On the coupling of resonance and Bragg scattering effects in three-dimensional locally resonant sonic materials.

Three-dimensional (3D) locally resonant sonic materials (LRSMs) are studied theoretically for purpose of optimising their sub-wavelength performance by coupling resonance and Bragg scattering effects together. Through the study of effective sound speeds of LRSMs, we find that the starting frequency of Bragg scattering can be shifted to sub-wavelength region by softening coats of resonators when the matrix is a low shear-velocity medium. A similar result can be achieved by compressing the lattice constant. By using a layer-multiple-scattering method, we investigate the complex band structure and the transmission spectrum of an LRSM whose Bragg gap is already close to the resonance gap in frequency. The wave fields of the composite simulated by COMSOL are further analysed at several typical frequencies. The result shows that the approaching of two kinds of gaps not only broadens the bandwidth of the resonance gap, but also increases the depth of the Bragg gap since the interaction between resonant modes and scattering waves are enhanced. By varying the shear velocity of coats, we obtain a coupled gap, which exhibits a broad transmission gap in the sub-wavelength region. When the loss of coats is considered, the coupled gap can not only maintain a good sound blocking performance, but also perform an efficient absorption in the low frequency region.

Analysis of absorption performances of anechoic layers with steel plate backing.

Rubber layers with air-filled cavities or local resonance scatters can be used as anechoic coatings. A lot of researches have focused on the absorption mechanism of the anechoic coatings. As the anechoic coatings are bonded to the hull of submarine, the vibration of the hull should not be neglected when the analysis of the absorption characters is carried out. Therefore, it is more reasonable to treat the anechoic coating and the backing as a whole when the acoustic performance is analyzed. Considering the effects of the steel plate backing, the sound absorption performances on different models of anechoic coatings are investigated in this paper. The Finite Element Method is used to illustrate the vibrational behaviors of the anechoic coatings under the steel backings by which the displacement contours is obtained for analysis. The theoretical results show that an absorption peak is induced by the resonance of the steel slab and rubber layer. At the frequency of this absorption peak, the steel plate and the coating vibrates longitudinally like a mass-spring system in which the steel slab serves for mass and the coating layer is the spring. To illuminate the effects of the steel slab backing on the acoustic absorption, the thicknesses of the steel slab and the anechoic layer are discussed. Finally, an experiment is performed and the results show a good agreement with the theoretical analysis.

Effects of locally resonant modes on underwater sound absorption in viscoelastic materials.

Recently, by introducing locally resonant scatterers with spherical shape proposed in phononic crystals into design of underwater sound absorption materials, the low-frequency underwater sound absorption phenomenon induced by the localized resonances is observed. To reveal this absorption mechanism, the effect of the locally resonant mode on underwater sound absorption should be studied. In this paper, the finite element method, which is testified efficiently by comparing the calculation results with those of the layer multiple scattering method, is introduced to investigate the dynamic modes and the corresponding sound absorption of localized resonance. The relationship between the resonance modes described with the displacement contours of one unit cell and the corresponding absorption spectra is discussed in detail, which shows that the localized resonance leads to the absorption peak, and the mode conversion from longitudinal to transverse waves at the second absorption peak is more efficient than that at the first one. Finally, to show the modeling capability of FEM and investigate shape effects of locally resonant scatterers on underwater sound absorption, the absorption properties of viscoelastic materials containing locally resonant scatterers with ellipsoidal shape are discussed.

Two-dimensional locally resonant phononic crystals with binary structures.

The lumped-mass method is applied to study the propagation of elastic waves in two-dimensional binary periodic systems, i.e., periodic soft rubber/epoxy and vacuum/epoxy composites, for which the conventional methods fail or converge very slowly. A comprehensive study is performed for the two-dimensional binary locally resonant phononic crystals, which are composed of periodic soft rubber cylinders immersed in epoxy host. Numerical simulations predict that subfrequency gaps also appear because of the high contrast of mass density and elastic constant of the soft rubber. The locally resonant mechanism in forming the subfrequency gaps is thoroughly analyzed by studying the two-dimensional model and its quasi-one-dimensional mechanical analog. The rule used to judge whether a resonant mode in the phononic crystals can result in a corresponding subfrequency gap or not is found.