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

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

Abstract

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

Keywords

Perturbation Analysis Stop Band Granular Chain Periodic Chain Diatomic Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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
  • 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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