Analytical Modeling of an Elastic Metamaterial System with Simultaneously Negative Modulus and Mass

Authors : Kingsley N. Nwankwo, Sylvester A. Aye, Samuel M. Gbashi

Volume/Issue : Volume 4 - 2019, Issue 9 - September

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Interest in metamaterials arises because they produce novel properties like negative mass and modulus which cannot be realized in conventional materials. As the field of metamaterials develops, and research efforts are directed towards fabricating and realizing them physically, it is necessary to exhaustively understand their dynamics. In this study, the detailed analytical modeling of the design of a chiral mass-spring metamaterial system is presented. The conditions and frequency interval(s) where the effective dynamic parameters are negative are clearly established. Simulation result indicates that when both the translational and rotational resonance frequencies of the material coincide, a perfectly single negative parameter metamaterial is realized, which alternate from purely (single) negative modulus to purely (single) negative mass material at the point of resonance. It is shown that the frequency band in which the system exhibit simultaneously double negative (modulus and mass) behavior can be widened by reducing the stiffness of the horizontal spring, and maximum when the stiffness is zero. Hence, the horizontal spring is apparently a redundant member and may not necessarily be needed when fabricating the chiral system in three-dimension.

Keywords : Double Negativity, Effective Bulk Modulus, Effective Mass/Mass Density, Metamaterial.


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