Topology optimization of seismic metamaterials for low-frequency lamb waves attenuation based on a genetic algorithm

This paper presents a topology optimization framework based on a genetic algorithm for seismic metamaterials (SMs) to achieve low-frequency Lamb waves attenuation. In this framework, the relative bandgap width (RWBG) is adopted as the objective function for the inverse design of the structure layout. The performance of the obtained structure is systematically evaluated through dispersion analysis, transmission analysis, and time domain simulations. The results show that the proposed optimization framework effectively regulates the low-frequency dispersion characteristics and generates multiple bandgaps (BGs). Vibration mode analysis indicates that the low-frequency BGs are associated with a transition from extended skeleton-dominated modes at the lower band edges to localized resonant modes at the upper band edges, arising from the dynamic contrast between the concrete and rubber regions. The attenuation regions of the finite periodic structures agree well with the BG intervals predicted by the dispersion analysis. Moreover, under Taft and El Centro seismic wave excitations, the mean absolute acceleration at the output is reduced by 53.99% and 59.80%, respectively. The corresponding dominant spectral peaks are reduced by 20.4% and 33.9%, respectively, compared with the pristine case without SMs. The attenuation ranges of the three-dimensional (3D) models are generally consistent with the BGs predicted by the two-dimensional (2D) dispersion analysis, demonstrating the effectiveness of the optimized SMs for low-frequency Lamb waves attenuation and their potential for seismic protection.