Evaluation of the effects of different materials on the dynamic properties of thin-walled and sandwich metamaterial structures

This paper investigates the effects of different materials on the dynamic properties of thin-walled metamaterial structures. The study focuses on changes in natural frequency and associated modal shapes as external load, either in-plane or transverse, increases. Central to the discussion is an analysis of the evolution of the bandgap, defined as the frequency interval between two consecutive vibrational modes; this is a critical dynamic property that informs the design of structural metamaterials. The numerical models of these complex structures are developed using the Carrera Unified Formulation (CUF), enabling the modeling of such structures with one-dimensional (1D) finite elements while still capturing three-dimensional (3D) effects. This approach allows for the use of the full 3D Green-Lagrange strain tensor in formulating the nonlinear governing equations, which significantly reduces the computational cost compared to traditional 3D finite elements and overcomes the limitations and nonlinear assumptions inherent in two-dimensional (2D) finite elements. The results demonstrate that different materials influence the dynamic response and bandgap evolution of the structures under increasing external loads. Specifically, various combinations and patterns of materials are analyzed, and the nonlinear dynamic behavior is examined for each case. These findings provide valuable insights for the design of metamaterials with specific bandgap characteristics. A similar behavior is observed in the nonlinear dynamic analysis of the sandwich structure. However, as this structure is much stiffer than the thin-walled case described above, the nonlinear effects on the dynamic response and bandgap evolution are less prominent.