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2013 | OriginalPaper | Chapter

3. Band-Gap Properties of Prestressed Structures

Authors : M. Gei, D. Bigoni, A. B. Movchan, M. Bacca

Published in: Acoustic Metamaterials

Publisher: Springer Netherlands

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Abstract

The design of periodic and quasiperiodic structures possessing innovative filtering properties for elastic waves opens the way to the realization of elastic metamaterials. In these structures prestress has a strong influence, ‘shifting’ in frequency, but also ‘annihilating’ or ‘nucleating’ band gaps. The effects of prestress are demonstrated with examples involving flexural waves in periodic and quasiperiodic beams and periodic plates. Results highlight that prestress can be employed as a ‘tuning parameter’ for continuously changing vibrational properties of elastic metamaterials.

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previous chapter Locally Resonant Structures for Low Frequency Surface Acoustic Band Gap Applications

next chapter Ultrasound Transmission Through Periodically Perforated Plates

In terms of generation sequence F _i dimensionless buckling loads are

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Aynaou, H., El Boudouti, E.H., Djafari-Rouhani, B., Akjouj, A., Velasco, V.R.: Propagation and localization of acoustic waves in Fibonacci phononic circuits. J. Phys. Condens. Matter 17, 4245–4262 (2005) CrossRef

Bacon, M.D., Dean, P., Martin, J.L.: Proc. Phys. Soc. 80, 174 (1962) CrossRef

Bigoni, D., Capuani, D., Bonetti, P., Colli, S.: A novel boundary element approach to time-harmonic dynamics of incremental non-linear elasticity: The role of pre-stress on structural vibrations and dynamic shear banding. Comput. Methods Appl. Mech. Eng. 196, 4222 (2007) CrossRef

Bigoni, D., Capuani, D.: Time-harmonic Green’s function and boundary integral formulation for incremental nonlinear elasticity: Dynamics of wave patterns and shear bands. J. Mech. Phys. Solids 53, 1163 (2005) CrossRef

Bigoni, D., Gei, M., Movchan, A.B.: Dynamics of a prestressed stiff layer on an elastic half space: filtering and band gap characteristics of periodic structural models derived from long-wave asymptotics. J. Mech. Phys. Solids 56, 2494–2520 (2008) CrossRef

Chen, A.L., Wang, Y.S.: Study on band gaps of elastic waves propagating in one-dimensional disordered phononic crystals. Physica B 392, 369–378 (2007) CrossRef

Cremer, L., Leilich, H.O.: Zur theorie der biegekettenleiter. Arch. Elektr. Übertrag. 7, 261 (1953)

Feynman, R.: The Feynman Lectures on Physics, vol. 2. Addison-Wesley, Reading (1965)

Gei, M.: Elastic waves guided by a material interface. Eur. J. Mech. A, Solids 27, 328–345 (2008) CrossRef

10.

Gei, M.: Wave propagation in quasiperiodic structures: Stop/pass band distribution and prestress effects. Int. J. Solids Struct. 47, 3067–3075 (2010) CrossRef

11.

Gei, M., Bigoni, D., Franceschini, G.: Thermoelastic small-amplitude wave propagation in nonlinear elastic multilayer. Math. Mech. Solids 9, 555–568 (2004) CrossRef

12.

Gei, M., Movchan, A.B., Bigoni, D.: Band-gap shift and defect induced annihilation in prestressed elastic structures. J. Appl. Phys. 105, 063507 (2009) CrossRef

13.

Gei, M., Ogden, R.W.: Vibration of a surface-coated elastic block subject to bending. Math. Mech. Solids 7, 607–629 (2002) CrossRef

14.

Gurtin, M.E., Murdoch, A.I.: A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57, 291–323 (1975) CrossRef

15.

Hladky-Hennion, A.-C., Vasseur, J., Dubus, B., Djafari-Rouhani, B., Ekeom, D., Morvan, B.: J. Appl. Phys. 104, 094206 (2008) CrossRef

16.

Hou, Z., Wu, F., Liu, Y.: Acoustic wave propagating in one-dimensional Fibonacci binary composite systems. Physica B 344, 391–397 (2004) CrossRef

17.

John, S.: Strong localization of photons in certain disordered dielectric superlattices. Phys. Rev. Lett. 58, 2486–2489 (1987) CrossRef

18.

King, P.D.C., Cox, T.J.: Acoustic band gaps in periodically and quasiperiodically modulated waveguides. J. Appl. Phys. 102, 014908 (2007) CrossRef

19.

Kohmoto, M., Kadanoff, L.P., Tang, C.: Localization problem in one dimension: Mapping and escape. Phys. Rev. Lett. 50, 1870–1872 (1983) CrossRef

20.

Kohmoto, M., Oono, Y.: Cantor spectrum for an almost periodic Schroedinger equation and a dynamical map. Phys. Lett. A 102, 145–148 (1984) CrossRef

21.

Kohmoto, M., Sutherland, B., Iguchi, K.: Localization in optics: Quasiperiodic media. Phys. Rev. Lett. 58, 2436–2438 (1987) CrossRef

22.

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

23.

Lin, Y.K.: Free vibrations of a continuous beam on elastic supports. Int. J. Mech. Sci. 4, 409–423 (1962) CrossRef

24.

Liu, Z., Chan, C. T, Sheng, P.: Analytic model of phononic crystals with local resonances. Phys. Rev. B 71, 014103 (2005) CrossRef

25.

Liu, Z., Zhang, W.: Bifurcation in band-gap structures and extended states of piezoelectric Thue-Morse superlattices. Phys. Rev. B 75, 064207 (2007) CrossRef

26.

Mead, D.J.: Wave propagation in continuous periodic structures: Research contributions from Southampton. J. Sound Vib. 190, 495 (1996) CrossRef

27.

Mead, D.J.: Wave propagation and natural modes in periodic systems. II. Multi-coupled systems, with and without damping. J. Sound Vib. 40, 19 (1975) CrossRef

28.

Miles, J.W.: Vibrations of beams on many supports. J. Eng. Mech. 82, 1–9 (1956)

29.

Milton, G.W., Willis, J.R.: On modifications of Newton’s second law and linear continuum elastodynamics. Proc. R. Soc. Lond. A 463, 855 (2007) CrossRef

30.

Movchan, A.B., Slepyan, L.I.: Band gap Green’s functions and localized oscillations. Proc. R. Soc. Lond. A 463, 2709 (2007) CrossRef

31.

Ogden, R.W., Steigmann, D.J.: Plane strain dynamics of elastic solids with intrinsic boundary elasticity, with application to surface wave propagation. J. Mech. Phys. Solids 50, 1869–1896 (2002) CrossRef

32.

Page, J.H., Sukhovich, A., Yang, S., Cowan, M.L., Van Der Biest, F., Tourin, A., Fink, M., Liu, Z., Chan, C.T., Sheng, P.: Phys. Status Solidi B 241, 3454 (2004) CrossRef

33.

Parnell, W.J.: Effective wave propagation in a prestressed nonlinear elastic composite bar. IMA J. Appl. Math. 72, 223–244 (2007) CrossRef

34.

Pendry, J.B.: Negative refraction makes a perfect lens. Phys. Rev. Lett. 85, 3966 (2000) CrossRef

35.

Sheng, P., Zhang, X.X., Liu, Z., Chan, C.T.: Physica B 338, 201 (2003) CrossRef

36.

Sigalas, M.M., Economou, E.N.: Elastic and acoustic-wave band-structure. J. Sound Vib. 158, 377–382 (1992) CrossRef

37.

Steigmann, D.J., Ogden, R.W.: Plane deformations of elastic solids with intrinsic boundary elasticity. Proc. R. Soc. Lond. A 453, 853–877 (1997) CrossRef

38.

Timoshenko, S.P., Weaver, W., Young, D.H.: Vibration Problems in Engineering. Wiley, New York (1974)

39.

Yablonovitch, E.: Inhibited spontaneous emission in solid-state physics and electronics. Phys. Rev. Lett. 58, 2059–2062 (1987) CrossRef

40.

Yang, S., Page, J.H., Liu, Z., Cowan, M.L., Chan, C.T., Sheng, P.: Phys. Rev. Lett. 93, 024301 (2004) CrossRef

41.

Zhang, X., Liu, Z.: Appl. Phys. Lett. 85, 341 (2004) CrossRef

Title: Band-Gap Properties of Prestressed Structures
Authors: M. Gei
D. Bigoni
A. B. Movchan
M. Bacca
Publisher: Springer Netherlands
Book: Acoustic Metamaterials
Print ISBN: 978-94-007-4812-5

Electronic ISBN: 978-94-007-4813-2

Copyright Year: 2013
DOI: https://doi.org/10.1007/978-94-007-4813-2_3

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