The ability to control the dynamic effective parameters with these metamaterials has attracted considerable attention. Comparing with the novel materials, one of the significant properties of the elastic wave metamaterials is the negative dynamic effective material parameter in some frequency regions. Recently, elastic wave metamaterials have been widely applied to the acoustic fields, e.g., sound radiation, nonreciprocal wave propagation, acoustic clock and sound transmission. Moreover, elastic waves cannot propagate at some frequency ranges because of the band gaps. As periodic artificial materials and structures, phononic crystals are characterized by the regulation and control of their elastic properties, including elastic constants, moduli and mass densities, etc. Phononic crystals have received a great deal of attention since nearly two decades ago. This paper is expected to be helpful for understanding the sound transmission properties of both pure single- and double-plate models. The results for sound transmission by two methods are compared, i.e., the virtual work principle for double plates and the dynamic equivalent method corresponding to a single one. In addition, the dynamic response and the STL are also changed obviously by different values of structural damping, incident angle (i.e., the elevation and azimuth angles) and Mach number of the external fluid with the mean flow property. This research shows the influence of effective mass density on sound transmission properties, and the STL in both modes can be tuned by the acceleration and displacement feedback constants. With the coupling between the fluid and structure, the expression of the sound transmission loss (STL) is derived. Based on the dynamic equivalent method, the metamaterial is equivalent as a single-layer plate by the dynamic effective parameter. The vertical resonator is attached by the active feedback control system and connected with two four-link mechanisms. The elastic wave metamaterial consists of double plates and the upper and lower four-link mechanisms are attached inside. The metamaterial is subjected to an incident pressure and immersed in the external mean flow. Using the active feedback control system on the elastic wave metamaterial, this research concentrates on the sound transmission with the dynamic effective model.
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