Acoustic band gaps and elastic stiffness of PMMA cellular solids based on triply periodic minimal surfaces

Abstract

In this paper, the acoustic band structure, sound attenuation, and uniaxial elastic modulus of three cellular solids are studied computationally. The cellular solids are generated based on mathematical surfaces, called triply periodic minimal surfaces (TPMS), which include Schwarz Primitive, Schoen IWP, and Neovius surfaces. Finite element method is used to find the acoustic band gaps and sound attenuation of the TPMS structures. The numerical investigation revealed the existence of acoustic bandgaps at low frequencies and low relative densities compared to other cellular structures reported in the literature. The band gap analysis is numerically validated using structures with finite dimensions subjected to varying pressure with multiple frequencies. The influence of the porosity of TPMS on the width of the band gaps is also reported. In the considered porosity range, it is found that lower porosities result in wider acoustic band gaps. Furthermore, the uniaxial moduli of these TPMS are numerically determined using periodic boundary conditions. When the uniaxial modulus of the TPMS-structures is studied against their porosities, it is found that the response of the TPMS-structures lies between stretching- and bending-dominating.