Extending and lowering band gaps by multilayered locally resonant phononic crystals

Locally resonant phononic crystals (LRPCs) have band gaps with low frequencies and the size of the cell is much smaller than the wave lengths of the band gaps. This unique property makes them good candidates for vibration control. Considering that the band gaps of the LRPCs are determined by the single cell rather than the periodic arrangement, it is important to design the microstructure of the cell. In this paper, band structures and transmission spectra of two dimensional multilayered LRPCs are investigated by the finite element method (FEM). It is found that the band gaps of the LRPCs can be extended to several frequency ranges by periodically embedding multilayered coaxial inclusions (i.e., alternate shells of soft rubber and hard metal) into a matrix. Moreover, the frequency responses of the multilayered periodic structures with different number of cells are simulated. There are several sharp dips which refer to high attenuation efficiency in the transmission spectra of the periodic structures with multilayered inclusions. The increase in the number of cells is also found to enhance the attenuation efficiency. Meanwhile, the geometrical effects of the layers on the band structures are investigated. By carefully designing the size and number of the shells in the multilayered inclusions, the band gaps can be extended and lowered. These results are helpful for the applications of LRPCs in noise and vibration control.