Modeling and multi-objective optimization of hybrid metamaterials for tailored low-frequency and ultra-broadband wave attenuation

Abstract Periodic metamaterials have emerged as a promising solution, demonstrating the dual functionality of enhanced wave attenuation and lightweight design. The local-resonance mechanism is central to achieving low-frequency attenuation in such structures. Motivated by this, we propose a novel hybrid design (DRHM) that leverages local resonance by embedding a unique combination of cantilever-inspired and double-arrowed elements within a re-entrant honeycomb. To analyze its attenuation performance, a new semi-analytical framework is developed, with the DRHM serving as a representative testbed. This framework is founded on the dynamic stiffness method (DSM) with a Schur-complement reduction scheme, and is further enhanced by the linear expression method (LEM) for the systematic enforcement of periodic boundary conditions. Numerical fidelity is established through cross-verification with finite element simulations for the dispersion predictions and by comparing transmission responses obtained from independent frequency-domain analyses. A comprehensive parametric study is then conducted to quantify the effects of geometric variations on the low-frequency band gap characteristics. The results reveal a clear trend: increasing the length of cantilever-inspired elements not only induces new band gaps but also widens band gap coverage, an ultra-low-frequency band gap is achieved by increasing the double-arrowed element angle and broadband gaps are attainable by increasing the cross-sectional dimensions. However, broadband performance often conflicts with the lightweight design philosophy inherent to periodic metamaterials. To address this, a multi-objective optimization framework is developed by coupling the DSM-based solver with the intelligent searching capability of the non-dominated sorting genetic algorithm II (NSGA-II). A linear-gradient mistuning pattern is subsequently adopted, and the transmission response of an aperiodic DRHM supercell is optimized to identify designs exhibiting ultra-broadband characteristics. Consequently, the results provide clear evidence that mistuning enables ultra-broadband attenuation performance. This study not only extends beyond the presentation of a new hybrid design but also provides innovative insights into the rapid development of metamaterials with precisely tailored attenuation performance.