A theoretical framework for joining multiple locally resonant bandgaps of metamaterials towards a super-wide bandgap

In this paper, we establish a theoretical framework for joining multiple locally resonant bandgaps of composites that consist of a continuous matrix and discrete particles towards a super-wide bandgap through the damping effect of the inclusions or interphases. The binary locally resonant material is taken as an example. The analytical expressions of its first bandgap, effective mass and transmission characteristics are obtained by virtue of the equivalent discrete models. The theoretical framework and the optimized results are validated by numerical examples and experiments. Then, the theoretical framework is further used to design composite metamaterials that have the merits of small characteristic size, light weight, high static stiffness, and low -frequency bandgaps simultaneously which are characterized by a dimensionless comprehensive performance index. The results demonstrate that the generalized bandwidth can be increased by four folds, and the comprehensive performance index can be doubled through optimization. The methods developed in this work are applicable to other kinds of locally resonant metamaterials, and can be used to guide the design of high-performance metamaterials.

Automated summary

In this paper, a theoretical framework is established to connect multiple locally resonant bandgaps of composites into a super-wide bandgap through the damping effect of inclusions or interphases. The analytical expressions of the first bandgap, effective mass and transmission characteristics are obtained for a binary locally resonant material using equivalent discrete models. The framework and optimized results are validated through numerical examples and experiments. Furthermore, the framework is used to design composite metamaterials with small characteristic size, light weight, high static stiffness, and low-frequency bandgaps, characterized by a dimensionless comprehensive performance index. The results show a four-fold increase in generalized bandwidth and a doubling of the comprehensive performance index through optimization. The methods developed in this work are applicable to other types of locally resonant metamaterials and can guide the design of high-performance metamaterials.