Acoustic band gaps of three-dimensional periodic polymer cellular solids with cubic symmetry

The band structure and sound attenuation of the triply periodic co-continuous composite materials with simple cubic lattice, body-centered cubic lattice, and face-centered cubic lattice consisting of PMMA and air are investigated using finite element method. Complete band gaps are found in these structures and the width of band gaps is depending on volume fraction. It is shown that the width of band gaps along different directions in the first irreducible Brillouin zone enlarges as the volume fraction increases from 0.2 to 0.7. The largest complete band gap widths of the three types of co-continuous structures are 0.29, 0.54, and 0.55, respectively. As the complete band gaps appear in audible range of frequencies, these triply periodic co-continuous composite materials can be utilized to control noise.