Evolution of Band Gaps in the Nonlinear Dynamics of Metamaterials

This paper proposes the study of the dynamic properties of thin-walled metamaterial structures under large displacements and rotations. The focus is given to the analysis of the vibration modes, and to their evolution as the equilibrium states change. The analysis of the evolution of the band gap, i.e. the frequency intervals between the different vibrational modes, is of main interest. The investigation of this characteristic, discussed in the paper for thin-walled structures composed of combinations of different materials, allows the design of metamaterial structures with specific and tailored physical properties. In this article, thin-wall structures consisting of repeating units are considered; these are used as benchmarks to support the theoretical discussion of the used models. Numerical simulations are conducted by means of a model based on the Carrera Unified Formulation (CUF). This formulation allows for nonlinear dynamic analysis in a more efficient computationally way compared to traditional methodologies based on 3D finite elements, yet guaranteeing the same level of accuracy. The use of CUF for nonlinear dynamic studies of thin-walled metamaterial structures, therefore, overcomes limitations related to the computational bottlenecks of more traditional FEM-based methodologies, opening up the effective exploration of the dynamic behaviour of metamaterials.