On the dynamic behavior of mono-coupled continuous structures attached to nonlinear resonators

Abstract

Acoustic metamaterials are structures built using repetitive assemblies of identical elements to explore Bragg-scattering or internal resonance to control mechanical waves. These structures have frequency bands in which waves do not propagate, allowing acoustic and vibration reduction at various frequency ranges. In this work, the effects of nonlinear resonators on continuous mono-coupled periodic structures based on the concept of transmissibility of a single cell of a finite structure are investigated, which can be related to the dispersion diagram of an infinite structure. To find isolated solutions and control the numerical process internally, a strategy using the Homotopy continuation algorithm for a system of algebraic nonlinear polynomials using the package Bertini is proposed. This investigation contributes to understanding improvements provided by nonlinear elements for vibration control of a periodic structure via single cell analyses.