Wave modulation in a nonlinear acoustic metamaterial

Abstract The nonlinear modulation of waves in a metamaterial mass-in-mass lattice model is studied. The governing continuum nonlinear equation is obtained from the original discrete model. The important differences in the modulated nonlinear wave dynamics on the acoustic or optical bands are described analytically. It is shown that the choice of the band can affect the shape of the modulated nonlinear wave and the modulation velocity. The nonlinearity affects the width of the band gap early obtained in the linear approximation. An inclusion of viscoelastic interaction in the original model results in a new variation of the amplitude of the modulated wave.