Acoustic Energy Harvesting Using Quarter-Wavelength...

1 Copyright © 2012 by ASME

Proceedings of the ASME 2012 International Mechanical Engineering Congress & Exposition IMECE2012

November 9-15, 2012, Houston, Texas, USA

IMECE2012-86989

ACOUSTIC ENERGY HARVESTING USING QUARTER-WAVELENGTH STRAIGHT-TUBE RESONATOR

Bin Li Department of Mechanical Engineering,

Southern Methodist University, Dallas, Texas, 75205, USA

[email protected]

Andrew J. Laviage Department of Mechanical Engineering,


[email protected]

Jeong Ho You Department of Mechanical Engineering,


[email protected]

Yong-Joe Kim Department of Mechanical Engineering,

Texas A&M University, College Station, Texas, 77843, USA

[email protected]

ABSTRACT Although there have been significant efforts in harvesting

environmental energy, our environment is still full of wasted and unused energy. As clean, ubiquitous and sustainable energy source, acoustic energy is one of the wasted energies and is abundant in our life. Therefore, it is of great interest to investigate acoustic energy harvesting mechanism as an alternative to existing energy harvesters. In this study, in order to harvest acoustic energy, piezoelectric cantilever beams are placed inside a quarter-wavelength straight-tube resonator. When the straight-tube resonator is excited by an incident wave at its acoustic eigenfrequency, an amplified acoustic resonant wave is developed inside the tube and drives the vibration motion of the piezoelectric beams. The piezoelectric beams have been designed to have the same structural eigenfrequency as the acoustic eigenfrequency of the tube resonators to maximize the amount of the harvested energy. With a single beam placed inside the tube resonators, the harvested voltage and power become the maximum near the tube open inlet where the acoustic pressure gradient is at the maximum. As the beam is moved to the tube closed end, the voltage and power gradually decrease due to the decreased acoustic pressure gradient. Multiple piezoelectric beams have been placed along the centerline of the tube resonators in order to increase the amount of harvested energy. Due to the interruption of acoustic air particle motion caused by the beams, it is found that placing piezoelectric beams near the

closed tube end is not beneficial. The output voltage of the piezoelectric beams increases linearly as the incident sound pressure increases.

I. INTRODUCTION

Energy harvesting technology as self-powering sources has

been studied theoretically and experimentally, focusing on harvesting solar [1], thermal [2], and mechanical vibration [3] energies. Due to the high electro-mechanical energy conversion efficiency of piezoelectric materials, micro power piezoelectric generators have received much attentions in the past decades [4-9]. In particular, the applications of piezoelectric materials to harvest ambient energies, such as wind flow, water current, and raindrops, have become increasingly interesting. Priya [10, 11] reported a theoretical model of piezoelectric windmill which converts wind energy to electrical power. Li et al. [12] proposed and tested a bioinspired piezo-leaf architecture to harvest wind energy by the wind-induced fluttering motion. Matova et al. [13] used a Helmholtz resonator with a piezoelectric plate to harvest air flow energy. Taylor et al. [14] used piezoelectric polymers to convert the flow energy available in oceans and rivers to electric power. Guigon et al. [15] investigated harvesting the kinetic energy of raindrops theoretically and experimentally.

Compared with the abovementioned energy resources, less efforts have been devoted to developing acoustic energy harvesting methods. Since acoustic energy is a clean,


ubiquitous, sustainable energy source, it is of great interest to study acoustic energy harvesting mechanisms. Horowitz et al. [16] first introduced a micromachined acoustic energy harvester using a Helmholtz resonator with a piezoelectric ring attached to one of the resonator walls. A maximum output power of ~0.1 nW was obtained with an incident sound pressure level (SPL) of 149 dB (referenced 20 μPa) at 13.6 kHz. Liu et al. [17, 18] developed an electromechanical Helmholtz resonator which utilized a uniform acoustic pressure in a resonator chamber to bend a piezoelectric back plate. The resonator was excited by an incident SPL of 160 dB at 2.6 kHz, generating a maximum output power of 30 mW which could be enough to supply energy to low power electronic devices. Kim et al. [19] also used a Helmholtz resonator in which a permanent magnet/coil system was driven by acoustic pressure to harvest airflow and aeroacoustic energy. An output voltage of 4 mV was measured with an input pressure of 0.2 kPa (i.e., 140 dB SPL) at 1.4 kHz. Lallart et al. [20] used a synchronized switch to improve the power gain in acoustic energy harvesting.

Most previous studies have focused on harvesting acoustic energy at high frequencies from a few kHz to MHz. However, sound sources available in everyday life contain predominantly low frequency components since the low frequency sound travels a longer distance due to its lower spatial attenuation rate. Therefore, it is necessary to develop an innovative acoustic energy harvesting mechanism to harvest low-frequency sound energy.

In this study, a quarter-wavelength straight-tube acoustic resonator with multiple piezoelectric cantilever beams placed inside the tube is proposed to harvest acoustic energy from a travelling wave at a low frequency. When the tube is excited by an external sound wave at its eigenfrequency, a resonant standing wave is generated inside the tube. When piezoelectric cantilever beams are placed perpendicular to the tube axis, the resonant standing wave excites the vibration motion of the piezoelectric beams resulting in the generation of electricity.

This paper is organized as follows. In Section II, the acoustic resonant behavior in the quarter-wavelength resonator is described. The mechanism to convert the acoustic energy inside the resonator to electrical power using a single piezoelectric beam is presented in Section III. 1. In Section III. 2, the effects of placing multiple PVDF and PZT beams inside quarter-wavelength tube resonators on the output voltage and power are discussed. Finally, discussion and conclusion are presented in Sections IV and V.

II ACOUSTIC RESONANCE IN QUARTER-WAVELENGTH TUBE RESONATOR

Acoustic resonators such as Helmholtz and quarter-

wavelength resonators have been widely used for both sound augmentation and noise attenuation. When these resonators are excited by an incident wave at their acoustic resonant frequencies, acoustic energy is collected inside the resonators

in a form of standing resonant waves. A typical Helmholtz resonator consists of a neck and a cavity as shown in Fig. 1(a). For the first eigenmode, the air in the neck oscillates as a mass while the static air in the cavity undergoes compression and expansion as a spring. Including energy dissipations, such as the sound radiation from neck opening and the friction between air and walls, the Helmholtz resonator can be modeled as a mass-spring-damper system.

Assuming the wavelength of the incident wave is much larger than the dimensions of the Helmholtz resonator, the first eigenfrequency f1 can be obtained from the lumped mass-spring-damper model as [21]

lV

Scf

20

1 , (1)

where c0 is the sound speed, S is the cross-sectional area of the neck, V is the cavity volume, and l is the effective neck length. When the resonator is excited at f1, the sound pressure in the cavity is resonantly amplified. The amplification ratio A of the cavity pressure to the incident pressure is expressed as [21]

3

3

2S

Vl

p

PA

incident

cavity

(2)

A quarter-wavelength resonator is a tube-like resonator with open and closed ends as shown in Fig. 1(b). In a quarter-wavelength resonator, the one-third of tube length near the open inlet acts as a neck of Helmholtz resonator, and the two-third of tube length acts as a cavity [22]. Also, it has been found that a quarter-wavelength resonator has the highest efficiency of collecting acoustic energy with a high amplification factor at a given volume, compared with Helmholtz resonator and half-wavelength resonators [23-24].

Fig. 1: Sketches of (a) Helmholtz and (b) Quarter-wavelength

resonators.

In the quarter-wavelength resonator, the longitudinal particle velocity u(x,t) and acoustic pressure p(x,t) at the n-th resonant mode are represented as sinusoidal functions [22]:

)exp(2

)12(cos),( 0 ti

L

xnutxu n

, (3)

)exp(2

)12(sin),( 0 ti

L

xnptxp n

, (4)


where L is the tube length which is equal to (2n-1)λ/4, x is the distance measured from the tube open inlet, ωn is the angular eigenfrequency, and n is the mode number, n = 1, 2, 3, ···. At the first eigenmode (i.e., n = 1), the tube length is equal to a quarter wavelength, L = λ/4. From Eqs. (3) and (4), the maximum magnitude of particle velocity u0 occurs at the tube inlet while the acoustic pressure reaches the maximum magnitude p0 at the closed end of tube [23].

In order to verify the first eigenmode of the quarter-wavelength tube resonator, a loudspeaker (Audioengine 5) is used to generate an incident sound with SPL of 100 dB. Two straight tubes have been fabricated with a half-inch thick polycarbonate with different lengths of 58 cm and 42 cm. Both tubes have the rectangular cross section of 4 cm × 5 cm. Quarter-inch microphones (model 377C10 manufactured by PCB Piezotronics) are used to measure acoustic pressures along the tubes and at the open inlet as shown in Fig. 2.

Fig. 2: (a) Sketch and (b) experimental setup for testing the first eigenmode of quarter-wavelength straight-tube resonator.

Figure 3 shows the magnitudes of the first eigenmode

acoustic pressure along the straight-tubes, normalized by the incident pressure at 100 dB. The eigenfrequency at the first mode has been measured as 146 Hz for the 58 cm long tube and 199 Hz for the 42 cm long tube. For both tubes, the measured resonant acoustic pressures are well represented by the sinusoidal functions in Eq. (4) with the maximum magnitudes at the closed end of the tube. In a quarter-wavelength resonator, the amplification ratio can be defined as

the ratio of the maximum pressure inside tube to the incident sound pressure amplitude. As shown in Fig. 3, the amplification ratio at the first eigenmodes is found to be 59.1 and 97.2 for the 58 cm and 42 cm long tube resonators, respectively.

Fig. 3: Magnitudes of the first eigenmode acoustic pressures

measured along the 42 cm and 58 cm long tubes, normalized by the incident pressure at 100 dB. The tube has the open inlet at x = 0 and the closed end at x = 42 cm and 58 cm for the 42 cm

and 58 cm long tubes, respectively.

III. ACOUSTIC ENERGY CONVERSION USING PIEZOELECTRIC BEAMS INSIDE QUARTER-WAVELENGTH RESONATORS

In order to harvest the acoustic energy at the first

eigenmodes of the tube, piezoelectric cantilever beams are placed inside the tube as shown in Fig. 4(a). PVDF and PZT are the two most commonly used piezoelectric materials in vibration energy harvesting devices. In this study, unimorph PVDF beams (model LDT-028k manufactured by Measurement Specialties) and parallel bimorph PZT (model Stripe Actuator 40-2010 manufactured by APC International, Ltd.) have been used. The piezoelectric beams have been clamped on the bottom panel of the tube resonators. The bottom panel of the tube consists of several polycarbonate blocks. The thin PVDF beams have been clamped between the perfectly matched polycarbonate bottom blocks. For the thick PZT beams, a small notch is fabricated between the bottom blocks, and the PZT beams are inserted and clamped by the bottom blocks. Therefore, the dynamic behavior of piezoelectric beam is similar to one of a clamped cantilever beam. Each piezoelectric beam has been designed to have the same structural eigenfrequency as the first acoustic eigenfrequency of the tube resonator. The structure and materials properties of PVDF and PZT piezoelectric beams are provided in Table 1.


Table 1. Structure and materials properties of PVDF and PZT piezoelectric beams

PVDF beams (LDT-028k by Measurement)

PZT beams (SA 40-2010 by APC International, Ltd.)

Structure and composition

Unimorph PVDF: 14%; Adhesive: 24% Polyester: 62%

Parallel bimorph PZT: 80% Carbon fiber: 20%

Height Width Thickness

2 cm 4 cm 1.61 cm 2 cm 0.2 mm 0.7 mm

d31 23 pC/N 750 pC/N d33 -33 pC/N -320 pC/N ε/ε0 12~13 4500 E 2~4 GPa 40~60 GPa Cp 5.5 nF 75 nF k 0.12 0.72 ζ 0.05 0.025

PVDF piezoelectric beams have been placed in the 58 cm-

long tube and PZT beams have been installed in the 42 cm tube in order to match the structural eigenfrequency of beams with the acoustic eigenfrequency of tube. For example, the 58 cm long polycarbonate straight tube with PVDF piezoelectric beams is shown in Fig. 4(b). The PVDF and PZT beams are clamped tightly at the bottom polycarbonate plate.

Fig. 4: Quarter-wavelength straight-tube acoustic energy harvester with piezoelectric beams placed inside. (a) Sketch

and (b) PVDF piezoelectric beams placed inside the 58 cm long polycarbonate straight-tube acoustic energy harvester.

III.1. Single piezoelectric beam

A single piezoelectric beam has been placed at various positions inside the tube as shown in Fig. 5. The first position A is located at 5 cm from the tube inlet and additional positions are set at 5 cm increments. The quarter-wavelength acoustic energy harvesters are excited by an incident wave of 100 dB at f1 = 146 Hz and 199 Hz for the 58 cm and 42 cm long tubes, respectively.

Fig. 5: (a) Output voltage and power by single PVDF beam at

various positions along the 58 cm tube resonator with the incident sound wave of 100 dB at 146 Hz. (b) Output voltage and power by single PZT beam at various positions along the the 42 cm tube resonator with the incident sound wave of 100

dB at 199 Hz.

Figure 5(a) shows the output voltage and power generated by a single PVDF beam placed from positions A to J. The maximum output voltage of 0.105 V is measured when the beam is placed at the position A near the inlet of the tube. For PZT beam in Fig. 5 (b), the maximum output voltage is measured as 1.433V, which is 13.6 times larger than that by the PVDF beam. In both cases, as the piezoelectric beam moves


toward the closed end of the tube, the output voltage decreases gradually. This result is in agreement with the particle velocity u in Eq. (3), which is proportional to the acoustic pressure gradient. Since the piezoelectric beam is placed in spatially fluctuating pressure field, the pressure difference across the beam thickness causes the beam to bend along the x-direction, resulting in voltage generation via the direct piezoelectric effect. When the piezoelectric beam is placed near the tube inlet, where the pressure gradient is at the maximum, the largest output voltage is obtained by a large beam deflection. When the beam is placed near the tube closed end, the small pressure gradient induces a small beam deflection, although the acoustic pressure magnitude is at the maximum at the tube closed end.

The amount of power harvested by vibrating piezoelectric beams depends on the external electrical loading. The harvested power can be maximized when the external loading resistance is optimized as [25]

424

21

kCR

pnopt

, (5)

where k is the piezoelectric coupling coefficient, ζ is the damping ratio, and Cp is the capacitance of piezoelectric beam. Then, the harvested power can be estimated as V2/Ropt. As shown in Fig. 5, the maximum power of 0.056 µW and 0.193 mW can be harvested by using the single PVDF and PZT beam respectively, when the single beam is placed at the position A with the incident SPL of 100 dB.

It is worthy to mention that a synchronized switch harvester on inductor (SSHI) based on nonlinear optimization can potentially increase the power gain and bandwidth in energy harvesting [26]. This method can be used to further increase the acoustic energy harvesting efficiency. III. 2. Multiple piezoelectric beams

In order to increase the output voltage and power, multiple

piezoelectric beams have been placed in the tube resonators. All beams are placed along the centerline of tube as shown in Fig. 6(a) and (d). The spacing between beams along the longitudinal tube axis is 5 cm for both cases.

For the 58 cm long tube with multiple PVDF beams, the output voltage is shown in Fig. 6(b) as a function of the number of piezoelectric beams placed in the tube. Piezoelectric beams are placed in the tube starting from the first position A near the open inlet to the last position J near the closed end. For example, the number of piezoelectric beams equal to 4 indicates that four beams are placed at the positions of A, B, C and D. In this study, the voltage from each piezoelectric beam has been measured simultaneously and the total voltage is obtained by the summation of voltage from each beam, which corresponds to the connection in series between piezoelectric beams. From the measured voltage for each beam, the power

can be calculated using the optimized resistance Ropt (Eq. (5)) and the total power is the summation of power from each beam.

As shown in Fig. 6(b), the total output voltage increases as the number of beams increases until seven PVDF beams are placed at the positions A to G. A maximum total output voltage of 0.417 V has been measured. In addition to the seven beams at A through G, one or more additional beams at the positions H to J reduces the total output voltage. This is caused by the alteration of the acoustic resonance due to the additional beams near the tube closed end.

Similarly, multiply PZT beams are placed along the centerline of the 42 cm long tube resonator. As shown in Fig. 6(e) and (f), the total output voltage and power reach the maximum at 3.789 V and 0.311 mW respectively, which are 9 and 1813 times larger than those by the PVDF beams.

Fig. 6: Sketches of (a) PVDF beams in 58 cm long tube and (d) PZT beams placed in 42 cm long tube. Output voltage of (b) PVDF and (e) PZT beams, and power from (c) PVDF and (f)

PZT beams with the incident SPL of 100 dB at 146 Hz and 199 Hz, respectively. The spacing between beams along the tube

axis is 5 cm for both acoustic energy harvesters.


For multiply piezoelectric beam cases, the total power can decrease even when the total output voltage increases because the power is proportional to the square of voltage. For example, the total power (Fig. 6(f)) by the 42 cm long tube becomes the maximum when 4 PZT beams are placed and starts to decrease if additional beams are placed, while the total voltage (Fig. 6(e)) still increases until 7 PZT beams are placed.

The maximum total output voltage and power using the 42 cm long tube with PZT beams are 9 and 1813 times larger than those by the 58 cm long tube with PVDF beams. The first reason is the higher amplification ratio of the 42 cm long tube resonator than the 58 cm long tube as shown in Fig. 3. The higher amplification ratio induces the larger pressure gradient, resulting in the more deflection of the piezoelectric beam. Another reason is from the structural and materials properties of the PVDF and PZT piezoelectric beams used in this study. From Table 1, it can be seed that the PVDF beam contains only 14% piezoelectric materials while the PZT beam has 80%. Also, the piezoelectric charge constants d31 of PZT is 32.7 times larger than that of PVDF. The dielectric constant of PZT is also 375 times than that of PVDF, which leads to a larger capacitance, resulting in more harvested power. Even with the more flexibility of PVDF, a bimorph PZT piezoelectric beam is a preferred choice for acoustic energy harvesting mechanisms in this study. Potential energy losses in the present acoustic energy harvesters may include the acoustic energy leakage through the tube walls, the friction between air particles and tube, the acoustic resistive due to the resonant sound emission to surrounding media, the damping of the piezoelectric materials, etc.

Figure 7 shows the measured output voltage when four PZT beams are placed inside the 42 cm long tube resonator from the positions A to D. It can be seen that all PZT piezoelectric beams are vibrating in the same phase, indicating that all beams have the same structural eigenfrequency of 199 Hz.

Fig. 7: Output voltage when four PZT piezoelectric beams

placed from A to D along the centerline of the 42 cm long tube resonator. The incident sound is at 199 Hz with 100 dB.

Figure 8 shows the output voltage and power as a function of incident acoustic pressure using the four PZT beams placed at the positions A (x = 5 cm) through D (x = 20 cm) in the configuration of Fig. 6(d). The output voltage is linearly proportional to the incident acoustic pressure, which confirms that the driving force of beam deflections is the acoustic pressure gradient of resonant standing waves. The voltage of 8.691 V is measured with an incident pressure of 9 Pa (i.e., SPL = 110 dB at 199 Hz). The corresponding estimated power is 1.774 mW and the power density of 0.055 mW/cm2 is obtained at SPL = 110 dB.

Fig. 8: Effects of incident acoustic pressure on total output voltage and power using four PZT beams placed at the

positions A (x = 5 cm) through D (x = 20 cm) in the configuration of Fig. 6(d).

IV. CONCLUSION A novel acoustic energy harvesting mechanism using the

quarter-wavelength straight-tube resonator with multiple piezoelectric beams is proposed and tested experimentally. The 58 cm and 42 cm long tube resonators with PVDF and PZT beams have been used to harvest the acoustic energy at 146 Hz and 199 Hz, respectively. The amplification ratios of 59.1 and 97.2 have been measured at the first eigenmode (f1 = 146 Hz and 199 Hz) in the 58 and 42 cm long tubes, respectively. With a single piezoelectric beam placed inside the tube, the voltage and power become the maximum near the tube open inlet where the largest acoustic pressure gradient derives the vibration motion of the beam. The voltage and power gradually decrease as the beam is moved to the tube closed end. With the incident wave of 100 dB at f1 = 146 Hz, the single PVDF beam near the tube inlet has generated the voltage of 0.105 V, which corresponds to the power of 55.6 nW. For PZT beam, the maximum output voltage and power are 1.433V and 0.193 mW at f1 = 199 Hz. In order to increase the output voltage and power, multiple piezoelectric beams have been placed inside the tube along the centerline of the tube resonators. It has been found that the number of beams


to generate the maximum voltage is limited by the interruption of acoustic air particle motion caused by the presence of beams. For PVDF piezoelectric beams, the maximum output voltage and power are 0.42 V and 171.48 nW when 7 and 5 beams are placed with the incident SPL of 100 dB. For PZT piezoelectric beams, the maximum output voltage and power are 3.789 V and 0.311 mW by placing 6 and 4 PZT beams, which are 9 and 1813 times larger than those by the PVDF beams. The voltage increases linearly with the incident sound pressure. At the incident SPL of 110 dB, the voltage of 1.48 V has been measured which corresponds to the power of 1.774 mW with the power density of 0.055 mW/cm2.

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