ESTONIAN ACADEMY
PUBLISHERS
eesti teaduste
akadeemia kirjastus
PUBLISHED
SINCE 1952
 
Proceeding cover
proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2021): 1.024
Excitation of intrinsic localized modes in finite mass-spring chains driven sinusoidally at end; pp. 417–421
PDF | doi: 10.3176/proc.2015.3S.12

Authors
Yosuke Watanabe, Takunobu Nishida, Nobumasa Sugimoto
Abstract

Localized oscillations in finite mass-spring chains, driven sinusoidally at one end with the other fixed, are studied numerically. It is assumed that the restoring force of the spring is given by a piecewise linear function of a relative displacement between neighbouring masses, i.e. a spring constant changes at a threshold of the displacement. Linear damping proportional to the velocity of the mass is taken into account. The mass at one end is forced to be displaced in the direction of the chains at a frequency above the cut-off frequency. It is shown that when the amplitude exceeds the threshold, localized oscillations are excited intermittently at the driving end and propagated down the chain at a constant speed.

References

 

  1. Sievers, A. J. and Takeno, S. Intrinsic localized modes in anharmonic crystals. Phys. Rev. Lett., 1988, 61(8), 970–973.
http://dx.doi.org/10.1103/PhysRevLett.61.970

  2. Aubry, S. Breathers in nonlinear lattices: existence, linear stability and quantization. Physica D, 1997, 103, 201–250.
http://dx.doi.org/10.1016/S0167-2789(96)00261-8

  3. Flach, S. and Willis, C. R. Discrete breathers. Phys. Rep., 1998, 295, 181–264.
http://dx.doi.org/10.1016/S0370-1573(97)00068-9

  4. Kivshar, Y. S. and Flach, S. (eds). Focus issue: Nonlinear localized modes: physics and applications. Chaos, 2003, 13, 586–799.
http://dx.doi.org/10.1063/1.1577332

  5. Campbell, D. K., Flach, S., and Kivshar, Y. S. Localizing energy through nonlinearity and discreteness. Phys. Today, 2004, 57, 43–49.
http://dx.doi.org/10.1063/1.1650069

  6. Yoshimura, K. and Doi, Y. Moving discrete breathers in nonlinear lattice: resonance and stability. Wave Motion, 2007, 45, 83–99.
http://dx.doi.org/10.1016/j.wavemoti.2007.04.004

  7. Geniet, F. and Leon, J. Energy transmission in the forbidden band gap of a nonlinear chain. Phys. Rev. Lett., 2002, 89(13), 134102.
http://dx.doi.org/10.1103/PhysRevLett.89.134102

  8. Geniet, F. and Leon, J. Nonlinear supratransmission. J. Phys.-Condens. Mat., 2003, 15, 2933–2949.
http://dx.doi.org/10.1088/0953-8984/15/17/341

  9. Spire, A. and Leon, J. Nonlinear absorption in discrete systems. J. Phys. A-Math. Gen., 2004, 37, 9101–9108.
http://dx.doi.org/10.1088/0305-4470/37/39/004

10. Leon, J. Nonlinear supratransmission as a fundamental instability. Phys. Lett. A, 2003, 319, 130–136.
http://dx.doi.org/10.1016/j.physleta.2003.10.012

11. Khomeriki, R., Lepri, S., and Ruffo, S. Nonlinear supratransmission and bistability in the Fermi-Pasta-Ulam model. Phys. Rev. E, 2004, 70, 066626.
http://dx.doi.org/10.1103/PhysRevE.70.066626

12. Sato, M., Hubbard, B. E., Sievers, A. J., Ilic, B., Czaplewski, D. A., and Craighead, H. G. Observation of locked intrinsic localized vibrational modes in a micromechanical oscillator array. Phys. Rev. Lett., 2003, 90, 044102.
http://dx.doi.org/10.1103/PhysRevLett.90.044102

13. Kimura, M. and Hikihara, T. Coupled cantilever array with tunable on-site nonlinearity and observation of localized oscillations. Phys. Lett. A, 2009, 373, 1257–1260.
http://dx.doi.org/10.1016/j.physleta.2009.02.005

14. Cuevas, J., English, L. Q., Kevrekidis, P. G., and Anderson, M. Discrete breathers in a forced-damped array of coupled pendula: modeling, computation, and experiment. Phys. Rev. Lett., 2009, 102, 224101.
http://dx.doi.org/10.1103/PhysRevLett.102.224101

15. Gallavotti, G. (ed.). The Fermi-Pasta-Ulam Problem. Springer, Berlin, Heidelberg, 2008.
http://dx.doi.org/10.1007/978-3-540-72995-2

 

Back to Issue