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

• LRs can obviously reduce effective speeds of LRSMs with low-shear-speed matrices.
• Bragg gaps can occur at sub-wavelength region by reducing effective speeds of LRSMs.
• The approaching of gaps broadens the bandwidth and increases the depth of gaps.
• The gap-coupled LRSM exhibits a broad transmission gap in sub-wavelength region.
• A coupled gap has a good sound blocking and absorbing performance if loss considered.

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.