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We theoretically report on an innovative and practical acoustic energy harvester based on a defected acoustic metamaterial (AMM) with piezoelectric material. The idea is to create suitable resonant defects in an AMM to confine the strain energy originating from an acoustic incidence. This scavenged energy is converted into electrical energy by attaching a structured piezoelectric material into the defect area of the AMM. We show an acoustic energy harvester based on a meta-structure capable of producing electrical power from an acoustic pressure. Numerical simulations are provided to analyze and elucidate the principles and the performances of the proposed system. A maximum output voltage of 1.3 V and a power density of 0.54 μW/cm3 are obtained at a frequency of 2257.5 Hz. The proposed concept should have broad applications on energy harvesting as well as on low-frequency sound isolation, since this system acts as both acoustic insulator and energy harvester.
Acoustic energy harvesting based on a planar acoustic metamaterial
Shuibao Qi, Mourad Oudich, Yong Li, and Badreddine Assouar
Citation: Appl. Phys. Lett. 108, 263501 (2016);
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Published by the American Institute of Physics
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Acoustic energy harvesting based on a planar acoustic metamaterial
Shuibao Qi,
Mourad Oudich,
Yong Li,
and Badreddine Assouar
Institut Jean Lamour, CNRS, Vandœuvre-le`s-Nancy F-54506, France
Institut Jean Lamour, Universit
e de Lorraine, Boulevard des Aiguillettes, BP: 70239,
Vandœuvre-le`s-Nancy 54506, France
(Received 20 April 2016; accepted 17 June 2016; published online 27 June 2016)
We theoretically report on an innovative and practical acoustic energy harvester based on a defected
acoustic metamaterial (AMM) with piezoelectric material. The idea is to create suitable resonant
defects in an AMM to confine the strain energy originating from an acoustic incidence. This
scavenged energy is converted into electrical energy by attaching a structured piezoelectric material
into the defect area of the AMM. We show an acoustic energy harvester based on a meta-structure
capable of producing electrical power from an acoustic pressure. Numerical simulations are provided
to analyze and elucidate the principles and the performances of the proposed system. A maximum
output voltage of 1.3V and a power density of 0.54 lW/cm
are obtained at a frequency of
2257.5 Hz. The proposed concept should have broad applications on energy harvesting as well as on
low-frequency sound isolation, since this system acts as both acoustic insulator and energy harvester.
Published by AIP Publishing. []
With the increase in the environmental issues caused by
traditional resources, renewable and clean forms of energy
have attracted worldwide attention nowadays. Energy har-
vesting is defined as gathering and storing various forms of
ambient energy such as sunlight,
biochemical effect,
etc., for later use. As a kind
of sustainable and pervasive energy yet sometimes undesired
interference, sound may act as a renewable and clean power
source for energy production, as well as for microelectronic
devices, especially in remote or embedded systems.
Due to the intrinsic drawback of low power density,
sound energy generally needs to be confined or localized
before it can be effectively harvested and converted into
electric energy through piezoelectric, electrostatic, or elec-
tromagnetic means. Intuitionally, traditional resonating
structures, such as Helmholtz resonators
and other cham-
ber resonators,
are utilized to achieve acoustic energy
harvesting (AEH).
On the other hand, innovative engineered materials,
such as phononic crystals (PCs)
and acoustic metamaterials
emerging recently with rich physics and many
extraordinary capabilities,
have intrigued compelling in-
terest among scientists and engineers for the applications in
energy harvesting field.
Based on the mechanisms of the
Bragg scattering and local resonance, the acoustic band gaps
(BGs) of PCs and AMMs can be tuned or designed to realize
AEH. Wu et al.
proposed an acoustic energy harvester
composed of a square sonic crystal consisting of polymethyl
methacrylate cylinders in the air back-ground. A power har-
vesting efficiency 625 times larger than that without sonic
crystal is achieved in their report.
However, the property of
a phononic crystal that large lattice constant leads to low
central frequency may hinder its engineering applications in
low-frequency situations due to the space and intensity limi-
tations. Overcoming the mass density law of ordinary PCs,
the previously proposed planar AMMs
show the proper-
ties of low sound transmission loss (STL) and strong strain
energy confinement properties at a low frequency range,
which provides the potentials of sound insulation and acous-
tic energy harvesting. Meanwhile, the planar AMMs possess
the advantages of easy fabrication, spatial efficiency, and
tough durability, favoring their applications in various situa-
tions. Metamaterial-inspired planar structures for mechanical
wave energy harvesting have been proposed by Carrara
et al.
based on the concepts of wave focusing, wave guid-
ing, and energy localization. Their stub-plate structure with a
defect in the center
cannot support the propagation of the
mechanical wave from the side of the plate, thus leading to
limited energy confinement efficiency in the defected area.
Instead of concerning the vibration source, we propose in this
letter an innovative concept to scavenge the airborne acoustic
wave energy by using a planar AMM with piezoelectric ma-
terial, which can effectively address the issues of noise and
efficiently harvest the sound energy as well, regardless of low
frequency limitations.
The proposed AEH system consists of acoustic energy
confinement part (acoustic model) and strain energy conver-
sion part (electrical model). As schematically illustrated in
Fig. 1(a), an array of silicone rubber stubs are periodically de-
posited on a thin homogenous aluminum plate lying in the x-y
plane, and a defect is created by removing four stubs to
confine the strain energy originating from the acoustic wave
incidence in zdirection. The plan wave radiation boundary
conditions are used for acoustic wave in the zdirection. Fig.
1(a) is considered as a supercell of the AMM structure for
AEH. Since an infinite structure is assumed in the x-y plane,
the Bloch–Floquet periodic boundary conditions are employed
for connections in xand ydirections. The repeated cycle of
the supercell, the radius and height of the rubber stubs, and
the thickness of the aluminum plate are set to be a¼60 mm,
r¼3mm, h¼5mm, and t¼0.4 mm, respectively. The geo-
metries are optimized for the best performance with reference
Author to whom correspondence should be addressed. Electronic mail:
0003-6951/2016/108(26)/263501/4/$30.00 Published by AIP Publishing.108, 263501-1
APPLIED PHYSICS LETTERS 108, 263501 (2016)
to previous works.
The acoustic properties of the planar
metamaterials were analyzed
based on Bloch theorem and
the plane wave expansion method, and the displacement field
components can be revisited as
where ~
Gr, and Xl;~
Grare the wave vectors in the x-y plane,
the reciprocal lattice vector and the weighting coefficient,
respectively, and eðlÞ
is the associated eigenvector of the
eigenvalue kðlÞ
. Considering the wave propagation in air,
STL (dB) can be expressed as 20log10 ðjPin=Ptr , where P
and P
are the incident acoustic pressure and transmitted
acoustic pressure, respectively. The confined elastic strain
energy in the planar AMM can be expressed as
cijklSij Skl;(2)
where c
is the elastic stiffness tensor, and Sij and Skl are the
A PZT-5H patch connecting to an electric circuit is
attached to the defected area (see Fig. 1(a))fortheenergy
conversion part. An equivalent circuit for mechanical and
electrical parts of the AEH system is presented in Fig. 1(b),
where r
,andRrepresent the confined
stress, system mass, mechanical damping, mechanical stiff-
ness, capacitance of the PZT patch, and the load resistance,
respectively. The piezoelectric energy conversion model
illustrated in Fig. 1(b), developed by Roundy and Wright,
is applied. The output voltage of the resistive load Ris
given as
31 þ2nx
where cpd31
eand k2
31 ¼cpd2
eare the piezoelectric coupling coef-
ficient terms, with k,A
,n, and xthe geometric constant,
scavenged vibration acceleration, mechanical damping, and
driving angular frequency, respectively. The capacitance and
the density of the piezoelectric patch are 0.43 nF and
7500 kg/m
. The coupling coefficient k
and the mechanical
damping ratio nare 0.36 and 0.015, respectively. The root
mean square (RMS) power Pcan be readily transferred as
jVj2=2R, and the optimal load resistance for maximum out-
put Pcan be yielded as
Ropt ¼1
Commercial simulating software COMSOL Multiphysics
Version 5.2 is utilized to analyze and simulate the AEH sys-
tem shown in Fig. 1. Pressure acoustics, solid mechanics,
and electrostatics modules are applied for the coupling of the
acoustic, mechanical, and electrostatic fields. The band struc-
ture of the supercell is computed with considering the struc-
tural effect of the PZT patch. The parameters of aluminum
plate and rubber silicone stubs for computation are listed in
Table I. The geometries of the defect and supercell are opti-
mized with considering the band gap and the coupling effect
of adjacent defects. Figure 2(a) presents the band structure of
the defected AMM structure along the directions of the first
irreducible Brillouin zone. A complete acoustic band gap
illustrated as the shaded area in Fig. 2(a) is obtained in the
frequency range of 2144–2331 Hz. A flat defect mode with
frequency around 2254 Hz (dotted line in the shadow) is
achieved after creating the defect and adding the PZT patch
in the perfect supercell, which opens a gate of transmission
in the gap and provides the possibility of energy confine-
ment. In order to further validate the acoustic model, an
acoustic plane wave incidence with a sound pressure of 2 Pa
(100 dB) is considered, and STL curves of the AMM system
with and without defect are depicted as a blue line with sym-
bols and a black line in Fig. 2(b), respectively. It can be seen
in Fig. 2(b) that the defect mode (see the blue curve with
solid circles) with the frequency of 2257.5 Hz shows high
sound transmission (STL 0) in the band gap as expected,
while the transmission maintains low under no defect condi-
tion (refer to the black line). It worth noting that there is
anther mode (2847.5 Hz) generated by the defect beyond the
band gap with high transmission (STL ¼3.3 dB), which also
possesses the capability of energy confinement. At the fre-
quency of the defect mode, strong strain energy confinement
FIG. 1. (a) Sketch of the AEH system composed of a defected supercell with
a piezoelectric patch and a load circuit. (b) Equivalent circuit representation
of the piezoelectric converter with a resistive load.
TABLE I. Parameter values of materials in calculations.
Parameters Silicone rubber Aluminum
Density (kg/m
) 1300 2700
Young’s modulus (MPa) 1.89 7 104
Poisson ratio 0.4998 0.33
263501-2 Qi et al. Appl. Phys. Lett. 108, 263501 (2016)
can be readily observed, and most of the energy is central-
ized in the defect region as illustrated in Fig. 2(c). The con-
centrated energy density can be up to 1.65 J/m
, and the
strain energy directly determines the output power of the
PZT circuit.
In order to efficiently and effectively pick up the con-
fined strain energy, the geometries of the circular PZT-5H
patch need to be optimized. The piezoelectric patch should
be light enough to minimize the mass effect to the system,
yet large enough to completely cover the strain energy con-
fined area. Specifically, the radius is sufficiently swept and
set to be 12 mm with a small thickness of 0.2 mm for the
maximum output voltage. Moreover, the structural resonance
of the patch is checked to well match the defect mode.
Electrostatic module for electromechanical coupling is con-
ducted and a floating potential boundary is set for the upper
layer of the PZT patch. The frequency of incident sound
is swept to obtain the maximum output electrical potential
on the PZT patch. Fig. 3shows the curve of voltage magni-
tudes as a function of frequency, and the peak voltage mag-
nitudes of 1.3 V and 0.78 V are obtained at the frequency
of 2257.5 Hz and 2847.5 Hz, respectively. The defect mode
(2257.5 Hz) exhibits strong energy confinement capability
and thus high output voltage. The other voltage peak results
from the mode (2847.5 Hz) present in Fig. 2(b) out of other
resonant mechanism. As given in Eq. (3), the output voltage
is a function of the resistive load. A circuit module is con-
nected to the floating potential terminal to calculate the out-
put electrical voltage and power. Ris constantly swept at the
frequency of the defect mode to determine its value produc-
ing the optimal generated power. As shown in Fig. 4, the out-
put voltage and power increase rapidly with the increase in
R, and then, the power reaches its maximum value at
R¼38 kXand then decreases with increasing R, while the
voltage remains increasing until becoming flat. The opti-
mized load resistance R
can also be determined from
Eq. (4), and the value is calculated to be 37.8 kXwith the rel-
ative parameters provided above, which validates the electri-
cal simulation. The maximum output voltage and power are
1.3 V and 8.8 lW, respectively. Considering the geometries
of the whole AEH system, the obtained power density is
around 0.54 lW/cm
with 2 Pa acoustic incidence at the fre-
quency of 2257.5 Hz.
In summary, applying the properties of the acoustic
band gap and the wave localization of AMMs, an acoustic
energy harvester based on a planar AMM with piezoelectric
material is realized and analyzed. For the stub-plate AMM
structure, the coupling between the Lamb and stub modes is
very weak, and the localized modes in the rubber stubs occur
at relatively low frequencies, leading to strong localization
in the stub and thus large strain energy confinement in the
FIG. 2. (a) Band structure in the frequency range (1.8–2.5 kHz) computed
by finite element method (FEM) for the supercell with piezoelectric patch
illustrated in Fig. 1. (b) STL in frequency range (1.8–2.5 kHz) of the planar
AMM with and without a defect. (c) Strain energy density distribution of the
planar AMM at the defect mode (2257.5 Hz) with 2 Pa acoustic wave
FIG. 3. Electrical voltage magnitude versus frequency from the PZT patch.
263501-3 Qi et al. Appl. Phys. Lett. 108, 263501 (2016)
defected region. A PZT-5H patch with a load circuit is
applied to convert the strain energy into electrical energy.
The maximum output voltage and power of 1.3 V and 8.8 lW
are acquired with an acoustic incidence of 2 Pa at a frequency
of 2257.5 Hz. The output power would increase with the
acoustic incidence and the coupling coefficient of the PZT
patch. Meanwhile, our AEH system shows in Fig. 2(b) ahigh
STL of 40 dB in the band gap excluding the defect mode,
which greatly favors its application in sound insulation.
Compared with the existing AEH systems based on piezoelec-
tric effects listed in Table V of the review paper on AEH,
innovative system proposed here excels in competitive power
density and construction simplicity. The proposed planar AEH
system exhibits the advantages of high power efficiency, small
dimensions at relatively low frequencies, easy fabrication, and
tough durability, which can achieve both sound insulation and
energy harvesting in various applications.
This work was supported by the FEDER “Fonds
een de D
eveloppement R
egional” (project “MASTER”)
and by the “R
egion Lorraine.”
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FIG. 4. Output electrical voltage magnitude (black solid line) and power
(red dashed line) from the circuit versus the load resistance Rat the defect
mode (2257.5 Hz).
263501-4 Qi et al. Appl. Phys. Lett. 108, 263501 (2016)
... As the frequency increases, the output power increases, even though the output voltage decreases because the frequency and optimal R load are inversely proportional. 35 As the optimal R load decreases, the output power increases according to Eq. (16). Consequently, the power amplification ratios are 3.76, 2.63, and 2.65, respectively, implying a drastic enhancement in the output performance. ...
In this study, we analytically, numerically, and experimentally investigated a high-performance confocal piezoelectric energy harvesting system. We achieved a significantly enhanced electrical performance through a Mikaelian lens, which achromatically focuses ambient elastic waves, resulting in the formation of a highly amplified strain energy field in the piezoelectric energy harvester. Previous studies on piezoelectric energy harvesting platforms have limitations, such as the focal position changing with operating frequencies and impedance mismatching owing to inclusions or holes. To address these problems, we utilized the self-focusing ability based on the conformal mapping theory and achromatic ability based on the Kirchhoff–Love thin plate theory to design our Mikaelian lens-based piezoelectric energy harvesting platform. The proposed platform demonstrates a remarkable elastic wave focusing ability at an identical focal position for a broad frequency range. The experimentally visualized wave fields matched well with the numerically calculated full-wave harmonic simulation results. We achieved highly amplified output power up to 1.44 mW within a broad range from 40 to 60 kHz out of the same focal point owing to confined elastic wave energy; the output power extracted at this confocal position was up to 3.76 times higher than that extracted at the lens start position. Our highly performance and broadband achromatic piezoelectric energy harvesting platform lays an attractive foundation for designing potential applications, such as wireless sensing, structural health monitoring, and biomedical devices.
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... (2) Acoustic Metamaterial Harvester Acoustic metamaterials are periodically arranged structures or cavities which focus and confine the acoustic energy. This acoustic wave localization can be achieved by array of cylindrical silicone rubber stubs (Qi et al., 2016), cavity with zig-zag elements (K. H. Sun et al., 2017), and Helmholtz resonators (Ma et al., 2021). ...
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... (2) Acoustic Metamaterial Harvester Acoustic metamaterials are periodically arranged structures or cavities which focus and confine the acoustic energy. This acoustic wave localization can be achieved by array of cylindrical silicone rubber stubs (Qi et al., 2016), cavity with zig-zag elements (K. H. Sun et al., 2017), and Helmholtz resonators (Ma et al., 2021). ...
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A novel and practical acoustic energy harvesting mechanism to harvest traveling sound at low audible frequency is introduced and studied both experimentally and numerically. The acoustic energy harvester in this study contains a quarter-wavelength straight tube resonator with lead zirconate titanate (PZT) piezoelectric cantilever plates placed inside the tube. When the tube resonator is excited by an incident sound at its acoustic resonance frequency, the amplified acoustic pressure inside the tube drives the vibration motions of piezoelectric plates, resulting in the generation of electricity. To increase the total voltage and power, multiple PZT plates were placed inside the tube. The number of PZT plates to maximize the voltage and power is limited due to the interruption of air particle motion by the plates. It has been found to be more beneficial to place the piezoelectric plates in the first half of the tube rather than along the entire tube. With an incident sound pressure level of 100 dB, an output voltage of 5.089 V was measured. The output voltage increases linearly with the incident sound pressure. With an incident sound pressure of 110 dB, an output voltage of 15.689 V and a power of 12.697 mW were obtained. The corresponding areal and volume power densities are 0.635 mW cm−2 and 15.115 μW cm−3, respectively.
Conventional acoustic absorbers are used to have a structure with a thickness comparable to the working wavelength, resulting in major obstacles in real applications in low frequency range. We present a metasurface-based perfect absorber capable of achieving the total absorption of acoustic wave in an extremely low frequency region. The metasurface possessing a deep subwavelength thickness down to a feature size of ∼λ/223 is composed of a perforated plate and a coiled coplanar air chamber. Simulations based on fully coupled acoustic with thermodynamic equations and theoretical impedance analysis are utilized to reveal the underlying physics and the acoustic performances, showing an excellent agreement. Our realization should have an high impact on amount of applications due to the extremely thin thickness, easy fabrication, and high efficiency of the proposed structure.
We report theoretically and numerically on the sound transmission loss performance through a thick plate-type acoustic metamaterial made of spring-mass resonators attached to the surface of a homogeneous elastic plate. Two general analytical approaches based on plane wave expansion were developed to calculate both the sound transmission loss through the metamaterial plate (thick and thin) and its band structure. The first one can be applied to thick plate systems to study the sound transmission for any normal or oblique incident sound pressure. The second approach gives the metamaterial dispersion behavior to describe the vibrational motions of the plate, which helps to understand the physics behind sound radiation through air by the structure. Computed results show that high sound transmission loss up to 72 dB at 2 kHz is reached with a thick metamaterial plate while only 23 dB can be obtained for a simple homogeneous plate with the same thickness. Such plate-type acoustic metamaterial can be a very effective solution for high performance sound insulation and structural vibration shielding in the very low-frequency range.
For portable and embedded smart, wireless electronic systems, energy harvesting from the ambient energy sources has gained immense interest in recent years. Several ambient energies exist in the environment of wireless sensor nodes (WSNs) that include thermal, solar, vibration and acoustic energy. This paper presents the recent development in the field of acoustic energy harvesters (AEHs). AEHs convert the acoustic energy into useful electrical energy for the operation of autonomous wireless sensors. Mainly, two types of AEHs (electromagnetic and piezoelectric based) have been developed and reported in literature. The power produced by the reported piezoelectric AEHs ranges from 0.68 pW to 30 mW; however, the power generation of the developed electromagnetic AEHs is in the range of 1.5–1.96 mW. The overall size of most of the developed piezoelectric and electromagnetic AEHs are quite comparable and in millimeter scale. The resonant frequencies of electromagnetic AEHs are on the lower side (143–470 Hz), than that of piezoelectric AEHs (146 Hz–16.7 kHz).
Nowadays broadband vibration energy harvesting using piezoelectric effect has become a research hotspot. The innovation in this paper is the widening of the resonant bandwidth of a piezoelectric harvester based on phononic band gaps, which is called one-dimensional phononic piezoelectric cantilever beams (PPCBs). Broadband characteristics of one-dimensional PPCBs are analyzed deeply and the vibration band gap can be calculated. The effects of different parameters on the vibration band gap are presented by both numerical and finite element simulations. Finally experimental tests are conducted to validate the proposed method. It can be concluded that it is feasible to use the PPCB for broadband vibration energy harvesting and there should be a compromise among related parameters for low-frequency vibrations.
A vibration energy harvesting generator was studied in the present research using point-defect phononic crystal with piezoelectric material. By removing a rod from a perfect phononic crystal, a resonant cavity was formed. The elastic waves in the range of gap frequencies were all forbidden in any direction, while the waves with resonant frequency were localized and enhanced in the resonant cavity. The collected vibration energy was converted into electric energy by putting a polyvinylidene fluoride film in the middle of the defect. This structure can be used to simultaneously realize both vibration damping and broad-distributed vibration energy harvesting.
We show experimentally that plate-type acoustic metamaterials can serve to totally prohibit low frequency structure-borne sound at selective resonance frequencies ranging from 650 to 3500 Hz. Our metamaterial structures are consisting of a periodic arrangement of composite stubs (tungsten/silicone rubber) deposited on a thin aluminium plate. We report that these metamaterials present a broadband gap of out-of-plane modes at frequencies where the relevant sound wavelength in air is about three orders of magnitude larger than the plate thickness. Confinement and waveguiding of structure-borne sound in this sub-wavelength resonant regime is also experimentally evidenced and discussed.
Broadband structure-borne wave energy harvesting is reported by wave focusing using an elliptical acoustic mirror (EAM). The EAM is formed by an array of cylindrical stubs mounted along a semi-elliptical path on the surface of a plate. The array back-scatters incoming guided waves and focuses them at the focal location where a piezoelectric energy harvester is located. Multiple scattering simulations and experiments illustrate the broadband focusing characteristics of the EAM. More than an order of magnitude improvement in piezoelectric power generation is documented for an EAM-based energy harvester with respect to a free harvester over the 30–70 kHz frequency range.
We report on the theoretical analysis of the enlargement of locally resonant acoustic band gap in two-dimensional sonic crystals based on a double-side stubbed plate. A significant enlargement of the relative bandwidth by a factor of 2 compared to the classical one-side stubbed plates is obtained and discussed. Based on an efficient finite element method, we show that this band gap enlargement is due to the coupling between the same nature of the resonant eigenmodes (in-plane or out-of-plane) of the stubs located in each plate side, producing a strong interaction with the plate’s Lamb modes. Acoustic displacement fields are computed to illustrate such mechanism and to discuss the physics behind it.