2nd Place Winner in the Student Paper Competition of the KSME (2018).

Heonjun Yoon is a Postdoctoral Research Associate in the Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul, Republic of Korea. Dr. Yoon received the B.S. degree from Inha University, Incheon, Republic of Korea, in 2011, the M.S. degree and the Ph.D. degree from Seoul National University, Seoul, Republic of Korea, in 2013 and 2018, respectively. Dr. Yoon was the recipient of two Best Thesis Awards from the KSME (2013 and 2018); several Best Paper Awards from the BAMN (2013), the KSNVE (2014), the ENGE (2016), and the KSME (2018); Featured Article from Smart Materials and Structures (2014); the 1st Place Winner in the Student Paper Competition of the KSME (2016); Bronze Prize from KSME-SEMES Open Innovation Challenge (2016); Outstanding Doctoral Dissertation Award from the Department of Mechanical and Aerospace Engineering at Seoul National University (2018); and Young Scientist Award from the ASSMO (2018).

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Wonjae Choi is a Principal Research Scientist at Korea Research Institute of Standards and Science (KRISS) in Korea. He received his Master from Gwangju Insititute of Science and Technology (GIST), Korea and his Ph.D. degree from Cambridge University, U.K. Before joining KRISS, he was at Imperial College London in U.K. as Research Associate. His research interests are acoustic metamaterial, phononic crystal and ultrasonic non-destructive evaluation.

Byeng D. Youn is a Full Professor in the Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul, South Korea. Dr. Youn received the B.S. degree in mechanical engineering from Inha University, Incheon, South Korea, in 1996, the M.S. degree in mechanical engineering from Korea Advanced Institute of Science & Technology, Daejeon, South Korea, in 1998, and the Ph.D. degree in mechanical engineering from the University of Iowa, Iowa City, IA, USA, in 2001. Dr. Youn was the recipient of ASME IDETC Best Paper Awards (2001 and 2008), the ISSMO/Springer Prize for a Young Scientist (2005), the IEEE PHM Competition Winner (2014), the PHM Society Data Challenge Competition Winner (2014, 2015, 2017), etc.

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Miso Kim is a senior research scientist at Korea Research Institute of Standards and Science (KRISS). She received her undergraduate degree in Materials Science and Engineering from Seoul National University, South Korea (2004). She received her M.S. (2007) and Ph.D. degrees (2012) in Materials Science and Engineering from the Massachusetts Institute of Technology (MIT). She joined the Center for Safety Measurement of KRISS as a senior research scientist in 2012 and has happily pursued her passion for research at KRISS since then. Her primary research interests cover analytical modeling, design, and experimental characterization of piezoelectric materials and smart structures (including mechanical metamaterials) for energy harvesting and sensing.

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Highlights:  Systematic design of two-dimensional octagonal phononic crystals (PnCs) with a single defect through geometric and band gap optimization to realize a highly dense piezoelectric energy harvesting system.  Theoretical analysis and simulation of elastic wave propagation behavior to confirm band gap effects as well as energy localization.  Experimental demonstration of elastic wave generation, visualization of elastic wave visualization, and harvesting performance characterization.  Drastic enhancement of energy harvesting capability via the designed PnC structures, more than 20 times of output power amplification at the level of micro-watts.

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