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Wave Propagation in Linear and Nonlinear Periodic Media pp 33–108Cite as

Piezoelectric Superlattices and Shunted Periodic Arrays as Tunable Periodic Structures and Metamaterials

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Part of the book series: CISM Courses and Lectures ((CISM,volume 540))

Abstract

Two examples of internally resonating metamaterials with behavior based on multi-field coupling are illustrated. The first example consists in a 1D waveguide with a periodic array of shunted piezoelectric patches. Each patch is shunted through a passive circuit which induces resonance in the equivalent mechanical impedance of the waveguide. Analytical, numerical and experimental studies illustrate the characteristics of the system and quantify such resonant mechanical properties due to electro-mechanical coupling. Piezoelectric superlattices are presented as additional examples of internally resonant metamaterials. Multi-field coupling is identified as the enabler mechanism for the generation of the internal resonance. Numerical studies for 1D and 2D piezoelectric superlattices and analytical studies developed on the basis of the long wavelength approximation support the interpretation of the coupling as an internally resonant mechanism.

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Bibliography

  • B.A. Auld. Acoustic Fields and Waves in Solids. Krieger Pub Co, 1990.

    Google Scholar 

  • S. Behrens, S.O.R. Moheimani, and J. Fleming. Multiple mode current flowing passive piezoelectric shunt controller. Journal of Sound and Vibration, 266:929–942, 2003.

    Article  Google Scholar 

  • L. Brillouin. Wave Propagation in Periodic Structures. McGraw-Hill, 1946.

    Google Scholar 

  • F. Casadei, M. Ruzzene, L. Dozio, and K.A. Cunefare. Broadband vibration control through periodic arrays of resonant shunts: experimental investigation on plates. Smart Materials and Structures, 19(1):015002, 2010.

    Article  Google Scholar 

  • Y. Cheng, J. Y. Xu, and X. J. Liu. One-dimensional structured ultrasonic metamaterials with simultaneously negative dynamic density and modulus. Phys. Rev. B, 77(4):045134, Jan 2008. doi: 10.1103/Phys-RevB.77.045134.

    Article  Google Scholar 

  • Y. Chou and M. Yang. Energy conversion in piezoelectric superlattices. Proc. SPIE, 6526(65260L), 2007.

    Google Scholar 

  • L. De Marchi, S. Caporale, N. Speciale, and A. Marzani. Ultrasonic guidedwaves characterization with warped frequency transforms. In Ultrasonics Symposium, 2008. IUS 2008. IEEE, pages 188–191, 2008. doi: 10.1109/ULTSYM.2008.0046.

    Google Scholar 

  • Yiqun Ding, Zhengyou Liu, Chunyin Qiu, and Jing Shi. Metamaterial with simultaneously negative bulk modulus and mass density. Phys. Rev. Lett., 99(9):093904, Aug 2007.

    Article  Google Scholar 

  • N. Fang, D. Xi, J. Xu, M. Ambati, W. Srituravanich, C. Sun, and X. Zhang. Ultrasonic metamaterials with negative modulus. Nature Materials, 5(6): 452–456, 2006.

    Article  Google Scholar 

  • R.L. Forward. Electronic damping of vibrations in optical structures. Journal of applied optics, 18(5):690–697, 1979.

    Article  Google Scholar 

  • K.F. Graff. Wave Motion in Elastic Solids. Dover, 1975.

    Google Scholar 

  • N. Hagood and N. von Flotow. Damping of strucutal vibrations with piezoelectric materials and passive electical networks. Journal of Sound and Vibration, 1991.

    Google Scholar 

  • Hassani. A review of homogenization and topology optimization iii-topology optimization using optimality criteria. Computers and Structures, 69(6): 739–756, 1998.

    Article  Google Scholar 

  • J. Hollkamp. Multimodal passive vibration suppression with piezoelectric materials and resonant shunt. Journal of Intelligent Material Systems and Structures, 1994.

    Google Scholar 

  • G. L. Huang and C. T. Sun. Band gaps in a multiresonator acoustic metamaterial. Journal of Vibration and Acoustics, 132(3):031003, 2010.

    Article  Google Scholar 

  • H.H. Huang, C.T. Sun, and G.L. Huang. On the negative effective mass density in acoustic metamaterials. International Journal of Engineering Science, 47(4):610–617, 2009.

    Article  MathSciNet  Google Scholar 

  • J. Kim and Y.-C. Jung. Broadband noise reduction of piezoelectric smart panel featuring negative-capacitive-converter shunt circuit. Journal of the Acoustical Society of America, 120:2017–2025, 2006a.

    Article  Google Scholar 

  • J. Kim and Y.-C. Jung. Piezoelectric smart panels for broadband noise reduction. Journal of Intelligent Materials Systems and Structures, 17 (685–690), 2006b.

    Article  Google Scholar 

  • J. Kim and J.-H. Kim. Multimode shunt damping of piezoelectric smart panel for noise reduction. Journal of the Acoustical Society of America, 116:942–948, 2004.

    Article  Google Scholar 

  • J. Kim and J.-K. Lee. Broadband transmission noise reduction of smart panels featuring piezoelectric shunt circuits and sound-absorbing material. Journal of the Acoustical Society of America, 116:9908–998, 2004.

    Google Scholar 

  • C. Kittel. Elementary Solid State Physics: A Short Course. Wiley, 1962.

    Google Scholar 

  • M. S. Kushwaha, P. Halevi, L. Dobrzynski, and B. Djafari-Rouhani. Acoustic band structure of periodic elastic composites. Phys. Rev. Lett., 71 (13):2022–2025, Sep 1993.

    Article  Google Scholar 

  • M.S. Kushwaha and B. Djafari-Rouhani. Giant sonic stop bands in twodimensional periodic system of fluids. Journal of Applied Physics, 84(9): 4677–4683, 1998.

    Article  Google Scholar 

  • B.S. Lazarov and J.S. Jensen. Low-frequency band gaps in chains with attached non-linear oscillators. International Journal of Non-Linear Mechanics, 42(10):1186–1193, 2007.

    Article  Google Scholar 

  • P. G. Martinsson and A. B. Movchan. Vibrations of Lattice Structures and Phononic Band Gaps. The Quarterly Journal of Mechanics and Applied Mathematics, 56(1):45–64, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  • O. Oleinik. On homogenisation problems. Milan Journal of Mathematics, 55:105, 1985.

    Google Scholar 

  • P.F. Pai. Metamaterial-based Broadband Elastic Wave Absorber. Journal of Intelligent Material Systems and Structures, 21(5):517–528, 2010.

    Article  Google Scholar 

  • A. Preumont. Vibration Control of Active Structures. Kluwer, 1997.

    Google Scholar 

  • R.H.S. Riordan. Simulated inductors using differential amplifiers. Eletronics Letters, 3:50–51, 1967.

    Article  Google Scholar 

  • Ping Sheng, X.X. Zhang, Z. Liu, and C.T. Chan. Locally resonant sonic materials. Physica B: Condensed Matter, 338(1–4):201–205, 2003.

    Article  Google Scholar 

  • Ping Sheng, Jun Mei, Zhengyou Liu, and Weijia Wen. Dynamic mass density and acoustic metamaterials. Physica B: Condensed Matter, 394(2):256–261, 2007.

    Article  Google Scholar 

  • M.M. Sigalas. Defect states of acoustic waves in a two-dimensional lattice of solid cylinders. Journal of Applied Physics, 84(6):3026–3030, 1998.

    Article  Google Scholar 

  • A. Spadoni, M. Ruzzene, and K. Cunefare. Vibration andWave Propagation Control of Plates with Periodic Arrays of Shunted Piezoelectric Patches. Journal of Intelligent Material Systems and Structures, 20(8):979–990, 2009.

    Article  Google Scholar 

  • H. Sun, X. Du, and P.F. Pai. Theory of Metamaterial Beams for Broadband Vibration Absorption. Journal of Intelligent Material Systems and Structures, 21(11):1085–1101, 2010.

    Article  Google Scholar 

  • O. Thorp, M. Ruzzene, and A. Baz. Attenuation and localization of wave propagation in rods with periodic shunted piezoelectric patches. Smart Materials and Structures, 10(5):979–989, 2001.

    Article  Google Scholar 

  • O. Thorp, M. Ruzzene, and A. Baz. Attenuation and localization of waves in shells with periodic shunted piezo rings. Smart Materials and Structures, 14(4):594–604, 2005.

    Article  Google Scholar 

  • S.Y. Wu. Piezoelectric shunts with a parallel r-l circuit for structural damping and vibration control. In Proceedings of SPIE — The International Society for Optical Engineering, volume 2720, pages 259–269, San Diego, CA, USA, 1996.

    Google Scholar 

  • M. Yang, L. Wu, and J. Tseng. Phonon-polariton in two-dimensional piezoelectric phononic crystals. Physics Letters A, 372(26):4730–4735, 2008.

    Article  MATH  Google Scholar 

  • S. Yao, X. Zhou, and G. Hu. Experimental study on negative effective mass in a 1d mass-spring system. New Journal of Physics, 10(4):043020, 2008.

    Article  Google Scholar 

  • X. Zhang, R. Zhu, J. Zhao, Y. Chen, and Y. Zhu. Phonon-polariton dispersion and the polariton-based photonic band gap in piezoelectric superlattices. Phys. Rev. B, 69(085118), 2004.

    Article  Google Scholar 

  • Y. Zhu, X. Zhang, Y. Lu, Y. Chen, S. Zhu, and N. Ming. New type of polariton in a piezoelectric superlattice. Phys. Rev. Lett., 90(053903), 2003.

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. D. Guggenheim School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    Luca Airoldi, Matteo Senesi & Massimo Ruzzene

Authors
  1. Luca Airoldi
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  2. Matteo Senesi
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  3. Massimo Ruzzene
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Editor information

Editors and Affiliations

  1. University “La Sapienza”, Rome, Italy

    Francesco Romeo

  2. Georgia Institute of Technology, Atlanta, USA

    Massimo Ruzzene

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© 2012 CISM, Udine

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Airoldi, L., Senesi, M., Ruzzene, M. (2012). Piezoelectric Superlattices and Shunted Periodic Arrays as Tunable Periodic Structures and Metamaterials. In: Romeo, F., Ruzzene, M. (eds) Wave Propagation in Linear and Nonlinear Periodic Media. CISM Courses and Lectures, vol 540. Springer, Vienna. https://doi.org/10.1007/978-3-7091-1309-7_2

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  • DOI: https://doi.org/10.1007/978-3-7091-1309-7_2

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-1308-0

  • Online ISBN: 978-3-7091-1309-7

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