Nonlinear dynamic and vibration characteristics of metamaterial shallow arches

Abstract

Metamaterial shallow arches have shown promise in enhancing the seismic resistance of structures due to their unique properties. In this study, we present a theoretical model for the nonlinear vibration and dynamic response of metamaterial shallow arches. The nonlinear motion equations consider lateral shear deformation and large deflection based on the third-order shear theory and von Kármán nonlinear theory. The study focuses on three aspects: establishing an effective model to capture the global characteristics of laminated structures with damage, designing members with auxetic and non-auxetic properties using the effective model, and obtaining an asymptotic solution of the motion equations using a two-perturbation approach. The presented model is applied to study the effect of initial thermal stress, negative Poisson's ratio, and internal damage on the forced and larger amplitude vibration of arches with damage. The results show that the auxetic effect can reduce the displacement of arches with and without damage, thus mitigating dynamic damage. Furthermore, the numerical results also reveal that deflection, linear, and nonlinear frequency are significantly dependent on the internal damage and auxetic property. Our findings represent an efficient approach to evaluating the dynamic and vibration response of metamaterial arches and optimally design the seismic resistance of arches.