Broadband acoustic energy harvesting metasurface with coupled Helmholtz resonators

Acoustic energy is currently ignored and being wasted. Compared with the solar,¹ wind,² and vibration energy,³ harvesting acoustic energy in air is more difficult due to the impedance mismatch limitation.^4,5 Nevertheless, it has potential advanced applications in charging or replacing batteries for low-power electronic devices and microelectromechanical systems (MEMS) devices.^6,7 In the past two decades, many artificial materials and structures have been proposed to improve the efficiency of harvesting acoustic energy in the air.^8–14 An electromechanical Helmholtz resonator (HR) with piezoelectric diaphragm was used to harvest acoustic energy in the air, and an approximately 30 mW of output power was harvested for an incident SPL of 160 dB at 2646 Hz with a flyback converter.⁸ After that, a quarter wavelength tube resonator was proposed to obtain 0.31 mW at 194 Hz with an incident SPL of 100 dB.⁹ Meanwhile, polyvinylidene fluoride (PVDF), MEMS structure, and phononic crystals were also applied to harvest acoustic energy in air.^10–14 It should be noted that most of the related works focus on how to increase the acoustic energy density and the output power on a single frequency or a narrow frequency band. Considering practical engineering applications, the unit structure of the acoustic energy harvester should be simple, small, and easy to integrate as needed, and the output voltage of each unit should be in the same phase to be directly connected in parallel. All of these will put forward higher requirements for the design of the acoustic energy harvester.

At the same time, acoustic metamaterials have received a lot of attention due to their rich physical properties and extraordinary capabilities, such as sound absorption^15–19 and acoustic energy harvesting^20–22 in recent years. Moreover, as a member of the acoustic metamaterial family, the acoustic metasurface has received increasing attention because of its unconventional phase regulation ability and subwavelength layered structure, which can realize anomalous reflection, acoustic focusing, and conversion of propagating waves into surface waves by different phase-shift structure units, such as coiling up space structures,^23–25 HRs,^26–28 small pipes,^29–31 and membrane cavities.^32–34 Recently, based on the coupled resonator³⁵ and hybrid membrane resonator,³⁶ sound absorbing metasurfaces have been presented, and the perfect absorption can be achieved at certain frequencies due to the impedance-matching with the background medium. However, so far, there are few acoustic energy harvesting applications based on acoustic metasurfaces.

In this letter, we propose a broadband acoustic energy harvesting metasurface consisting of two coupled HRs arranged periodically. The mechanism of the push-pull force on the piezoelectric composite sheet (PCS) caused by the phase difference between two cavities is revealed. A high output voltage can then be obtained from every PCS with the same phase.

The basic cycle unit is shown in Fig. 1(a). PCS is made of a planar copper sheet and a piezoelectric ceramics sheet (PZT-5H). The specific parameters in Fig. 1(a) are given as follows: the neck diameters of two HRs $a1=1.9 mm$ and $a2=1.4 mm$⁠, the wall thickness $l=6 mm$⁠, the thickness of planar copper $hc=0.10 mm$ and its radius $Rc=9 mm$⁠, the thickness of planar piezoelectric ceramics $hp=0.10 mm$ and its radius $Rp=7.5 mm$⁠, the height of cavity $h=20 mm$⁠, and the side length $d=20 mm$⁠. Then, the acoustic energy harvesting metasurface can be achieved by periodically arranging the two coupled HR unit as shown in Fig. 1(b), which also illuminates the corresponding operating principle. We find that a coupled vibration is generated in the two adjacent HRs when the metasurface is driven by the incident acoustic waves, and then, PCS between them will produce bending deformation under the alternating action of the push-pull force caused by the opposite phase between the two coupled cavities. The push-pull effect can obviously improve the acoustic-electric conversion efficiency of PCS. It is noteworthy that the phases of the output voltages of all PCS are the same due to the periodic symmetry of the metasurface. So, it is possible to parallel all output terminals of the metasurface without adding any rectification circuit.

In order to clarify the push-pull effect on PCS, the working mechanism of the two coupled HRs is studied through the corresponding 3D numerical simulation by using the commercial simulating software COMSOL Multiphysics. While maintaining the independence of PCS to facilitate numerical simulation and experimental measurement, the studied cycle unit is chosen as shown in Fig. 2(a). The cycle unit consists of a HR with a wide neck and two half HRs with a narrow neck. It means that HR with a narrow neck in Fig. 1(a) is equally divided into two parts along its central axis, and then, it is possible to construct a symmetrical acoustic field for the convenience of experimental measurement in a waveguide without changing any resonance characteristics of HRs. Meanwhile, due to the principle of mirroring, the acoustic field in the cycle unit will be the same as that in the infinite array when periodic or hard boundary conditions are added on the up and down sides of the unit. The parameters used in numerical simulations are given as in Fig. 1(a). From the acoustic field distribution in the longitudinal section at 550 Hz in Fig. 2(a), we can find that the air in the adjacent cavities alternately expands and contracts because of the nearly opposite phases in the adjacent cavities, which makes PCS receive a push-pull force from the two adjacent cavities. As we know, the phase of acoustic pressure in the cavity depends on the driving acoustic wave and the size of HR. So, by properly adjusting the parameters such as the cross-sectional area of the neck, the resonance frequencies of two different size HRs will be separated, and then, the opposite phases of acoustic pressures in the two adjacent coupled cavities can be obtained between the two resonance frequencies. Figure 2(b) shows that the phase difference between the acoustic pressures in the two adjacent cavities is close to $160°$ in a wide band 505 Hz–622 Hz. Then, the efficient output voltage can also be obtained in the same frequency band because PCS between the two cavities is continuously affected by the push-pull force between the two resonance frequencies. It is also worth noting that the coupled resonance of the two adjacent HRs works like an acoustic dipole, so that the reflected wave will be localized in the cavity instead of radiating outwards, which helps to improve the efficiency of acoustic energy harvesting by increasing the acoustic energy density in the cavities.

Here, a lumped element model is proposed because the operating wavelength is much larger than the size of HR. It is well known that HR behaves like a simple acoustic harmonic oscillator, the diastolic and compressed air in the cavity is equivalent to the spring, and the air in the neck is equivalent to the mass attached to the spring. Driven by the incident waves, HR works like a forced vibration of a spring vibrator. Here, the acoustic impedance of HR can be expressed as $Za=Ra+j(ωMa−1/ωCa)$⁠, where the acoustic resistance $Ra=Rm/Sn2$⁠, acoustic mass $Ma=Mm/Sn2$⁠, and acoustic capacity $Ca=CmSn2$⁠. $Rm$⁠, $Mm$⁠, and $Cm$ are the resistance, mass, and compliance of the system, respectively. $Sn=πa2$ is the cross-sectional area of the neck. Then, the acoustic vibration equation of this system can be obtained as³⁷ 

where $U=vS$ is the volume velocity, $P$ is the sound pressure, and $ω=2πf$ is the angular frequency. In order to simplify the result, the reactance is given as $Xa=ωMa−1/ωCa$⁠; then, the above equation can be easily solved as $U=P/(Ra+jXa)$⁠. When the air column in the neck vibrates, the volume of air entering the cavity $δV$ and increased pressure $δP$ can be expressed as $δV=U/(jω)$ and $δP=ρ0c02U/(jωV0)$⁠, where $ρ0=1.21 kg/m3$ is the density of air, $c0=343 m/s$ is the acoustic speed in the air, and $V0$ is the volume of the cavity. After taking into account the effects of the radiation and the damping of the neck, the acoustic impedance expression is modified as^37–39 

where $k=ω/c0$⁠, $a$ is the radius of the neck, $μ=1.983×10−5 Pa s$ is the dynamic viscosity of air, and $J1$ is the Bessel function of the first kind. Then, the phase of the acoustic pressure in the cavity can be obtained as $φP=arg δP$⁠. The corresponding phase difference between the two adjacent HRs versus frequency is calculated, and the result is given in Fig. 4(a).

Meanwhile, we also measure the acoustic pressure phases in the two cavities and the output voltage of PCS. The experiment is carried out in a rectangular waveguide with $L=400 mm$ as shown in Fig. 3(a), and the unit made by 3D printing technology and PCS is shown in Fig. 3(b). Since the operating frequency is much lower than the cut-off frequency of the waveguide, there are only plane wave modes in the waveguide and the rest of the higher-order modes decay within a short distance. By measuring the transfer function between the two microphones in Fig. 3(a), we can determine the reflection coefficient of the metasurface and calculate the amplitude of the incident wave. Then, by keeping the incident sound pressure amplitude of 1 Pa, the phase difference of two HRs and output voltage versus frequency can be achieved.

Figure 4(a) gives the theory and numerical simulation results of the phase difference between the two adjacent cavities as a function of frequency. The two results agree well with each other. The variation of the output voltage with the frequency is also given by the red line in Fig. 4(a). We can find that the frequency range for the high output voltage is just the frequency range for the almost $160°$ phase difference. Note that the phase of the internal air vibration could theoretically have a phase shift of $180°$ when the incident frequency exceeds the resonance point. However, the slope of the phase shift is related to the quality factor of the resonance, which leads to the fact that the phase difference between the two sides of PCS is only close to $180°$⁠. Figure 4(b) gives the corresponding experimental results. The frequency band of high output voltage agrees well with the frequency band for the large phase difference in Fig. 4(b). At one-half of the maximum output voltage, the acoustic energy harvesting metasurface provides an objective voltage output in the bandwidth of 220 Hz (460 Hz–680 Hz), which exceeds one third of the center frequency of 570 Hz. As we know, the energy is mainly consumed by the viscous effect of the narrow area rather than the thermal effect in the resonant acoustic-absorbing structure.⁴⁰ Then, we simulate the output power at several frequencies by taking into account the energy loss in the narrow area of neck. Figure 4(c) shows the relationship between output power and external load of one PCS at three frequencies with an incident SPL of 160 dB. In general, for one PCS, the output voltage is up to 20 mV with 1 Pa incident acoustic pressure and the power is above 40 mW (the corresponding energy density is 10 mW/cm²) with an incident SPL of 160 dB as shown in Fig. 4.

To further reveal the advantage of the composite structure unit proposed in this letter, we compare the output voltages of several different structure units as shown in Fig. 5. It is easy to find that the type A situation proposed in this letter has the highest efficiency and the widest working bandwidth in Fig. 5(e). For the type B situation, these two HRs will resonate at the same frequency because they have the same size neck. Thus, acoustic pressure in each HR has the same phase, and the acoustic pressure difference will not appear on the two sides of the PCS. The output voltage peak only appears when HR is resonating and the efficiency is relatively low. For the type C situation, PCS becomes the sidewall of the cavity. The acoustic pressure inside the cavity will make PCS produce bending vibration and radiate acoustic waves outward. However, the acoustic pressure difference between the two sides of PCS is only half of the type A situation, so the output voltage is about half of the type A situation. It is worth noting that the output voltage of type C in Fig. 5(e) is higher than that of type A in the non-operating frequency band of the type A situation. It is because there is no phase difference appeared between the two coupled HRs in the non-operating frequency band and the effective bending vibration cannot be excited on PCS. For the type D situation, the bending vibration cannot be excited because the bottom of PCS is fixed on the sidewall, and then, the serious impedance mismatch results in almost no output voltage.

In summary, we have demonstrated a broadband acoustic energy harvesting metasurface with the thickness less than 1/20 of the working wavelength. The proposed metasurface is formed by the periodic arrangement of the two coupled HRs with different neck widths. The acoustic pressure phases in the two adjacent HRs are nearly opposite to each other between the two different resonance frequencies corresponding to the two adjacent HRs, which can generate a push-pull force on PCS between the two cavities. Due to PCS's bending deformation caused by the alternating action of the push-pull force, the high output voltage can be derived from PCS. Furthermore, the output of each PCS can be directly connected in parallel without any rectification circuit because the output voltage from every PCS has the same phase under the conditions of the plane wave incidence and the symmetry of the proposed metasurface. Even for oblique incidence situations, due to the deep subwavelength structure, the output voltage phases closely match with each other. Meanwhile, the dipole-like working mode of the two coupled HRs will effectively increase the acoustic energy density by localizing the reflected waves in the cavities instead of radiating outwards, which helps to improve the efficiency of acoustic energy harvesting. The coupling of PCS and cavity is also proved to obtain a higher output voltage in a wide band. Specifically, for one PCS of the two coupled HR units, the output voltage is up to 20 mV with 1 Pa incident acoustic pressure and the power is above 40 mW (the corresponding energy density is 10 mW/cm²) with an incident SPL of 160 dB. The proposed combination design of the acoustic metasurface and piezoelectric composite materials has proven to be an efficient and easy-to-integrate structure, and it can be widely used in acoustic energy harvesting devices and acoustic insulators.

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11634006 and 81127901), State Key Laboratory of Acoustics, Chinese Academy of Sciences, and A Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.