Acoustic energy harvesting based on a planar acoustic metamaterial

Abstract

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.

Full text

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);
View online: https://doi.org/10.1063/1.4954987
View Table of Contents: http://aip.scitation.org/toc/apl/108/26
Published by the American Institute of Physics
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Acoustic energy harvesting based on a planar acoustic metamaterial
Shuibao Qi,
1,2
Mourad Oudich,
1,2
Yong Li,
1,2
and Badreddine Assouar
1,2,a)
1
Institut Jean Lamour, CNRS, Vandœuvre-le`s-Nancy F-54506, France
2
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
3
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. [http://dx.doi.org/10.1063/1.4954987]
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,
1
wind,
2
heat,
3
mechanical
vibration,
4
biochemical effect,
5
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.
6
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
7,8
and other cham-
ber resonators,
9,10
are utilized to achieve acoustic energy
harvesting (AEH).
On the other hand, innovative engineered materials,
such as phononic crystals (PCs)
11
and acoustic metamaterials
(AMMs),
12
emerging recently with rich physics and many
extraordinary capabilities,
13–15
have intrigued compelling in-
terest among scientists and engineers for the applications in
energy harvesting field.
16–19
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.
20
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.
20
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
21,22
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.
16,23
based on the concepts of wave focusing, wave guid-
ing, and energy localization. Their stub-plate structure with a
defect in the center
16
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
a)
Author to whom correspondence should be addressed. Electronic mail:
Badreddine.Assouar@univ-lorraine.fr
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.
24,25
The acoustic properties of the planar
metamaterials were analyzed
22
based on Bloch theorem and
the plane wave expansion method, and the displacement field
components can be revisited as
um¼X
~
Gr
ei~
krþ~
Gr
ðÞ
~
rixt
X
l¼1:6
Xl;~
GreðlÞ
m;~
Gr
eikðlÞ
z;~
Grz
!
;m¼x;y;z;(1)
where ~
kr;~
Gr, and Xl;~
Grare the wave vectors in the x-y plane,
the reciprocal lattice vector and the weighting coefficient,
respectively, and eðlÞ
m;~
Gr
is the associated eigenvector of the
eigenvalue kðlÞ
z;~
Gr
. Considering the wave propagation in air,
STL (dB) can be expressed as 20log10 ðjPin=Ptr jÞ, where P
in
and P
tr
are the incident acoustic pressure and transmitted
acoustic pressure, respectively. The confined elastic strain
energy in the planar AMM can be expressed as
Es¼1
2X
ijkl
cijklSij Skl;(2)
where c
ijkl
is the elastic stiffness tensor, and Sij and Skl are the
strains.
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
in
,L
m
,R
b
,C
k
,C
b
,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,
26
is applied. The output voltage of the resistive load Ris
given as
V¼
jx2cpd31t
e
jxx
2k2
31 þ2nx
RCb

2nx3
Ain
k;(3)
where cpd31
eand k2
31 ¼cpd2
31
eare the piezoelectric coupling coef-
ficient terms, with k,A
in
,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
3
. The coupling coefficient k
31
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
xCb
2n
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
4n2þk4
31
q:(4)
Commercial simulating software COMSOL Multiphysics
TM
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
3
) 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
3
, 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
opt
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
3
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
incidence.
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,
6
the
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
Europ
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)