Keywords: seismic metamaterial, periodic structure, frequency band gap, optimization technique, meta-barier, vibration mitigation.

Seismic metamaterials have attracted increasing attention as an effective alternative to conventional vibration mitigation techniques due to their ability to attenuate elastic waves through the formation of frequency band gaps. However, the design and optimisation of three-dimensional seismic metamaterials that simultaneously consider band-gap performance and construction cost remain insufficiently explored. In order to address this gap, this study proposes a systematic multi-objective optimisation framework for the design of seismic metamaterial structures, accounting for both targeted band-gap characteristics and material usage efficiency. Numerical models have been developed to evaluate the vibration attenuation performance of the optimised configurations in the frequency domain. The present study investigates the effects of key system parameters, including the number of meta-block columns and layers, in order to elucidate their influence on wave attenuation behaviour. The findings indicate that the optimised metamaterial configurations attain substantial reductions in ground vibration in comparison with the reference case, while concurrently preserving practical feasibility. The proposed optimization framework provides a flexible and effective approach for three-dimensional metamaterial design and shows strong potential for applications in structural vibration control and seismic protection engineering.

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