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Dynamics of periodic mechanical structures containing bistable elastic elements: From elastic to solitary wave propagation

Nadkarni, Neel and Daraio, Chiara and Kochmann, Dennis M. (2014) Dynamics of periodic mechanical structures containing bistable elastic elements: From elastic to solitary wave propagation. Physical Review E, 90 (2). Art. No. 023204. ISSN 1539-3755. https://resolver.caltech.edu/CaltechAUTHORS:20140926-083716624

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Abstract

We investigate the nonlinear dynamics of a periodic chain of bistable elements consisting of masses connected by elastic springs whose constraint arrangement gives rise to a large-deformation snap-through instability. We show that the resulting negative-stiffness effect produces three different regimes of (linear and nonlinear) wave propagation in the periodic medium, depending on the wave amplitude. At small amplitudes, linear elastic waves experience dispersion that is controllable by the geometry and by the level of precompression. At moderate to large amplitudes, solitary waves arise in the weakly and strongly nonlinear regime. For each case, we present closed-form analytical solutions and we confirm our theoretical findings by specific numerical examples. The precompression reveals a class of wave propagation for a partially positive and negative potential. The presented results highlight opportunities in the design of mechanical metamaterials based on negative-stiffness elements, which go beyond current concepts primarily based on linear elastic wave propagation. Our findings shed light on the rich effective dynamics achievable by nonlinear small-scale instabilities in solids and structures.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1103/PhysRevE.90.023204DOIArticle
ORCID:
AuthorORCID
Daraio, Chiara0000-0001-5296-4440
Kochmann, Dennis M.0000-0002-9112-6615
Additional Information:© 2014 American Physical Society. Received 5 January 2014; published 22 August 2014. The authors gratefully acknowledge financial support from the National Science Foundation (NSF) under Grant No. CMMI-1200319. D.M.K. acknowledges support from the NSF through CAREER Award No. CMMI-1254424.
Group:GALCIT
Funders:
Funding AgencyGrant Number
NSFCMMI-1200319
NSFCMMI-1254424
Issue or Number:2
Classification Code:PACS: 42.65.Tg, 46.32.+x, 46.40.−f, 62.20.D−
Record Number:CaltechAUTHORS:20140926-083716624
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20140926-083716624
Official Citation:Dynamics of periodic mechanical structures containing bistable elastic elements: From elastic to solitary wave propagation Neel Nadkarni, Chiara Daraio, and Dennis M. Kochmann Phys. Rev. E 90, 023204 (2014) – Published 22 August 2014
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:50047
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:26 Sep 2014 15:57
Last Modified:10 Jun 2020 23:56

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