Dynamic FE² multiscale modeling of periodic acoustic black holes using PLA-TPU composites

Acoustic black holes (ABHs) attenuate flexural waves through thickness tapering, but practical implementations are limited by truncated tips and externally bonded damping layers. This study proposes a multi-material ABH in which dissipation is embedded within the tapered region through PLA/TPU composite architectures compatible with multi-material additive manufacturing. The layout combines the stiffness of PLA with the high loss factor of TPU, providing intrinsic damping without post-applied treatments. A dynamic FE² multiscale homogenization framework is adapted to periodic ABH beams by coupling the microscale unit-cell response and micro-inertial effects to macroscopic wave propagation through an enriched one-dimensional continuum with plane-section beam kinematics. Single-leaf and double-leaf periodic ABH configurations are analyzed. Verification against fully resolved FEM simulations for homogeneous, heterogeneous, and ABH media shows close agreement while reducing the computational cost per frequency by more than two orders of magnitude. For the composite beams, the enriched model predicts transmissibility over 100–3000 Hz with mean absolute errors of 0.88 dB and 1.31 dB for the single- and double-leaf cases, respectively. Sensitivity results show that attenuation is governed mainly by the TPU loss factor. Relative to a bonded-neoprene benchmark, the composite gives stronger high-frequency attenuation over 1500–3000 Hz.