A Method for Obtaining Dispersion Diagrams Suitable for Training Surrogate Models
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Dispersion diagrams for the mechanical characterization of periodic structures were introduced several decades ago. In recent years, alongside advances in additive manufacturing, they have become an established approach for characterizing the dynamic mechanical behaviour of lattice-based mechanical metamaterials [1]. This work presents a computational tool for obtaining dispersion diagrams — a key resource for identifying the frequency bandgaps within which these metamaterials provide vibration attenuation. Two main challenges are addressed. First, the Floquet–Bloch boundary conditions required to enforce periodicity on the unit cell are mathematically complex and cannot be directly implemented in standard commercial finite element software. Second, the automation needed to generate and solve the training cases for a surrogate model —built via machine learning — introduces a meshing conflict: automatic mesh generators cannot easily ensure the node congruency at the boundary faces of the cell unless the geometry possesses triple symmetry. The solutions to both challenges are presented, and examples of their implementation are shown for a parametric unit cell.