Bragg Rainbow Reflection in Functionally Graded TPMS Metamaterial Plates

  • Lomazzi, Luca (Politecnico di Milano)
  • Patino, Nicholas (University of Colorado Boulder)
  • Manes, Andrea (Politecnico di Milano)

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Controlling how elastic waves propagate through a structure is central to applications such as vibration isolation, ultrasonic filtering, and guided-wave sensing. Conventional treatments add mass or dissipate energy broadly, and although effective, they are hard to tune to specific frequencies or locations. This work explores a complementary, fully elastic strategy based on wave control, aiming to reject elastic waves over a broad frequency band by design rather than relying on absorption alone. The proposed approach leverages functionally graded metamaterials based on Triply Periodic Minimal Surfaces (TPMS), whose self-supporting, additively manufacturable microstructure is multifunctional, simultaneously bearing mechanical load and shaping wave propagation. The unit-cell size a(x) of a TPMS inclusion embedded in a plate is graded continuously along the propagation direction at constant solid fraction. Each local cell carries a complete Bragg bandgap whose edges scale inversely with a, so stacking these narrow per-cell gaps across position builds a wide, position-resolved effective stop band that exceeds 1 MHz of continuous rejection, several times wider than the bandgap of any single cell. Direct time-domain simulations confirm this behavior: pulses at several carrier frequencies reflect at their predicted turning points to within a few millimeters, forming a spatial rainbow of position-dependent, frequency-selective reflection. Along the plate centerline the unit cell is reflection-symmetric, whereas away from it the cell becomes sheared. Together with the Bragg origin of the gaps, this suggests that the effect is a Bragg rainbow reflection along the centerline and rainbow trapping away from it. The work provides a predictive and tunable computational framework for graded architected materials that reject and localize elastic waves by design.