Antioptimization of mass-in-mass acoustic metamaterials based on interval analysis

Abstract

In this study, an integrated analytical and experimental study on a type of one-dimensional periodic acoustic metamaterial with mass-in-mass unit cells is presented. Then, this paper proposes an antioptimization strategy to study the effect of the design parameters of the local resonators of the mass-in-mass acoustic metamaterial model on the band gap behavior. In this antioptimization strategy, the interval model is used to deal with the inner mass, spring stiffness and damping coefficient of the local resonators, and an interval mass-in-mass acoustic metamaterial model is established. Both the rational series expansion-interval perturbation finite element method (RSE-IPFEM) and interval affine finite element method (IAFEM) are used to evaluate the lower and upper bounds of the dynamic response interval vector, based on which an interval vibration transmission analysis can be implemented. Meanwhile, Monte Carlo method and experiments are also presented to demonstrate the efficiency and accuracy of the RSE-IPFEM and IAFEM. Results show that the design parameters of the local resonators significantly affect the beginning frequency of the band gap. Compared with the traditional optimization algorithm, the calculation accuracy of the antioptimization algorithm based on RSE-IPFEM and IAFEM can meet the engineering requirements, and the calculation efficiency is also significantly improved. Since IAFEM is more effective than RSE-IPFEM in suppressing conservatism, IAFEM is a better antioptimization strategy for dealing with the interval mass-in-mass acoustic metamaterial model. Therefore, the proposed antioptimization scheme is expected to inspire future researchers to analyze regulation rules of the band gap following the same procedures.