Smart controllable wave dispersion in acoustic metamaterials using magnetorheological elastomers

The success in the flexible design of smart acoustic metamaterials is crucially contingent upon the degree of control over the parameters that uniquely define the spectrum of band structure and morphology of dispersion surfaces. In this work, we have studied the driving physical mechanisms, the control of which makes possible operating, in real-time, on the set of band gaps formed in 3D metamaterials based on magneto elastomers. In such acoustic structures, the stiffness of the medium in which unit cells are immersed, as well as the stiffness of the shells surrounding multi-particle cores depend on the induction, B(t), of an external magnetic field. The results obtained are systematized through the qualitative analysis of diversе scenarios for the evolution of the frequency characteristics of the metamaterial and summarized in the following complete physical picture of their dynamics. Variation of the stiffness of the medium/shells changes the wavelength of the shell's surface waves at characteristic frequencies of the core vibrations and, as a result, the level of coupling between the vibration modes of the flexible shells and cores. Consequently, with an increase/decrease in the stiffnesses of the shells/medium, the dispersion surfaces of the entire acoustic system shift up/down along the frequency axis with noticeably different 'mobilities' that reversibly lead either to the formation of the band gaps in initially dense frequency spectrum or to the transformation of the band gaps formed into pass bands. The tuning of the set of dispersion surfaces depending on the range of changes in the magnetic field induction can be carried out in dynamic, quasi-stationary, and over-critical regimes when some of the dispersion surfaces degenerate into planes. In anisotropic metamaterials, simultaneously with creating full band gaps, it is possible to create tunable directional band gaps with adjustable frequency and angular widths. The results obtained, within the framework of the idealized discrete mass-spring model, are in good agreement with the data presented in the available experimental works and can be useful in the design of acoustic systems with desirable properties.