Abstract
Effect of the graded variation in terms of separation gap between the two successive resonators and their mass on the resultant band structure of the graded metabeam is investigated in this paper. The band-structure are explored by implementing the transfer matrix method in conjunction with Bloch-Floquet's theorem. The graded arrangement of oscillators modifies the relative position of the coupling coefficient in the transfer matrix, which plays a pivotal role in altering the band-gap formation. The flexural band-structure is highly sensitive to the natural frequency and the distance between two resonators. It is evidenced that around 20% shifting of attenuation band in lower frequency side and 2.5 times widening of overall attenuation band gap is achievable by proper graded arrangement of resonators in metamaterial unit cell. However, the level of attenuation deteriorates over the wider frequency range.
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