Assessment of the flat-top stable GFEM for free vibration analysis

The stable Generalized Finite Element Method, SGFEM, has been used for numerical stabilization of the generalized finite element method during enrichment process of shape functions. However, some troubles persist in dynamic analysis. The flat-top strategy is an alternative to hold up the SGFEM but, despite its good performance in quasi-static problems, for dynamic problems some points remain opened, such as the accuracy of natural frequencies, the computational effort to reach a desired degree of precision (for each natural frequency), and the conditioning of mass and stiffness matrices. The main objective of this work is to assess the performance of the flat-top SGFEM in the context of free vibration analysis Based in many numerical simulations, the sensitivity of the method is verified for different parameters, such as, the size of the flat-top partition of unity (PU) intervals, the smoothness of enriched functions, and the stabilization parameter. Despite the flat-top SGFEM improves the numerical stability for modal analysis, it is shown that the convergence rates can be degraded.