Journal Club Theme of December 2012: Metamaterials Inspired Concepts for Elastic Wave Energy Harvesting

ruzzene's picture

Recent journal club posts have illustrated the interesting and unique dynamic properties of phononic crystals and acoustic metamaterials (see April and May journal club entries by M. Hussein and A. Spadoni respectively). The ability of this class of engineered materials and structures to guide and focus elastic and sound waves can be exploited in a number of new applications and exciting functionalities. Among these, Alper Erturk, Michael Leamy (both from Georgia Tech) and I have recently explored the possibility of using configurations inspired by the phononic/metamaterials literature for wave-based energy harvesting. The objective of our initial investigations is to exploit simple concepts in mechanics such as wave scattering and wave localization in order to concentrate the elastic energy associated with a propagating wave at desired locations. The conversion of such energy with optimized efficiency has yet to be addressed and will be the object of further work.
The harvesting of vibrational energy has been extensively investigated in the last decade [1-3]. However, limited effort has been devoted to exploiting the energy of propagating waves in structures or fluids. Only a few research groups have proposed the use of Helmholtz resonators [4], sonic crystals [5], and polarization-patterned piezoelectric solids [6] for structure-borne or air-borne wave energy harvesting. Our work has focused on simple configurations whereby waves propagating in aluminum plates are controlled through arrays of surface bonded cylindrical stubs acting as acoustic scatterers. The scatterers are laid out according to spatial patterns that guide and focus elastic Lamb waves propagating in the plate. A first concept, illustrated in detail in [7], features an array of such scatterers laid out along an elliptical path that concentrates incoming spherical waves to the geometrical focus of the ellipse (Fig. 1a), where a piezoelectric energy harvester is located. The resulting elliptical acoustic mirror (EAM) provides broadband focusing capabilities and energy harvesting performance that are vastly superior with respect to a harvester located in the free field.  Specifically, across all resistance and frequency levels considered (in the 25-100 kHz range) the system showed a 3075% increase over the free harvester case. Alternative acoustic mirror configurations (such as a parabolic mirror) are currently being investigated to focus and harvest structure-borne plane waves rather than waves emanating from point sources. In addition, current studies are investigating the potential integration of acoustic mirrors as part of structural components such as sandwich plates and perforated panels for noise control.

 

 Figure 1

 

Figure 1: EAM configuration showing the location of the point source of excitation and of the piezoelectric energy harvester at the focus (a); velocity amplitude distribution over the region bounded by the dashed rectangle in (a) exhibiting focusing of the wave energy at the location of the energy harvester (b); velocity amplitude field along the major axis (x = 60 mm) of the ellipse for the frequency range of 25-150 kHz showing the locations of the source and the energy harvester (c), and comparison of energy harvested with and without the EAM configuration: power versus load resistance and frequency surfaces for the frequency range of 30-70 kHz covering the region of the optimal electrical load at each frequency (c).

A second concept exploits the localization characteristics of a defect in an otherwise periodic array. The internal defect (Fig. 2a) produced by a missing stub localizes the elastic energy at the frequency of resonance of the imperfection (in this case approximately 37.5 kHz), which is located within a bandgap of the array. Such resonance, along with bandgaps, can be designed to match frequency content of specific applications. The experimental dynamic response map of Fig. 2b shows clear evidence of strong localization of wave motion achieved within the lattice at the defect location. This design may be transitioned for practical application through tailored design of foams with periodic inclusions, or of a structural substrate with an imperfect array of holes. Both concepts demonstrate how several basic concepts related to wave motion in periodic and non-periodic metamaterials with strategically located imperfections or scatterers can lead to interesting applications such as energy harvesting and can be exploited to achieve substantial enhancements in performance.

I am hoping this post generates some discussions on the potential application of phononic structures and metamaterials for harvesting and conversion of energy. I am particularly interested in learning what others have done in this area, which appears to be very promising.

 

Figure 2 

 

Figure 2: Lattice structure with an imperfection (a); and RMS displacement field showing energy localization at the imperfection for harmonic excitation at 37.5 kHz (b).

M. Ruzzene, A. Erturk and M. Leamy acknowledge the contributions of Matteo Carrara and Martin Cacan who, through hard work and dedication, have produced all experimental results presented above. 

References

1. N. S. Hudak and G. G. Amatucci, Journal of Applied Physics 103, 101301 (2008).

2. K. A. Cook-Chennault, N. Thambi and A. M. Sastry, Smart Materials and Structures 17, 043001 (2008).

3. A. Erturk, J. Hoffmann and D. J. Inman, Applied Physics Letters 94, 254102 (2009).

4. S. B. Horowitz, M. Sheplak, L. N. Cattafesta, and T. Nishida, Journal of Micromechanics and Microengineering 16, S174 (2006).

5. L. Y. Wu, L. W. Chen, and C. M. Liu, Applied Physics Letters 95, 013506 (2009).

6. C. J. Rupp, M. L. Dunn and K. Maute, Applied Physics Letters 96, 111902 (2010). 

7. M. Carrara, M. Cacan, M. Leamy, M. Ruzzene, A. Erturk, "Dramatic enhancement of structure-borne wave energy harvesting using an elliptical acoustic mirror." Applied Physics Letters 100.20 (2012): 204105-204105.


mihussein's picture

Design questions

Massimo,

It is delightful to see energy harvesting being added to the
growing list of applications for acoustic and elastic metamaterials. The elliptical
acoustic mirror shown in Fig. 1 is very interesting indeed. It appears that the
elliptical shape was chosen intentionally to interact favorably with the
spherical waves, correct? What would happen if the mirror is set up following a
circular, rather than an elliptical, shape? Also, would you get better
performance if you add one or more layers of stubs to thicken this elliptical
mirror?


ruzzene's picture

Hi Mahmoud interesting

Hi Mahmoud

interesting questions. The elliptical mirror was the first case that we considered, and the intention was to be able to focus waves coming in from a point source to a different point. Thus the choice of a geometrical shape that is characterized by two foci. We are currently working on a parabolic mirror that is capable of focusing plane waves. Adding more stubs would ideally improve the performance. We have some experiments in that direction, but the single layer was already behaving almost like a perfect reflector, possibly because of the large impedance mismatch created by the addition of the stubs. Their geometry was selected based on intuition and prior experience, also guided by the literature, so it is far from being optimized.

 Sorry for the delay in responding....the site has been acting up a little lately 

 

Massimo Ruzzene