A modified generalized Bloch-mode synthesis for the efficient modeling of periodic structures using the wave-based finite element method

Resumo

© 2024 Proceedings of ISMA 2024 - International Conference on Noise and Vibration Engineering and USD 2024 - International Conference on Uncertainty in Structural Dynamics. All rights reserved.Periodic structures have been attracting increasing interest due to their potential for manipulating waves. The Wave-based Finite Element Method (WFEM) is typically employed to model such systems, involving the examination of a finite element mesh of a single unit cell of the periodic lattice. However, the utilization of the WFEM with more challenging problems, encompassing unit cell models with several degrees of freedom, can be challenging, as it involves operating with large-sized matrices. To tackle this matter, one developed a modified generalized Bloch-mode synthesis that, in conjunction with the WFEM, can efficiently and accurately model periodic structures. Simulations were performed on a plate-like elastic metamaterial, where relative errors between resonances of the reduced model and the reference solution less than 0.5% and cross signature scale factor close to one across frequency were found, demonstrating the outstanding performance of the MGBMS and WFEM in computing dispersion curves, wave shapes, and forced responses.