Active feedback control of effective mass density and sound transmission on elastic wave metamaterials.

• The effective mass density is derived and the dynamic responses are presented by the dynamic effective medium method. • The sound transmission loss (STL) is obtained based on the principle of virtual work. • The negative mass density and STL in the lower frequencies can be adjusted by the active feedback control. With the active feedback control system on elastic wave metamaterials, this research is concentrated on the effective mass density and sound transmission by a harmonic incident sound pressure. The elastic wave metamaterials consist of double plates which are attached by the upper and lower four-link mechanisms being bonded with four lateral resonators. The vertical resonator in every unit cell is jointed by the active feedback control system which is connected by two four-link mechanisms. Using the dynamic effective medium method, the expressions of the effective mass density are obtained and the dynamic responses are presented. Based on the Bloch–Floquet theorem and Poisson summation formula, the sound transmission loss (STL) of this elastic wave metamaterial is shown by the principle of virtual work. This research also shows that the characteristics of the effective mass density and STL can be tuned by the acceleration and displacement feedback in the active control system. Furthermore, it is found that the dynamic response and STL are also changed obviously by different incident angles (including the elevation and azimuth angles), the periodicity spacing of local resonators and the structural damping. [Display omitted] Composite Figure: Elastic wave metamaterials is presented in this work as shown in (a) the structure with local resonators attached to the active feedback control systems. The effective mass density is derived and the dynamic responses are presented by the dynamic effective medium method, there are two modes and appear two negative density regions in the double plates model, (b) in-phase and (c) anti-phase modes of the dynamic effective mass density. Based on the incident sound pressure wave, the sound transmission loss (STL) is obtained by the principle of virtual work, the STL can be tuned in the lower frequency region by the active control, (d) influences of the positive acceleration and (e) the displacement feedback control on the STL. [ABSTRACT FROM AUTHOR]