Dynamic theory of blast-loaded circular meta-arch with mass-spring resonators

The arch structure has good pressure-bearing performance, while the local resonance metamaterial has good vibration reduction performance. Adding mass-spring resonators to the ordinary circular arch structure to form a meta-arch is expected to further improve the dynamic performance of the arch and can be applied in protective engineering. In this research, a theoretical model of meta-arch with mass-spring resonators is established. The analytical solution of displacement response of meta-arch under blast load is obtained based on the generalized two-degree of freedom system and mode superposition method. The theory is verified through finite element modelling (FEM). Meanwhile, the theory is degraded into the meta-beam theory, and comparative analysis is conducted with the explosion test results of metaconcrete slabs in references. Finally, theoretical parameter analysis is conducted to optimize the displacement attenuation effect of the meta-arch. With reasonable settings of resonator parameters, the displacement attenuation of the meta-arch relative to the ordinary arch of equal mass and stiffness can reach 30 %. Parameter analyses show that the displacement attenuation and optimal resonator parameters of the meta-arch are related to the duration of the blast load. The research provides a theoretical basis for the explosion resistance analysis of meta-arches and offers a new idea for the dynamic control design of arch structures. © 2025 Elsevier Ltd.