Experimental Study of Strongly Nonlinear Resonances and Anti-Resonances in Granular Dimer Chains

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• 作者：R. Potekin (1)
  K. R. Jayaprakash (1)
  D. M. McFarland (2)
  K. Remick (1)
  L. A. Bergman (2)
  A. F. Vakakis (1)
  
• 关键词：Nonlinear resonance ; Solitary wave ; Granular dimer
• 刊名：Experimental Mechanics
• 出版年：2013
• 出版时间：June 2013
• 年：2013
• 卷：53
• 期：5
• 页码：861-870
• 全文大小：452KB
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• 作者单位：R. Potekin (1)
  K. R. Jayaprakash (1)
  D. M. McFarland (2)
  K. Remick (1)
  L. A. Bergman (2)
  A. F. Vakakis (1)
  
  1. Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA
  2. Department of Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA
  
• ISSN：1741-2765

文摘

Previous theoretical works considered the intrinsic dynamics of one-dimensional uncompressed granular dimer (diatomic) chains composed of pairs of dissimilar spherical elastic beads in Hertzian interaction. Such ordered granular media exhibit essentially nonlinear acoustics and have been characterized as 鈥榮onic vacua鈥?due to the fact that the speed of sound in these media (as defined in classical acoustics) is zero. Yet, depending on the mass ratios of the pairs of dissimilar beads of these dimers, it was proven that they may possess countable infinities of anti-resonances leading to solitary waves (this in spite of their high inhomogeneity), or countable infinities of strongly nonlinear resonances leading to passive strong attenuation of propagating pulses through energy radiation by means of excitation of traveling waves. The aim of this work is to experimentally verify the existence of these strongly nonlinear dynamics through a series of experiments involving granular dimer chains supported by flexures. By carefully designing the supporting flexures so that their dynamics is sufficiently 鈥榮oft鈥?and thus separate from the 鈥榮tiff鈥?dynamics governing the bead to bead interactions, we overcome a basic limitation for the experimental realization of such dimer systems, namely the construction of one-dimensional dimer chains with beads of different radii. Our results confirm experimentally the occurrence of nonlinear resonances and anti-resonances in dimer chains, and conclusively prove the capacity of appropriately designed granular dimers for passive strong attenuation of propagating pulses due to nonlinear resonance. Moreover, we validate the theoretical prediction that within the elastic range of bead to bead dynamical interactions the results are fully re-scalable with respect to energy. This work provides the first experimental evidence of strongly nonlinear resonances and anti-resonances in essentially nonlinear ordered granular media.