Predicting low-frequency attenuation in additively manufactured mechanical metamaterials via complex dispersion analysis and uncertainty quantification

Generating phononic bandgaps in the challenging low-frequency range remains a significant hurdle for additively manufactured (AM) mechanical metamaterials, particularly given the critical impact of manufacturing uncertainties on structural performance. This paper presents a physics-informed framework for practical uncertainty quantification and attenuation interpretation of additively manufactured mechanical metamaterials. First, complex dispersion analysis elucidates the fundamental differences in attenuation mechanisms: a distributed Added Mass strategy offers precise frequency fine-tuning via inertial anisotropy, while a Meander strategy achieves an order-of-magnitude higher spatial decay rate via spatial folding. Second, a data-driven Uncertainty Quantification (UQ) framework based on Gaussian Process Regression reveals that manufacturing robustness is mode-dependent. Crucially, this framework successfully captured a highly nonlinear mode transition event, demonstrating the effectiveness of data-driven UQ over nominal sensitivity. Finally, experimental validation on finite prototypes reveals a critical modeling limit: for complex thin-walled AM lattices, the observed attenuation behavior is more consistently explained when material-property degradation is considered, corresponding in this study to an effective Young’s modulus lower than the nominal bulk value (e.g., 135 GPa rather than 160 GPa). This discrepancy-based analysis suggests that effective property characterization is essential for interpreting the practical attenuation performance of complex AM metamaterials. With this effective material-property correction, the proposed complex dispersion framework provides a quantitative interpretation of the attenuation amplitude (approximately 25 dB) and the frequency-dependent trend observed in the experiment. This work establishes that bridging the reality gap in AM mechanical metamaterials requires both data-driven UQ for geometric sensitivity and effective property characterization for material degradation.