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

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.

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