## 3 Results and Discussion
### Additional Advantages of Layered Metamaterial Structures  
Furthermore, the effect of increasing the number of local resonators per beam is explored. Here, the number of local resonators that are attached to the single-beam metamaterial structure, shown in Figure 1, is increased from 8 to 12 and then 16. In effect, the number of unit cells are increased while the length of unit cells remains the same. This leads to changes in the overall length of the horizontal beams. The results are shown in Figure 7.  
Figure 7 shows that a single notable frequency bandgap is developed when the number of local resonators that are attached to the beam is increased from 8 to 16. The frequency bandgaps, marked by the shaded area in Figure 7, are 300-415 Hz, 298-438 Hz, and 296-438 Hz for 8, 12, and 16 local resonators, respectively. No additional significant frequency bandgaps open up when the number of local resonators is increased from 8 to 16, as shown in Figure 7. These single frequency bandgaps correspond to the region of the resonant frequency of the local resonators. In addition, the results from Figure 7 show that the width of the local resonator bandgap becomes broader when the number of local resonators increased from 8 to 12 and then 16 resonators. This broadband frequency bandwidth can be attributed to the merging of small Bragg's scattering bandgaps that are developing close to the local resonator bandgap with the fundamental local resonator  
Figure 6: Transmissibility and frequency bandgaps generated from model simulations of a double-layered beam-type metamaterial structure with 8 resonators and using the parameters shown in Table 1. Results show two significant frequency bandgaps, i.e., 238–275 Hz and 300–410 Hz, marked by the shaded area. bandgap. This widening of central local resonator bandgap as a result of [PERSON]'s scattering bandgaps developing close to it is called coupled-resonance-Bragg's bandgap and has been reported by multiple researchers in the literature [6; 32; 33]. In a similar fashion, the effect of increasing the number of local resonators per horizontal beam on the transmissibility of the double-beam metamaterial structure, shown in Figure 4, is analyzed next. Figure 8 displays the frequency bandgaps obtained when the number of local resonators is increased from 8 to 16 per horizontal beam. Figure 7: Transmissibility and frequency bandgaps of a single-beam metamaterial structure obtained using model simulations when the number of local resonators is increased: (**A**) A single-beam metamaterial structure with 8 local resonators; (**B**) a single-beam metamaterial structure with 12 local resonators; (**C**) a single-beam metamaterial structure with 16 local resonators. Figure 8 shows two main outcomes. First, a major broad frequency bandgap lives near resonance frequency of the local resonators, i.e., 298-410 Hz for 8, 12, and 16 local resonators, respectively. These frequency bandgaps did not witness a significant change in their width as the number of local resonators increased. This is likely because there was no alteration to the shape and design of the local resonators. Moreover, as the number of local resonators per horizontal beam is increased from 8 to 16 additional bandgaps  
Figure 8: Transmissibility of a double-beam metamaterial structure when the number of local resonators per horizontal beam is increased: (**A**) A double-beam metamaterial structure with 8 local resonators; (**B**) a double-beam metamaterial structure with 12 local resonators; (**C**) a double-beam metamaterial structure with 16 local resonators. opened up. These additional bandgaps tend to exist in the lower frequency region. For example, as shown in Figure 8, a second frequency bandgap opened up at 238-275 Hz, 267-281 Hz, and 279-286 Hz for 8, 12, and 16 local resonators, respectively. In Figure 8B, a third bandgap opened up at 126-157 Hz.