Date of Award

Summer 8-1-2022

Document Type


Degree Name

Doctor of Philosophy (PhD)


Micro and Nanoscale Systems

First Advisor

Hamzeh Bardaweel


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 research is primarily 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 Hz – 410 Hz and 550 Hz – 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 frequency values. Additionally, the ability of the fabricated metamaterial structure to harvest electric power in these bandgaps is examined. Results show that vibration attenuation and energy harvesting characteristics of the metamaterial structure are coupled. Stronger vibration attenuation within the first bandgap has led to enhanced energy harvesting capabilities within this bandgap. Power measurements at optimum load resistance of 15 Ω reveal that maximum power generated within the first bandgap reaches 5.2 µW at 245 Hz. Compared to state-of-the-art, the metamaterial structure presented here shows a significant improvement in electric power generation, at considerably lower load resistance, while maintaining the ability to attenuate undesired vibrations within the frequency bandgap. Lastly, the comparative advantages of layered-beam structures over single-beam metamaterial structures is studied. A beam prototype and dimension studied by multiple articles in literature is used in simulating the comparative study. Results show that in cases where spacing and 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. Results also suggest that increasing the number of resonators per horizontal beam further generates multiple lower bandgaps in layered metamaterial beams. In situations where the number of local resonators per beam are desired to remain constant, increasing the length of the unit-cells offers an alternative technique for lowering the bandgaps. This comparative study is particularly useful to engineers and researchers designing applications of beam-type metamaterial structures.