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Band gap transmission in periodic bistable mechanical systems

Frazier, Michael J. and Kochmann, Dennis M. (2017) Band gap transmission in periodic bistable mechanical systems. Journal of Sound and Vibration, 388 . pp. 315-326. ISSN 0022-460X. doi:10.1016/j.jsv.2016.10.041.

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We theoretically and numerically investigate the supratransmission phenomenon in discrete, nonlinear systems containing bistable elements. While linear waves cannot propagate within the band gaps of periodic structures, supratransmission allows large-amplitude waves to transmit energy through the band gap. For systems lacking bistability, the threshold amplitude for such energy transmission at a given frequency in the linear band gap is fixed. We show that the topological transitions due to bistability provide an avenue for switching the threshold amplitude between two well-separated values. Moreover, this versatility is achieved while leaving the linear dispersion properties of the system essentially unchanged. Interestingly, the behavior changes when an elastic chain is coupled to bistable resonators (in an extension of the well-studied linear locally resonant metamaterials). Here, we show that a fraction of the injected energy is confined near the boundary due to the resonators, providing a means of regulating the otherwise unrestrained energy flow due to supratransmission. Together, the results illustrate new means of controlling nonlinear wave propagation and energy transport in systems having multi-stable elements.

Item Type:Article
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Kochmann, Dennis M.0000-0002-9112-6615
Additional Information:© 2016 Elsevier Ltd. Received 13 February 2016, Revised 22 September 2016, Accepted 25 October 2016, Available online 9 November 2016.
Subject Keywords:Nonlinear dynamics; Supratransmission; Bistability; Chain of oscillators
Record Number:CaltechAUTHORS:20170106-151747130
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Official Citation:Michael J. Frazier, Dennis M. Kochmann, Band gap transmission in periodic bistable mechanical systems, Journal of Sound and Vibration, Volume 388, 3 February 2017, Pages 315-326, ISSN 0022-460X, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73315
Deposited By: Tony Diaz
Deposited On:07 Jan 2017 00:12
Last Modified:11 Nov 2021 05:14

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