## 4 Conclusions  
In this article, limitations and advantages of both single-beam metamaterial structures and layered-beam metamaterial structures are presented. The single-beam metamaterial structure presented in this article consists of a free-free horizontal beam with equally spaced local resonators attached to the horizontal beam. The layered-beam metamaterial structure is comprised of layered horizontal beams linked by vertical beams. In this work, the Euler-Bernoulli beam equation and superposition of mode shapes were used to analyze the displacement of the beams. The analysis of frequency bandgaps and transmissibility were carried out using the frequency response function (FRF). Figure 9: The effect of length of unit cells on transmissibility and frequency bandgaps: (**A**) A single-beam metamaterial structure with 8 local resonators per horizontal beam; (**B**) a double-beam metamaterial structure with 8 local resonators per horizontal beam. The lengths of the unit cells are changed from \(L_{C}\), to \([1.25\times L_{C}]\) and \([1.50\times L_{C}]\). Results from this work show differences between the bandgap developed in single-beam metamaterial structures and layered-beam metamaterial structures. These differences are vital points of interest for designers who are considering the choice of single-beam metamaterial structure or layered-beam metamaterial structure for a specific engineering application. The main conclusions from this work include:  
* For a single-beam metamaterial structure with equally spaced local resonators of the same design, there is a single notable frequency bandgap near the region of the resonant frequency of the local resonators. * Increasing the number of local resonators that are attached to the horizontal beam of the single-beam metamaterial structure does not yield multiple bandgaps. Nonetheless, increasing the number of local resonators that are attached to the horizontal beam of the single-beam metamaterial structure may slightly increase the width of the local resonator bandgap. This increase in width is likely due to the merging happening between the fundamental local resonator bandgap and adjacent, smaller, Bragg's scattering bandgaps. * When it is desirable to maintain the design of the local resonators in the metamaterial structure, layering the horizontal beams offers a means for both lowering the frequency bandgap and developing additional bandgaps. * Unlike single-beam metamaterial structures, increasing the number of local resonators per horizontal beams in the layered metamaterial leads to the birth of additional lower frequency bandgaps. * In applications where attempts to lower the transmissibility bandgap by increasing the number of local resonators is not feasible, small changes to the length of the unit cells can be a viable option. Changes to the length of the unit cells while keeping the number of local resonators constant also leads to lower frequency bandgaps. * The ability of the layered-beam metamaterial structure to generate both multiple and lower frequency bandgaps through a variety of parametric changes will offer a lot of options in application use-cases of dual-purpose vibration isolation energy harvesting. This is important as recent reports in the literature show increased interest in the use of layered-beam metamaterial structures for energy harvesting. [PERSON] was involved in the data collection, formal analysis, software, validation, investigation and visualization; [PERSON] was responsible for the conceptualization, funding acquisition, methodology, project administration, resources, software supervision, and writing, reviewing, and editing of the original draft. All authors have read and agreed to the published version of the manuscript.