Band gaps in the low-frequency range based on the two-dimensional phononic crystal plates composed of rubber matrix with periodic steel stubs

In this paper, the numerical investigation of elastic wave propagation in two-dimensional phononic crystals composed of an array of steel stepped resonators on a thin rubber slab is presented. For the first time the rubber material is used as the matrix of the PCs. With the finite-element method, the dispersion relations of this novel PCs structure and some factors of the band structure are studied. Results show that, with the rubber material as matrix, the PC structures exhibit extremely low-frequency band gaps, in the frequency range of hundreds of Hz or even tens of Hz; the geometrical parameters and the material parameters can modulate the band gaps to different extents. Furthermore, to understand the low-frequency band gaps caused by this new structure, some resonance eigenmodes of the structure are calculated. Results show that the vibration of the unit cell of the structure can be seen as several mass–spring systems, in which the vibration of the steel stepped resonator decides the lower boundary of the first band gap and the vibration of the rubber that is not in contact with the resonator decides the upper boundary.