Analytical and Experimental Analysis of Bandgaps in Nonlinear one Dimensional Periodic Structures

  • Nicholas Boechler
  • Chiara Daraio
  • Raj K Narisetti
  • M. RuzzeneEmail author
  • M. J. Leamy
Conference paper
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 26)


Wave propagation characteristics of nonlinear one-dimensional periodic structures are investigated analytically, numerically and experimentally. A novel perturbation analysis is first applied to predict the band gap location and extent in terms of linear and nonlinear system parameters. Approximate closed-form expressions capture the effect of nonlinearities on dispersion and depict amplitude dependent cut-off frequencies. The predictions from the perturbation analysis are verified through numerical simulations of harmonic wave motion. Results indicate the possibility of input amplitude as a tuning parameter through which cut-off frequencies can be adjusted to achieve filtering properties over selected frequency ranges. A periodic diatomic chain of stainless steel spheres alternating with aluminium spheres is experimentally investigated. The dynamic behavior of the chain is governed by Hertzian interaction of spheres and by a compressive pre-load which can be adjusted to obtain linear, weakly nonlinear and highly nonlinear behavior. For a weakly nonlinear case, preliminary results in experiments show the tendency for a shift in the band gap edges by varying input amplitude. The paper is a work in progress, for which the experimental results for a weakly nonlinear system are interpreted by the perturbation analysis developed for a specific case of linear and nonlinear power law interaction of exponent 3/2


Perturbation Analysis Stop Band Granular Chain Periodic Chain Diatomic Chain 
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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Nicholas Boechler
    • 1
  • Chiara Daraio
    • 1
  • Raj K Narisetti
    • 2
  • M. Ruzzene
    • 2
    Email author
  • M. J. Leamy
    • 3
  1. 1.Aeronautics and Applied PhysicsCalifornia Institute of TechnologyPasadenaUSA
  2. 2.Department of Aerospace EngineeringGeorgia Institute of TechnologyAtlantaUSA
  3. 3.Department of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA

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