Based on auxetic foam: A novel type of seismic metamaterial for Lamb waves

Seismic metamaterial (SM) has lately received significant attention in the field of vibration isolation and damping due to its wave manipulation and bandgap properties. However, the limitations of unit cell size and the difference of the material parameters of each component have made it challenging to generate an ultra-low frequency bandgap. In order to overcome this challenge, a novel type of 2D SM composed of auxetic foam and steel is proposed to attenuate seismic waves at ultra-low frequencies. Firstly, the band structure of the SMs and the vibration modes of the upper and lower bounds of the first complete bandgap are calculated and analyzed by using the finite element method, and the mechanism of the bandgap generation is clarified. The transmission spectrum under the Lamb wave incident on the SM is investigated. It is validated that Lamb waves have a good attenuation effect in the frequency range below 10 Hz. Secondly, a parametric study of the SM with auxetic foam-coated hollow steel columns is carried out. The numerical results show that the shape and height of the unit cell, the elastic modulus, density and Poisson's ratio of the auxetic foam play important roles in the formation of the bandgap. Finally, the numerical simulation verifies that adding through holes in the matrix which reduces the equivalent mass density of the matrix could widen the bandgap and enhance the effective attenuation of seismic waves. Based on theoretical model and combined with the exceptional material characteristics of auxetic foam, the focus of the study is to achieve a wide bandgap coverage for the seismic peak spectrum of 2 Hz which causes the principal damage of surface buildings.