Acoustic process of second harmonic generation in a one-dimensional diatomic granular chain
Résumé
The acoustic process of second harmonic generation in a diatomic granular chain is studied in the weakly nonlinear regime. The diatomic granular chain is a phononic crystal which exhibits band gaps and two modes of propagation for the longitudinal elastic waves. In the limit of a much higher applied static stress on the chain than the dynamic perturbation of the wave, the quadratic approximation for the elastic non-linearity of each constant is taken. Analytic results accounting for this quadratic nonlinearity of contacts and keeping a discrete description of the medium (which allows to consider strong dispersive regimes) are presented. They are compared to experimental results obtained in a 1D chain made with millimeter scale grains of two different masses arranged alternatively. Different cases are analyzed depending on the propagative or evanescent character of the fundamental on harmonic waves and on the acoustical or optical-type propagation modes. Finally, we observe and provide interpretations on the nonlinear resonances of the finite diatomic chain.
Domaines
Acoustique [physics.class-ph]
Origine : Fichiers éditeurs autorisés sur une archive ouverte