Stretched, Compacted and Skewed The Erratic Life of Waves in Nonlinear Phononic Chains
Stefano Gonella
Department of Civil Engineering
University of Minnesota
Abstract
Nonlinear phononic crystals owe their appeal to their ability to behave as flexible mechanical filters, which is due to the inherent nonlinearity-induced tunability of their wave propagation and attenuation zones. The main motive of this study is to understand the wave propagation characteristics that are intimately responsible for this macroscopic bandgap modulation. In parallel, we wish to provide a complete map of the complex packet distortion phenomena that appear in nonlinear phononic chains as a result of the tight interplay between nonlinear and dispersive mechanisms. These objectives are pursued by monitoring the spectro-spatial features of the wave profiles that are established in the chains through the excitation of tone bursts with variable frequency content. The first characterization is conducted on two benchmark mono-atomic chains, involving springs with cubic and quadratic hardening, respectively. For the cubic case, it is shown that the interplay between nonlinearity and dispersion can be recognized in the sustained motion of bi-modal wave packets with solitary-wave-like features and certain nonlinearity-insensitive energy propagation characteristics. For the quadratic case, the nonlinear behavior manifests as a non-symmetric modulation of the linear dispersive response by a long-wavelength sigmoidal profile. These observations are used to construct a set of simple inverse problems which can be used to distill the signature of the nonlinear effects from the dispersive response and consequently estimate the nonlinearity of systems with arbitrary complexity. The generality and versatility of the analysis is finally demonstrated though the inverse characterization of granular chains governed by different Hertzian power laws.