## 3 Results and Discussion
### Additional Advantages of Layered Metamaterial Structures
This opening of extra bandgap at the lower frequency in layered-beam metamaterial structure as the number of resonators increases has been witnessed in another generic work on layered metamaterial bandgaps [19]. It is of importance to note that increasing the number of local resonators (unit cells) per horizontal beam comes with an increase in the overall vertical linking beam. Increased forces act on the beam, increasing the overall internal changes on the structure in layered-beam metamaterial structures. In Figure 8C, in addition to the three major bandgaps marked by the shaded area, the sign of a fourth bandgap at a frequency below 100 Hz begins to open-up. Though this is not considered to be a major bandgap because the depth is not significant enough, following a similar approach adopted by [PERSON] et al, it is enclosed by the square in Figure 8C. These extra bandgaps are likely the result of [PERSON]'s scattering phenomena. Additionally, as the number of local resonators increased from 8 to 16, the transmissibility depth of the fundamental local resonator bandgap (292-430 Hz) decreased. This is mainly due to the increase in the number of vertical beams as the number of unit cells increased. That is, the vertical beams make the metamaterial structure stiffer. The advantage of increasing the number of local resonators that are attached to the double-beam metamaterial structure, shown in Figure 8, as compared with increasing the number of local resonators that are attached to the single-beam metamaterial structure, shown in Figure 7, is evident. As the number of local resonators in the double-beam metamaterial structure is increased, the number of vertical beams connecting these beams increases as well. This, consequently, manifests the development of Bragg's scattering frequency bandgaps in the double-beam metamaterial structure. This leads to the development of multiple frequency bandgaps in the double-beam metamaterial structure. Next, the effect of the length of unit cells on the frequency bandgaps is investigated. In Figure 9, the length of the unit cell \(L_{\mathrm{C}}\) is increased by 25% and 50%. Here, the number of local resonators per horizontal beam remained fixed at eight and the design of local resonators was unaltered. In Figure 9A, the results show that as the unit cell's length of the single-beam metamaterial structure was varied, no significant extra bandgaps opened up. The region of the local resonator bandgap remained mostly unaltered when the length of the unit cell was changed. However, in Figure 9B, the results show that altering the length of the unit cell's length for a double-beam metamaterial structure leads to the development of noticeable lower frequency bandgaps. For example, increasing the length of the unit cell by 25% resulted in a low frequency bandgap around 190-225 Hz in addition to the fundamental local-resonator influenced frequency bandgap at 298-410 Hz. In Figure 9A,B, the length of the unit cell \(L_{\mathrm{C}}\) was increased, while the number of local resonators per horizontal beam remained unaltered. A 25% increase in the length of the unit cell for double-layered structure shifted the [PERSON]'s scattering lower frequency bandgap from 238-275 Hz to 190-225 Hz. This is not uncommon, as multiple works in the literature have shown that an increase in the length of unit cells while the number of unit cells remained constant leads to the development of [PERSON]'s bandgap at the lower frequencies below the central local resonator bandgap [6; 32; 33]. Moreover, one can notice that the number of bandgaps generated by altering the length of the unit cell, i.e., Figure 9B, is less than the number of bandgaps generated from increasing the number of local resonators per beam, i.e., Figure 8. Nonetheless, as shown in Figure 9B, changing the length of the unit cell offers a good alternative for lowering frequency bandgaps when it is desired to keep the number of local resonator constant.