Active control for acoustic wave propagation in nonlinear diatomic acoustic metamaterials

Wave propagation through nonlinear acoustic metamaterials has generated numerous scientific interests for their enormous potential in practical applications these years. This study focuses on the effects of nonlinearity on the band properties of diatomic mass-in-mass chain with active control. By applying the Lindestedt-Poincaré (L-P) perturbation method, analytical dispersion relations of the linear and nonlinear diatomic mass-in-mass system have been established and investigated by numerical simulation. Different from the monatomic mass-in-mass chain, this two mass-in-mass units forming a unit cell of the periodic structure results in four branches of the dispersion relation. The effects of nonlinearity on the band gaps of the system have been exhaustively illustrated. By only tuning the nonlinear constitutive relation parameter of the spring, the fourth branch and the third gap are found to be more sensitive compared to the other branches and gaps. It is concluded that closing and re-opening of the band-folding-induced gap in this nonlinear system is still possible. Here, a piezoelectric spring model is applied to the diatomic mass-in-mass to make the system available for wider applications. With the negative proportional control, a new stop band is generated which can be also captured in the monatomic nonlinear system. The new results here will help better analyze the band gap properties in nonlinear mechanical metamaterials and emphasize the great potentials of the topological analysis of such a nonlinear local resonance system that induces band-folding-induced band gaps.