Abstract
In this paper, the layered cantilever-in-mass structures (LCIMs) will be theoretically investigated to reveal the effects of the layered structures on band gaps, which have great potential to bring in many useful material properties without much increasing the manufacturing difficulty by stacking the damped layers or other different component layers. Firstly, the negative effective mass model of LCIMs is derived based on the mass-in-mass model, which is applied to analyze the effective parameters of band gaps in terms of the geometrical features and material properties, the analytical results indicate the negative effective masses of LCIMs depend highly on the material parameter and thicknesses of each constituent layers. Then the LCIMs consist of the same thickness layers are further researched, which has found that their resonance frequency are independent on the layer thickness, and the numeric values of resonance frequencies are between the maximum and minimum local resonance frequency of their constituent layers. To validate the above analytical model, the three-dimensional model and the two-dimensional shell model of LCIMs are constructed in COMSOL Multiphysics. The obtained results show well agreement with the derived model in both the three-dimensional model and shell model. Finally, the dissipative LCIMs modeled by stacking the damped layers and metal layers are studied and discussed.
Highlights
Acoustic/elastic metamaterials (AM/EMs) with local resonant structures have attracted much attention for their band gaps at subwavelength scale.[1,2,3] As wave propagation would be greatly inhibited in the frequency regions of band gaps, a basic application of the elastic metamaterials is the acoustic/vibration absorption which is significant for both noise/vibration mitigation and interior acoustics optimization.[2]
As the cantilever-in-mass structure is a basic layout of the local resonant metamaterials which have well agreement with the theoretical models, here we will present a numerical study on the dissipative layered cantilever-in-mass structure (LCIM) to show the effects of the layered structures on the band gaps
It is obvious that the value of the resonance frequency ω2 of LCIM with the same thickness layers is independent of the constituent layer thickness tb, which is only depending on the material properties of constituent layers and the geometry of normal section
Summary
Acoustic/elastic metamaterials (AM/EMs) with local resonant structures have attracted much attention for their band gaps at subwavelength scale.[1,2,3] As wave propagation would be greatly inhibited in the frequency regions of band gaps, a basic application of the elastic metamaterials is the acoustic/vibration absorption which is significant for both noise/vibration mitigation and interior acoustics optimization.[2]. One typical strategy is designing multiple local resonators[6,7,8] to generate two or more closely located band gaps to broaden the band gaps. Another strategy is building dissipative elastic metamaterials,[9,10,11] which have been found some potentiality for optimizing band structures, including widening band gaps, shifting band gaps towards lower frequencies. As the cantilever-in-mass structure is a basic layout of the local resonant metamaterials which have well agreement with the theoretical models, here we will present a numerical study on the dissipative layered cantilever-in-mass structure (LCIM) to show the effects of the layered structures on the band gaps.
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