Magnetorheological Elastomer Plate-Based Acoustic Metamaterials: Mass Loading Versus Field Stiffening

Plate-based acoustic metamaterials (AMM) have demonstrated potential as a lightweight strategy to combat low frequency noise. One-dimensional unit cells are commonly composed of a plate or membrane separating two acoustic volumes bounded by rigid walls, which are then tiled in space to create a resonant lattice of plates set in a homogenous acoustic background. The robust dynamics of a plate-based AMM stem from the interaction between plate stiffness and density distributions, which control resonance frequencies and bands of acoustic transmission. However, a key challenge of this AMM approach is the limited ability to reprogram the plate for a new configuration of plate resonances.  To address this issue, we developed a programmable AMM unit cell based on a magnetorheological elastomer (MRE) plate with resonances that are readily tuned by adjusting the location and strength of permanent magnets distributed across the plate surface, or around the rigid rim of the plate fixture. When magnetic masses are added directly to the plate surface, the mass loading effect is largely responsible for changes in its vibrational pattern since the magnetic stiffening effect is masked by the attachment of the rigid permanent magnet. On the other hand, by placing the magnets at a motionless part of the plate (i.e. the part clamped in the rigid fixture at the rim) any changes in vibrational pattern are necessarily due to the magnetic field induced stiffening effect for which MRE are best known. Different combinations of polarity and magnetic source position cause different field distributions to develop in the MRE thereby providing a second method of mode shape control. Thus, the MRE approach enables exploration of coupling dynamics between the magnets as lumped masses and the role of local stiffening in the elastomer plate. In addition, the combination of the high-density and low-stiffness of the plate allows for near infrasonic frequencies to be addressed by a thin panel. In this study, comparisons are made between the acoustic transmission and absorption of the case with magnets attached directly to the plate (i.e. mass loaded) and the case where the magnets are placed in the fixture (i.e. field stiffened).  Impedance tube experiments are used to characterize the MRE-AMM transmission loss, and absorption, and measure the effective density of each plate configuration, and links are made between finite element derived plate mode shapes and the associated transmission/absorption behavior.  Transfer matrix method-based calculations are then used to predict the experimental dispersion curves of the unit cell and compared to those predicted by the finite element method.