Analytical and experimental investigation on sound transmission of double thin plates with magnetic negative stiffness

Transmission loss of acoustic metamaterials (AM) made of double thin plates with magnetic (negative) stiffness was analyzed using theory, finite element analysis and experimental techniques. The theoretical formulation was done using a rectangular duct below the first cut off frequency, the model is then validated against finite element method and experiment. Two cubic magnets were used, their interaction force and the resulted magnetic stiffness were calculated. The sound transmission loss (STL) of the structure is calculated for plane wave condition, the addition of magnetic mass shifts STL peaks to the lower frequency compared to a structure without mass. The slight increase in STL for small negative stiffness in experiment is not enough to cancel the effect of air compressibility. However, a significant enhancement could be expected if negative stiffness can be made large enough in the double thin plates. The developed AM can be employed as a prospective sound engineering control at low frequency.