Theoretical and Experimental Investigations on the Ultra-Low-Frequency Broadband of Quasi-Static Metamaterials

Abstract

This paper proposes an I-shaped radial elastic metamaterial with ultra-low-frequency broadband characteristics and studies the propagation characteristics of elastic waves in their quasi-static state. Through the calculation of the dispersion relationship, the frequency response function, and the eigenmode displacement field, it is found that the ultra-low-frequency wide band gap can be generated in the quasi-static metamaterial. The wide band gap is mainly caused by modal transitions. The equivalent mass–spring model reveals the modal changes of the I-shaped radial elastic metamaterial under the surface constraints. Furthermore, by studying the directional vibration displacement field of the finite period structure, it is demonstrated that the mechanism of the ultra-low-frequency broadband (0<Reduced frequency(Ω)<0.20) is the local resonance mechanism. Subsequently, the influence of the geometric and the material parameters on the location and width of the band gap is explored numerically. Finally, based on the model, through the hammer modal experiment, it is proven that the quasi-static structure yields an ultra-low-frequency stop band of 0.1–1012 Hz. The research conclusions can be applied to mechanical engineering fields such as ultra-low-frequency vibration reduction.