Sound transmission of active elastic wave metamaterial with double locally resonant substructures surrounded by external mean flow

Abstract

The elastic wave metamaterial with active feedback control is presented to discuss its dynamic effective parameter and sound transmission properties. Both studies are initiated from the local resonance with the active feedback control and dynamic structural response. The acoustic-structure coupling of the metamaterial with resonators and orthogonal stiffeners are analyzed with effects of the external mean flow. Different analytical methods are used to derive the effective mass density and sound transmission loss (STL) of the elastic wave metamaterial. The effective density is obtained by the dynamic effective medium method firstly. And the second one applies the spatial harmonic expansion method with the principle of virtual work for the STL based on the Bloch–Floquet theorem and Poisson summations. The effective mass density shows frequency-dependent properties and appears positive and negative values in a certain frequency region simultaneously. This research also illustrates both characteristics can be tuned by the active feedback control with the acceleration and displacement feedback control actions. Numerical results of coupled structures show that the changes of transmission characteristics in the certain frequency region are consistent with the effective mass density properties of uncoupled unit cell structure. In addition, influences of the lattice constants, incident angles and Mach number on the STL are illustrated and discussed.