Table 2 Cavity resonances predicted via Finite Element (narrow viscous model) and the analytical formulation for the various fractal orders. The Finite Element results related to each mode are calculated by averaging the values of those modes over the different gap widths considered in this work. The standard deviations of those frequencies are normalised against the corresponding average value. The last column refers to the analytical resonance frequency related to an open-closed cavity..
From: Acoustic transmission loss in Hilbert fractal metamaterials
Fractal order \(\xi \) | Mode number | FEM mean [Hz] | Normalised standard deviation (%) | Eq. (1) |
|---|---|---|---|---|
0th | 1st | 1472.2 | 1.6 | 1548.7 |
1st | 1st | 811.2 | 0.3 | 807.3 |
2nd | 1st | 426.6 | 0.8 | 412.6 |
2nd | 2nd | 1295.3 | 1.3 | 1237.7 |
3rd | 1st | 224.8 | 0.8 | 208.6 |
3rd | 2nd | 685.3 | 1.1 | 625.8 |
3rd | 3rd | 1148 | 1.5 | 1043 |
3rd | 4th | 1602.5 | 1.3 | 1460.2 |
4th | 1st | 328 | 0.8 | 314.7 |
4th | 2nd | 553.7 | 0.7 | 524.5 |
4th | 3rd | 781 | 1.1 | 734.3 |
4th | 4th | 1008 | 1.1 | 944.1 |
4th | 5th | 1235.3 | 1.0 | 1153.9 |
4th | 6th | 1462.7 | 1.2 | 1363.7 |
4th | 7th | 1689.3 | 1.3 | 1573.5 |
