Wave Dispersion in One-Dimensional Nonlinear Local Resonance Phononic Crystals with Perturbation Method

Abstract

Nonlinear phononic crystals are receiving increasingly greater attention in the field of sound absorption and vibration reduction. In this paper, we use the perturbation method to investigate elastic wave propagation in one-dimensional discrete local resonance nonlinear phononic crystals. The nonlinear force on the inner resonator is expressed in the form of a linear part plus a cubic nonlinear fluctuation. By combining Bloch wave theory and the perturbation method, the nonlinear dispersion relation is obtained by a first-order approximate analytical solution. The results show that the band’s cut-off frequency is not only affected by the degree of nonlinearity but is closely related to the wave amplitude. In addition, the finite element method is used for comparison and verification. Finally, an application example of a wave filter is provided based on the nonlinear characteristics.