Scientific Article

A gradient radial seismic metamaterial designed using the PSO algorithm

¹ School of Civil and Environmental Engineering, The University of New South Wales, Sydney 2052, Australia
² School of Civil Engineering and Architecture, Anyang Normal University, Anyang 455000, PR China
³ Henan Province Engineering Technology Research Center of Digital-Intelligent Building and Low-Carbon Building Materials, Anyang Normal University, Anyang 455000, Henan, PR China

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 24 September 2025
Accepted: 19 February 2026

Abstract

This study proposes a gradient radial seismic metamaterial that integrates typical engineering core geometries with particle swarm optimization (PSO) algorithm and placement optimization to realize low-frequency, broadband surface-wave attenuation in compact footprints. Under an equal-area constraint and a band-diagram objective focused on the first two bands, the T-shaped unit emerges as the most effective core, and a front-rear graded assembly superposes Bragg-scale gaps to span 5–35 Hz, aligning with the dominant frequencies of destructive surface waves. Cylindrical-coordinate finite-element dispersion analysis, 3D frequency-domain response spectra, and time-domain excitation with the 1984 Bishop record collectively verify marked reductions in stress, displacement, and peak acceleration within the target frequency, confirming engineering feasibility. The approach addresses scalability and material-use constraints while lowering onset frequency and widening the primary band gap, offering a practical pathway for building-level seismic shielding.