Skip to main content
SpringerLink
Log in

Wave Propagation Phenomena in Nonlinear Elastic Metamaterials

  • Conference paper
  • First Online:
New Trends in Nonlinear Dynamics

Abstract

The present chapter provides a general method to deal with nonlinear integro-differential equations, based on statistical linearization and Fredholm’s approach. In this context, the elastic metamaterial is characterized by long-range nonlocal interactions besides a nonlinear short-range constitutive relationship. Results are analytically obtained and unveil the birth of unconventional propagation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Laude, V., Korotyaeva, M. E.: Stochastic band structure for waves propagating in periodic media or along waveguides. arXiv preprint arXiv:1801.09914 (2018)

    Google Scholar 

  2. Robertson, W.M., Pappafotis, J., Flannigan, P., Cathey, J., Cathey, B., Klaus, C.: Sound beyond the speed of light: measurement of negative group velocity in an acoustic loop filter. Appl. Phys. Lett. 90(1), 014102 (2007)

    Article  ADS  Google Scholar 

  3. Mugnai, D., Ranfagni, A., Ruggeri, R.: Observation of superluminal behaviors in wave propagation. Phys. Rev. Lett. 84(21), 4830 (2000)

    Article  ADS  Google Scholar 

  4. Carcaterra, A., Coppo, F., Mezzani, F., Pensalfini, S.: Long-range retarded elastic metamaterials: wave-stopping, negative and hypersonic group velocity. Phys. Rev. Appl. 11(1), 014041 (2019)

    Article  ADS  Google Scholar 

  5. Mezzani, F., Coppo, F., Carcaterra, A.: Long-range coupling of waveguides. In: Proceedings of ISMA 2018—International Conference on Noise and Vibration Engineering and USD 2018—International Conference on Uncertainty in Structural Dynamics (2018)

    Google Scholar 

  6. Mezzani, F., Coppo, F., Pensalfini, S., Roveri, N., Carcaterra, A.: Twin-waves propagation phenomena in magnetically-coupled structures. Proc. Eng. 199, 711–716 (2017)

    Article  Google Scholar 

  7. Coppo, F., Rezaei, A.S., Mezzani, F., Pensalfini, S., Carcaterra, A.: Wave path in an elastic membrane with selective nonlocality. In: Proceedings of ISMA 2018—International Conference on Noise and Vibration Engineering and USD 2018—International Conference on Uncertainty in Structural Dynamics (2018)

    Google Scholar 

  8. Vaidya, V.D., Guo, Y., Kroeze, R.M., Ballantine, K.E., Kollár, A.J., Keeling, J., Lev, B.L.: Tunable-range, photon-mediated atomic interactions in multimode cavity QED. Phys. Rev. X. 8(1), 011002 (2018)

    Google Scholar 

  9. Puri, S., Andersen, C.K., Grimsmo, A.L., Blais, A.: Quantum annealing with a network of all-to-all connected, two-photon driven Kerr nonlinear oscillators. arXiv preprint arXiv:1609.07117 (2016)

    Google Scholar 

  10. Vlasov, A.A.: On high-frequency properties of electron gas. J. Exp. Theor. Phys. 8(3), 291–318 (1938)

    Google Scholar 

  11. Kozin, F.: The method of statistical linearization for non-linear stochastic vibrations. In: Ziegler, F., Schuëller, G.I. (eds.) Nonlinear Stochastic Dynamic Engineering Systems. IUTAM Symposium (International Union of Theoretical and Applied Mechanics). Springer, Berlin (1988)

    Google Scholar 

  12. Bernard, P., Wu, L.: Stochastic linearization: the theory. J. Appl. Probab. 35(03), 718–730 (1998)

    Article  MathSciNet  Google Scholar 

  13. Bernard, P.: Stochastic linearization: what is available and what is not. Comput. Struct. 67(1–3), 9–18 (1998)

    Article  Google Scholar 

  14. Roberts, J.B., Spanos, P.D.: Random Vibration and Statistical Linearization. Courier Corporation, New York (2003)

    MATH  Google Scholar 

  15. Culla, A., Carcaterra, A.: Statistical moments predictions for a moored floating body oscillating in random waves. J. Sound Vib. 308, 44–66 (2007)

    Article  ADS  Google Scholar 

  16. Fredholm, I.: Solution d’un problème fondamental de la théorie de l’élasticité. Arkiv. Mat. Astro. Fysik 2. 28, 3–8 (1906)

    Google Scholar 

  17. Meirovitch, L.: Elements of Vibration Analysis. McGraw-Hill Science, Engineering & Mathematics Publisher, New York (1975)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Sapienza University of Rome, Rome, Italy

    Federica Mezzani, Amir Sajjad Rezaei & Antonio Carcaterra

Authors
  1. Federica Mezzani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Amir Sajjad Rezaei
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Antonio Carcaterra
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Federica Mezzani .

Editor information

Editors and Affiliations

  1. Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Rome, Italy

    Walter Lacarbonara

  2. Department of Mechanical Engineering, University of Maryland, College Park, MD, USA

    Balakumar Balachandran

  3. Department of Physics, Lanzhou University of Technology, Lanzhou, Gansu, China

    Jun Ma

  4. Department of Electrical Engineering, Polytechnic of Porto - School of Engineering (ISEP), Porto, Portugal

    J. A. Tenreiro Machado

  5. Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary

    Gabor Stepan

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Mezzani, F., Rezaei, A.S., Carcaterra, A. (2020). Wave Propagation Phenomena in Nonlinear Elastic Metamaterials. In: Lacarbonara, W., Balachandran, B., Ma, J., Tenreiro Machado, J., Stepan, G. (eds) New Trends in Nonlinear Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-030-34724-6_4

Download citation

Publish with us

Policies and ethics

Search

Navigation