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Nonlinear Dynamics of Granular Chains

[+] Author Affiliations
Yuli Starosvetsky, Alexander F. Vakakis

University of Illinois at Urbana-Champaign, Urbana, IL

Paper No. DETC2010-29208, pp. 913-918; 6 pages
doi:10.1115/DETC2010-29208
From:
  • ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 22nd International Conference on Design Theory and Methodology; Special Conference on Mechanical Vibration and Noise
  • Montreal, Quebec, Canada, August 15–18, 2010
  • Conference Sponsors: Design Engineering Division and Computers in Engineering Division
  • ISBN: 978-0-7918-4413-7 | eISBN: 978-0-7918-3881-5
  • Copyright © 2010 by ASME

abstract

We study strongly nonlinear traveling waves in one-dimensional granular chains with no pre-compression. We directly study the discrete, strongly nonlinear governing equations of motion of these media without resorting to continuum approximations or homogenization, which enables us to compute families of stable multi-hump traveling wave solutions with arbitrary wavelengths. We develop systematic semi–analytical approaches for computing different families of nonlinear traveling waves parametrized by spatial periodicity (wavenumber) and energy. Our findings indicate that homogeneous granular chains possess complex nonlinear dynamics, including the capacity for intrinsic nonlinear energy transfer.

Copyright © 2010 by ASME

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