- Access by Xinjiang University
New family of solitary waves in granular dimer chains with no precompression
Phys. Rev. E 83, 036606 – Published 21 March, 2011
DOI: https://doi.org/10.1103/PhysRevE.83.036606
Abstract
In the present paper we report the existence of a new family of solitary waves in general one-dimensional dimer chains with elastic interactions between beads obeying a strongly nonlinear Hertzian force law. These dimers consist of pairs of “heavy” and “light” beads with no precompression. The solitary waves reported herein can be considered as analogous to the solitary waves in general homogeneous granular chains studied by Nesterenko, in the sense that they do not involve separations between beads, but rather satisfy special symmetries or, equivalently antiresonances in their intrinsic dynamics. We conjecture that these solitary waves are the direct products of a countable infinity of antiresonances in the dimer. An interesting finding is that the solitary waves in the dimer propagate faster than solitary waves in the corresponding homogeneous granular chain obtained in the limit of no mass mismatch between beads (i.e., composed of only heavy beads). This finding, which might seem counterintuitive, indicates that under certain conditions nonlinear antiresonances can increase the speed of disturbance transmission in periodic granular media, through the generation of different ways for transferring energy to the far field of these media. From a practical point of view, this result can have interesting implications in applications where granular media are employed as shock transmitters or attenuators.
Article Text
References (16)
- V. F. Nesterenko, Dynamics of Heterogeneous Materials (Springer, New York, 2001).
- S. Sen et al., Phys. Rep. 462, 21 (2008).
- A. Chatterjee, Phys. Rev. E 59, 5912 (1999).
- A. Molinari and C. Daraio, Phys. Rev. E 80, 056602 (2009).
- C. Coste et al., Phys. Rev. E 56, 6104 (1997).
- A. C. Scott et al., Proc. IEEE 61, 1443 (1973).
- E. B. Herbold et al., Acta Mech. 205, 85 (2009).
- M. A. Porter et al., Physica D 238, 666 (2009).
- N. Boechler et al., Phys. Rev. Lett. 104, 244302 (2010).
- G. Theocharis et al., e-print arXiv:1009.0885v1.
- M. A. Porter et al., Phys. Rev. E 77, 015601(R) (2008).
- Y. Starosvestky and A. F. Vakakis, Phys. Rev. E 82, 026603 (2010).
- A. F. Vakakis et al., Normal Modes and Localization in Nonlinear Systems (Wiley, New York, 1996).
- U. Harbola et al., Phys. Rev. E 82, 011306 (2010).
- S. Sen and M. Manciu, Phys. Rev. E 64, 056605 (2001).
- C. M. Bender and S. A. Orszag, Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory (Springer, New York, 1991).