Auxetic metamaterial systems have garnered significant attention for their unique properties and potential applications. This study aims to address a fundamental question concerning the suitability of the spring model in accurately describing the behavior of a disk bar metamaterial system. A comprehensive analytical derivation for spring-mass and finite-element formulation for disk-bar model has been carried out. The efficacy of the spring-mass model to capture the effective properties, dispersion relations, and band gap is compared with numerical simulation results of the disk-bar metamaterial. Varying the local structural parameter allows for the independent attainment of negative mass and negative modulus, and their unique frequency ranges can be adjusted to the desired range. Current findings shed light on the effectiveness of the spring model as a predictive tool for such complex systems and provide valuable insights into the behavior of metamaterial structures. Ultimately, this research contributes to a designing and engineering metamaterial structures with tailored negative characteristics, promising new avenues for application in diverse fields.
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