Two-stage optimization design of cylindrical lattice structures for low-frequency vibration attenuation

Introduction To address the mass-law limitation inherent in conventional passive vibration isolators, this study introduces a novel micro-scale hollow-scatterer cylindrical lattice architecture and develops a two-stage optimization framework for achieving broadband low-frequency vibration attenuation. Methods In the first stage, a locally resonant unit cell is engineered, comprising a lead-based hollow scatterer, a viscoelastic rubber coating, and a thermosetting resin connector. A Bloch-theory-informed two-degree-of-freedom (2-DOF) reduced-order model is formulated to provide a mechanistic and computationally efficient prediction of the first locally resonant bandgap. Leveraging parametric sensitivity analysis and the Box-Behnken response surface methodology, seven critical geometric parameters are systematically optimized. In the second stage, curvature is deliberately introduced as an additional design degree of freedom by transforming the planar connector into a single-curvature cylindrical configuration. Further parametric investigation and experimental validation are conducted to characterize the attenuation performance. Results The resulting optimized unit cell achieves a 32.7% reduction in the lower bandgap cutoff frequency (to 595.2 Hz) and a 64.9% expansion of the absolute bandgap width (to 762.8 Hz) with model prediction errors consistently below 10%. The curvature-induced geometric stiffening effect shifts the upper bandgap boundary mode from pure out-of-plane bending to a hybrid bending-membrane coupling mode, thereby broadening the bandgap to 1,418.16 Hz. Experimental validation using vibration testing shows reasonable agreement with numerical predictions in terms of attenuation onset and relative bandwidth trend. Discussion Collectively, this work establishes a synergistic design paradigm integrating data-driven parametric modeling with curvature-mediated structural tailoring, providing a robust, scalable methodology for the rational design of lightweight, high-performance low-frequency vibration isolation systems.