Nonlinear dispersion properties of metamaterial beams hosting nonlinear resonators and stop band optimization

The nonlinear dispersion properties of a metamaterial beam embedding nonlinear resonators are investigated. The metamaterial beam incorporates a distributed array of local resonators exhibiting softening or hardening cubic nonlinearity. The nonlinear dynamic behavior of the metamaterial beam is first investigated asymptotically via the method of multiple scales, which yields the closed-form nonlinear dispersion functions with the associated stop bands and the nonlinear dispersive waves as a combination of acoustic and optical bending waves. The effects of the resonators nonlinearity and the hosting beam nonlinear bending curvature on the stop bands are investigated in terms of sensitivity with respect to the strength and type of resonators nonlinearity. A full multi-variable optimization is carried out to study the nonlinear stop band size variations with respect to the resonators nonlinearity and the acoustic/optical wave amplitudes. The results show how the exploitation of the nonlinearities offers great possibilities to enlarge the size of the stop bands compared to the corresponding linear case and, hence, greatly enhance the energy absorption bandwidth.