Abstract
Layered metamaterial beam structures are gaining attention in a variety of fields including vibration attenuation and energy harvesting. Exhaustive research on single-beam metamaterial vibration attenuation structures using local resonators exists in literature. Moreover, there are recent attempts at modelling double-layered beams with different kinds of constraints. The double-layered beam models in literature are limited to simple beams and not extended to metamaterials with local resonators. This article is focused on developing a design criterion and a modelling platform for layered metamaterial structures with multiple beams and local resonators for vibration isolation. The model is developed using Euler-Bernoulli beam equations, superposition of mode shapes and Galerkin methods. A prototype layered metamaterial structure is fabricated and characterized experimentally. The prototype consists of horizontal beams, local resonators forming unit cells, and vertical beams linkages. Each local resonator consists of cantilevers with tip masses. Results show good agreement between model and experiment. Two major bandgaps are observed at 190–410 Hz and 550–710 Hz. Results reveal that the low frequency bandgap can be further reduced through the design of the local resonators. Results also show that alternating the length of the local resonators causes a shift in the first frequency bandgap. An increase in the number of local resonators opens up extra frequency bandgaps at lower frequencies with the drawback of reducing the depth in vibration transmissibility. Moreover, the higher frequency bandgaps are mostly affected by the horizontal beams. An increase in the length of the horizontal beams, while the number and design of the local resonators are fixed, broadens the second frequency bandgap and shifts it to lower values.
Highlights
Mechanical metamaterials have become the centerpiece of many research studies and engineering applications (Xia et al, 2020)
In the case of vibration attenuation, when the mechanical metamaterial is subject to vibrations by an external vibration source, it has the ability to suppress these oscillations, at low frequencies, that are closely aligned with the resonant frequency of the local resonators (Sugino et al, 2017)
For the purpose of model validation and design investigation, a layered metamaterial structure made of 3 unit cells per beam, three vertical columns between beams, and a total of four horizontal beams was manufactured (Figure 4)
Summary
Mechanical metamaterials have become the centerpiece of many research studies and engineering applications (Xia et al, 2020) This is mainly because of their unique properties including the presence of frequency bandgaps influenced by the local resonators (Wang et al, 2016; Jiang, He, 2017). This is of interest for many engineering applications including wave guiding, vibration attenuation and, more recently, dual-purpose vibration suppression and energy scavenging (Matlack et al, 2016; Reichl and Inman, 2017; Casablanca et al, 2018). In the case of vibration attenuation, when the mechanical metamaterial is subject to vibrations by an external vibration source, it has the ability to suppress these oscillations, at low frequencies, that are closely aligned with the resonant frequency of the local resonators (Sugino et al, 2017)
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