Folded sheet resonators that aim at low frequency attenuation of surface elastic waves in solids

Abstract

We report a folded sheet resonator for locally resonant metamaterials aiming at approximately 10 Hz attenuation of surface elastic waves in solids. Its design is based on a decorated membrane resonator replacing the stretched membrane with a folded steel sheet. The drape and constraint release on the two long sides of the sheet highly decrease the equivalent stiffness of the resonator in such a way that the working frequency can be one magnitude lower than 100 Hz. A locally resonant metamaterial sandwiching folded sheet resonators between supporting panels is further presented, and it is demonstrated that its dynamic mass is equal to the collective contributions of all resonators inside. To explore the attenuation of the surface elastic waves by this metamaterial, a finite element model of an earthquake is built that includes a barrier buried in the formation on the propagation path of the seismic waves. Calculation results indicate that the maximum attenuation of the Rayleigh wave reaches up to 11.5 dB when the length and depth of the barrier are less than one wavelength of the Rayleigh wave. Compared to the case of a steel barrier, this locally resonant metamaterial shows greater potential for Rayleigh wave attenuation. This resonator benefits the development of locally resonant metamaterials and applications in the low-frequency range.