Abstract
This work seeks to put forward an approach to enhance the voltage generated by an acoustic based piezoelectric energy harvester. When a flexible triangular foil is attached perpendicular to the PVDF cantilever beam there is an increase in strain in the beam, also there is an increment in the acoustic pressure amplification rate of the Helmholtz resonator due to the dimensional modification of its neck. The integrated effects of these modifications of the harvester on the output voltage have been investigated. When sound incident on the surface of the neck of the resonator, an oscillatory pressure is produced in the cavity, which in turns vibrates the PVDF cantilever beam and voltage generates. By amending the structure of the PVDF cantilever with a polyester foil attached perpendicular to it, the cantilever is driven into concurrent bending and twisting by the cavity pressure and therefore makes a noteworthy increase in the output voltage
Introduction
The rapid growth of consumer electronics is an intense trend today, which modernize the way we communicate and entertain ourselves. The huge deployment of these low power electronics has paved a great foundation for new mechanisms of converting unused available energy into usable (electrical) energy. The unharnessed energy from the surrounding environment have the benefit of being ample, pervasive and cause less environmental harm. The so called energy harvesting technology has therefore hit a tipping point providing energy security and stability in this era of energy crisis [1] . Advanced technical developments have sparked interest in the engineering community to develop more and more applications that utilize power from energy harvesting, thereby contributing to the realization of an infinite source of energy.
Introduction
Acoustic energy harvesting is a relatively young subfield within energy harvesting due to the low power density of its sources, but it is increasingly hunted due to the ubiquitous nature of the source as well as the technological developments in the realization of truly autonomous MEMS devices and energy storage systems. With the global concern for energy and environmental issues, growing interests have been devoted to acoustic energy harvesting and it becomes a research frontier [1] . Low frequency noise is an inherent by-product of this technology, which is hardly investigated to explore the possibility of harvesting or to effectively control yet.
Introduction
In reference [1] the authors have provided a detailed literature of acoustic based piezoelectric energy harvesting in macro and micro scales. There are many futuristic changes which scientists are trying to acquaint with both the resonators and transducer element to increase harnessed power. Earlier S K Tang proved that the smoother area change from the neck towards the cavity reduces the flow of resistance of the sound waves and hence increases the sound absorption capacity of the Helmholtz resonator [2] . Later Li et al. explored a piezo leaf where a PVDF cantilever is attached with a large triangular plastic leaf at its free end for wind energy harvesting [3, 4] . Making use of the above structural amendments, the proposed approach presents a compliant and economical technology which makes use of acoustic energy from ambient environment, with mutual applications in increased energy harvesting and environmental noise reduction.
Introduction
The concept of attaching a flexible triangular structure perpendicular to the thin cantilever film to induce torsional deflection along with the lateral bending deflection when it is subjected to the increased pressure inside the tapered neck Helmholtz resonator cavity thereby increasing the output voltage forms the main axis of this work. Due to its wide use in real time acoustic applications, Helmholtz resonator is used to effectively transmit the sound energy to the transduction element without significant loss [5] . Although several transduction mechanisms exist for transformation of acoustic pressure oscillations into electric energy, piezoelectric transduction seems to be an appropriate mechanism due to its simplicity and stable performance [6] .
Working Principle
Helmholtz resonator consists of a body to contain a volume of air and a neck in which a slug of air vibrates back and forth. The enclosed volume of air acts as a spring connected to the mass of the slug of air, and vibrates in an adiabatic fashion at a frequency dependent on the density, volume of the air, its molecular composition and the mass of the slug of air in the neck as shown in figure 1 [7, 8] . For a resonator with negligible wall losses, the pressure amplification factor, at its resonance frequency is the ratio of the acoustic pressure amplitude, within the cavity to the external driving pressure amplitude, of the incident sound wave and is given as [9] Since the pressure amplification factor of the resonator is proportional to the dimensions of the neck, the tapering of the neck towards the cavity; i.e. the smoother area change from the neck towards the cavity will reduce the flow of resistance of the sound waves and will increase the sound absorption capacity of the Helmholtz resonator. The resonant frequency of the Helmholtz resonator with tapered neck is given by [2] where is the area of cross section of the neck, is the volume of the cavity, is the effective length of the neck, is the slope of tapered neck and is the inlet radius of the neck. When sound pressure of same frequency as that of the resonator is applied across the opening of the neck, the sound pressure inside the cavity is increased. The pressure inside the tapered neck Helmholtz resonator changes along the length of the cavity of the resonator.
Working Principle
A flexible PVDF cantilever attached with a polyethylene foil of triangular shape at its free end is used as the transducer. The modified piezoelectric transducer inserted inside the cavity of the resonator is subjected to the cavity pressure. Although the cavity pressure acts as a longitudinal load for the beam and the flexible foil to undergo bending deflection, the bending of the flexible foil causes the beam to undergo torsional deflection also. Thus the beam undergoes transverse loading where it is subjected to coupled bending and torsion at the same operating frequency as depicted in figure 2. When the distributed cavity pressure , is applied to the beam, the concurrent bending and twisting motion of the beam is overseen by a system of two equations [10] where , mass per unit length of the beam, = flexural rigidity, h = distance from the center of the beam to the neutral axis, = density of the beam, = polar moment of inertia, = torsional rigidity, = warping rigidity, y = flexural displacement and = torsional displacement. Figure 3 presents the schematic of the proposed acoustic energy harvester using tapered neck Helmholtz resonator and a piezoelectric cantilever undergoing concurrent bending and twisting. When the acoustic resonator is excited by an incident sound wave at its resonant frequency, acoustic energy in the form of standing resonant waves get collected inside the resonator. When a piezoelectric unimorph cantilever attached with a flexible triangular foil at its free end is inserted into the resonator cavity, perpendicular to the axial direction, the standing wave cavity pressure will drive the cantilever into lateral and torsional vibrations. The Helmholtz resonator is designed to have a resonant frequency same as that of the piezoelectric transducer to harvest maximum power from acoustic energy. 
Experimental Set-up
The experimental set up of acoustic energy harvester is shown in figure 4 . The Helmholtz resonator used is made of acrylic material having a cavity volume of 2375.253 x and neck length of 5mm. The outer and inner neck radius of the resonator are 5mm and 25mm respectively forming a tapering angle of for the neck. A piezoelectric cantilever attached with a flexible triangular foil at its free end is inserted into the resonator cavity at a distance of 20mm from the neck of the resonator. The PVDF film cantilever (LDT0-028K) from measurement specialities is used as a piezoelectric transducer and the flexible foil is made up of polyethylene of 0.2mm thickness, 20mm base length and 10mm height. A sound level meter and its associated calibrator have been used for the accurate measurement of input sound pressure. A 2.1ch multimedia speaker equipped with 27W output power and high quality digital amplifier is used as an audio source. The input to the sound source is supplied through a function generator. When a sine wave of desired frequency and voltage level (according to the resonant frequency of Helmholtz resonator) is given to the speaker, it produces a sound signal of the same frequency. The generated peak to peak output voltage from PVDF cantilever due to acoustic pressure is measured using a digital storage oscilloscope.
Result and Discussions
The performance improvement of the harvester due to the geometrical modification of the acoustic resonator is verified experimentally. The output voltage generated by a simple, flexible unimorph cantilever placed in a conventional Helmholtz resonator with cylindrical neck is compared to that of one placed in a tapered neck Helmholtz resonator and the result is strategized in figure 5 .
Result and Discussions
When a sound wave of 98dB is fed directly to the tapered neck Helmholtz resonator, designed to have the same resonant frequency (125Hz) as that of the PVDF strip, an output voltage of 604 mV is produced. The modified piezoelectric transducer has been studied numerically using COMSOL Multiphysics 5.0 as shown in figure 6 . When the triangular foil is attached with the piezoelectric beam there is a reduction in the resonant frequency of the transduction element due to the increase in mass. The colour legend shows an increased beam deflection and hence strain towards the end where flexible foil has been attached, which approves the torsional deflection of the beam due to the attachment. For validating the performance improvement, first the original piezoelectric cantilever is subjected to direct sound source without Helmholtz resonator and the results are compared with that of a modified cantilever beam. The deflection at the tip of the cantilever is measured using a CMOS analog laser sensor IL-065 from Keyence and is shown in figure 7 . As can be seen, the deflection is more for the beam with proposed structural modification indicating an increased strain. But the deformations are highly irregular in magnitude which might need further investigation to explain the reason. It is also noted that an increased sound pressure level is required for producing this increased deflection. So it shows that there is a tradeoff between the increased strain and added mass of the beam.
Result and Discussions
For verifying the strain induced by the coupled bending and twisting of the modified beam the deflection at the tip of regular beam is compared with that of a counterpart with a triangular foil attached parallel to it at its tip. The structural modification put forward in this work gives more deflection compared to its testing counterpart. The resonator is redesigned so as to match the resonant frequency of the modified beam and the performance of the acoustic energy harvester is verified for both the structures subjected to the cavity pressure. Although the vibration amplitude of the cantilever beam could not be measured directly inside the resonator, the increase in induced voltage confirms the improved performance of the harvester as shown in figure 8 . The cantilever beam with triangular foil attached perpendicular to its tip inserted into the cavity wall of the tapered neck Helmholtz resonator of 100Hz produced an output voltage of 842mV when the resonator is excited by an input sound pressure level of 103dB as shown in figure 9 . The increased mass requires more input sound pressure to undergo concurrent twisting and bending at its first resonant frequency. Hence it is concluded that the efficiency of the proposed foil attached cantilever beam energy harvester is increased when input sound pressure level is more. 
Conclusion
This study has experimentally demonstrated that an integrated structural modification of the acoustic resonator and piezoelectric transducer in an acoustic energy harvester can augment the overall harvesting efficiency. This synergistic effect occurs due to the decrease in acoustic resistance at the neck of the Helmholtz resonator by the introduction of the smoother area change from the neck towards the cavity and also due to the increase in strain on the PVDF cantilever beam inserted in the cavity of the resonator by modifying the beam structure. In summary, by the introduction of tapering of the neck there is an increase in harvested output voltage of 43.8%, which is further increased by 25.11% by modifying the structure of the cantilever as the beam is subjected to concurrent bending and torsional vibrations.
Conclusion
The increased input sound pressure of 103dB, required by the beam signifies the existence of a critical input SPL for the beam to experience coupled bending and torsional vibrations. Introducing structural modification in order to approach higher harvesting efficiency can greatly affect the resonant frequency of the harvester as the mass and stiffness of the overall beam changes. It is also noted that there is a presence of non-linearity which makes the beam to undergo irregular deformation.
Conclusion
The theory of concurrent bending and torsional vibrations experienced by the piezoelectric beam subjected to cavity pressure of the resonator stands in contrast, when the dimensions of the flexible triangular foil are very small. Further research is necessary to optimize the dimensions of the flexible attachment such that it should be sturdy and at the same time pliable enough to twist the beam so as to produce maximum strain in it. The same is applicable for the acoustic resonator in which optimization of the slope of the neck to attain minimum acoustic resistance. Optimization of the neck and flexible attachment dimension will improve the overall efficiency of the acoustic energy harvester to obtain maximum harvested power at the desired frequency.

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