###### Abstract  
Recently, layered-beam metamaterial structures have been gaining popularity in a variety of engineering applications including energy harvesting and vibration isolation. While both single-beam metamaterial structures and layered-beam metamaterial structures are capable of generating bandgaps, it is important to understand the limitations of each type of metamaterial structure in order to make informed design decisions. In this article, a comparative study of bandgap development in single-beam metamaterial structures and layered-beam metamaterial structures is presented. The results show that for the single-beam metamaterial structure, with equally spaced local resonator designs, only one significant bandgap is developed at approximately 300-415 Hz. This bandgap occurs near the resonant frequency of the local resonators, i.e., 309 Hz. The results also show that when the spacing and the design of the local resonators are desired to remain fixed, layering the horizontal beams offers a significant pathway for both lowering the bandgap and developing additional bandgaps. The double-layered beam-type metamaterial structure studied in this work generates two bandgaps at approximately 238-275 Hz and 298-410 Hz. When the goal is to keep the number of local resonators per beam constant, increasing the length of the unit cells offers an alternative technique for lowering the bandgaps. layered-beam metamaterial; local resonators; transmissibility bandgaps; single-beam metamaterials; vibration isolation +
Footnote †: journal: Applied Sciences  
bandgaps are influenced by the design of the mechanical beam metamaterial structures. Moreover, the advent of local resonators contributed to greater flexibility in either lowering or expanding the bandgaps generated from metamaterial beam structures [6; 24]. These local resonator (LR) bandgaps result from the design of the local resonators and typically occur at frequencies around the resonant frequencies of the resonators [6; 7; 14; 18; 21; 24; 25]. Recently, various groups have worked on developing different designs for the local resonators in order to vary and control the bandgaps of these mechanical metamaterial beams. For instance, in his pioneer work, [PERSON] et al. modeled the bandgap characteristics of a simple beam-type metamaterial structure using Timoshenko beam model [7]. The results of their study showed that a single-beam metamaterial structure with attached local resonators could isolate vibrations at frequencies around the resonant frequency of these local resonators. Building on this effort, [PERSON] et al. showed that the bandgap of a simple Euler-Bernoulli beam could be shifted to lower frequencies by adding negative stiffness elements to the local resonators [18]. In another work, [PERSON] et al. showed that a beam with local resonator masses inserted into cavities that were filled with viscoelastic membrane had the ability to attenuate vibrations at low frequencies, i.e., less than 100 Hz [4]. [PERSON] et al. presented the use of two mass-spring-damper subsystems serving as multi-frequency local resonators at different locations in generating wide vibration stopbands [1]. Additionally, a chiral-lattice-based elastic metamaterial was investigated by [PERSON] et al. [26]. Their results demonstrated the ability to generate multiple bandgaps that were dependent on the distribution density of the local resonators in different sections of the structure. Bandgaps through a quasi one-dimensional structure comprised of harmonic oscillators have also been studied by [PERSON] et al. [27]. Their results showed the existence of a single bandgap in the high frequency region. [PERSON] et al. demonstrated the coexistence of both local resonance and Bragg-scattering bandgaps in a beam with continuum beam resonators [24]. Moreover, the effect of nonlinear local resonators on bandgaps of a single-beam metamaterial structure was studied by [PERSON] et al. [28]. The nonlinear local resonators were comprised of magnetoelastic materials as bistable attachments [28].