Building a metamaterial slab with gosper curve

Abstract

This research is aimed to quantify the extent of sound attenuation achievable through a slab formed by the Gosper structure. A metamaterial slab is designed using Gosper curve which are space coiling structures. The work also explores its potential applicability in creating quieter indoor environments, particularly in the context of creating acoustic barriers by stacking the slabs or making longer structures. The work proposes Peano-Gosper curve (PG), a space-filling and self-avoiding fractal that forms a hexagonal tiling pattern. These patterns were fabricated using concrete 3D printing techniques and evaluated for their sound attenuation. To investigate the sound attenuation capabilities of the Gosper structure, both experimental and numerical methods were employed. A harmonic excitation was applied as input to the structure, and sound transmission loss (STL) was calculated as a function of frequency. The experimental setup involved constructing a prototype slab of the Gosper structure created using additive manufacturing and subjecting it to controlled acoustic testing. Numerical simulations were carried out using finite element analysis, employing suitable material and boundary conditions to replicate real-world scenarios. The results obtained from the experimental and numerical analyses demonstrated a robust sound insulation capability by the single slab Gosper structure (28 dB). The findings suggest that the Gosper structure has the potential to serve as an effective multi-directional acoustic barrier in various architectural applications.