Abstract
In this research, the negative effective mass behavior of elastic/mechanical metamaterials is exhibited by a cantilever-in-mass structure as a proposed design for creating frequency stopping band gaps, based on local resonance of the internal structure. The mass-in-mass unit cell model is transformed into a cantilever-in-mass model using the Bernoulli-Euler beam theory. An analytical model of the cantilever-in-mass structure is derived and the effects of geometrical dimensions and material parameters to create frequency band gaps are examined. A two-dimensional finite element model is created to validate the analytical results, and excellent agreement is achieved. The analytical model establishes an easily tunable metamaterial design to realize wave attenuation based on locally resonant frequency. To demonstrate feasibility for 3D printing, the analytical model is employed to design and fabricate 3D printable mechanical metamaterial. A three-dimensional numerical experiment is performed using COMSOL Multiphysics to validate the wave attenuation performance. Results show that the cantilever-in-mass metamaterial is capable of mitigating stress waves at the desired resonance frequency. Our study successfully presents the use of one constituent material to create a 3D printed cantilever-in-mass metamaterial with negative effective mass density for stress wave mitigation purposes.
Highlights
This section briefly reviews the theory of negative effective mass density obtained by using a mass-in-mass spring system[20,21]
The analytical model described by Figure 6. 3D model and realization of cantilever-in-mass unit cell (a) Computer-Aided Design (CAD) model. (b) Prototype of 3D printed part
The negative effective mass behavior of the metamaterial is exhibited by significant wave attenuation when input frequency is within the stopping band region of the designed resonance frequency
Summary
3D printing offers possible realization of mechanical metamaterials, since in 3D printing, complex structural shapes and geometries can be achieved, without incurring assemblage and mold requirement, and reducing cost and increasing efficiency in fabrication[28]. Another manufacturing approach of elastic metamaterial is by the precision laser cutting system as demonstrated by Zhu et al.[29]. The lack of analytical model based design and the need to achieve a one constituent material tunable mechanical metamaterial to enable easy fabrication by 3D printing are the main motivations for this work.
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