# Seismic Isolation via I-Shaped and T-Shaped Large-Scale Phononic Metamaterials
## 4 Discussion and Conclusions  
The protection of critical infrastructure against a seismic event or ground vibrations that could be created from manmade sources, such as a railway or an industrial unit, is mandatory, and the scientific and technological community are seeking effective ways for achieving this goal. At the present contribution, the artificial structures that were studied numerically were based on the well-known concepts of PCs and AMs. This study included a first set of calculations of the band structure for each studied geometry. The results for the I-shaped LSPMs showed PBGs only along the \(\rm I\)X direction, whereas the relevant calculations for the T-shaped LSPMs provided complete PBGs along all directions of the first Brillouin zone. After a numerical research for the optimum parameters, the I-shaped geometry provided an optimal performance for length \(\rm L=0.9\alpha\) and \(\rm w=0.4\alpha\), whereas the best performance for the T-shaped geometry was achieved by minimizing the horizontal part of the T-shape and therefore for \(\rm L=0.9\alpha\), \(\rm w=0.25\alpha\), \(\rm w_{T}=0.65\alpha\), and for \(\rm L_{T}=0.1\alpha\). For all the examined cases, the lattice constant was kept at \(\rm\alpha=10\) m. The filling of each structure with a rubber-coated steel core reduced the lower limits of the PBGs for specific cases, although this reduction was not significant and the widths of the PBGs were smaller compared to those of the empty trenches, either of I-shape or T-shape. It is evident according to the results of the calculations that one major advantage of the T-shaped LSPMs is that they provide complete PBGs along all directions of the first Brillouin zone in contrast to the I-shaped LSPMs, for which the PBGs are only along the \(\rm I\)X direction. Furthermore, for both examined geometries, the empty trenches should be considered a preferable solution compared to the relevant with a rubber-coated steel core. Apart from the smaller PBGs provided by the latter, the empty trenches are much simpler in construction and, consequently, should be much more cost-effective. It should also be mentioned at this point that the gaps for both cases of the empty trenches could be further tailored by choosing a higher lattice constant, which will result in even lower limits of the PBGs. Another issue that arises from the numerical results concerning the case of the empty trenches, T-shaped or I-shaped, is which one should be preferable according to the results. As already mentioned, T-shaped LSPMs provide complete PBGs, whereas the PBGs of the I-shaped LSPMs are only along the \(\rm I\)X direction. On the other hand, the I-shaped LSPMs seem to be more effective as they provided the best studied performance. As already commented, for this case, the two calculated PBGs along the \(\rm I\)X direction were found within the lowest frequencies, between 1.68 and 3.10 Hz and between 3.26 and 3.74 Hz, and the first gap had the highest calculated width \(\Delta f/f_{g}=0.59\). The fact that this structure does not provide complete PBGs but only along the \(\rm I\)X direction could be technically overcome by placing a sequent of the relevant I-shaped trenches on the periphery of a structure to be protected and thus achieving protection from all possible directions of the incoming surface wave. Alternatively, I-shaped trenches could be an ideal solution for cases where the placement of the vibration source is known, such as a railway or, for the case of seismic waves, a known and well-established seismic fault. The calculations of the band structures were followed by a set of higher computational cost simulations in a more realistic scheme to have a more holistic approach to the studied geometries. The transmission spectrum was calculated for the I-shaped LSPM, which provided the most promising attenuation characteristics as explained in the previous section.