(Left) Porous matrix with periodically embedded spherical Helmholtz resonators. (Right) Period of the media with spherical Helmholtz resonator.
(Color online) (left) Granular media made of Helmholtz resonators of different resonant frequency; (right) period made of a porous matrix with embedded Helmholtz resonator whose the duct enables enhanced damping.
(Color online) Dimensionless wave velocity of a porous media with embedded resonators at concentration with . (Top) Modulus and (bottom) phase versus dimensionless frequency . Matrix of porosity (left) ; (right) . Bold line: low damped resonator . Bold dashed line: resonator with enhanced damping, namely, for (left); resonator with lower damping, namely, for (right). For comparison, the characteristics of the single porosity media that match the low [Eq. (19) ] and high [Eq. (20) ] frequency behavior are drawn in normal and dashed lines.
(Color online) Same as Fig. 3 except that and that the bold dashed lines correspond to resonators with enhanced damping (left) for and (right) for .
(Color online) Same legend as Fig. 3 except that and that the bold dashed lines correspond to damped resonator: (left) for ; (right) for .
(Color online) Wave characteristics versus frequency of resonator of eigen-frequency f 0 = 473 Hz embedded (left) in a dense fibrous media, and (right) in an open cell foam. (Top) Real part and Absolute value (dashed line) of the velocity divided by the sound velocity. (Bottom) Attenuation factor (presented with opposite value to enable correspondence with the velocity).
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