Elastic wave propagation in the elastic metamaterials containing parallel multi-resonators

This paper presents the modeling technique, design method, a new working mechanism and influence factors for elastic metamaterials (EMs) with parallel multi-resonators for broadband elastic vibration suppression. The general formula of the effective mass is deduced, and the effects of the relevant structural parameters on the frequency regions of the negative effective mass are illustrated in details. Subsequently, the dispersion relation and transmission spectrum of the EMs are studied. Based on the theoretical approach, the EMs plates were proposed, and the formation mechanism of the band gaps are analyzed by studying the displacement field of the eigenmodes at the band gaps edges. The related results well confirm that the novel EMs induces multi-frequency negative effective mass, and the number of the regions is equal to the number of the local resonators. The start frequencies of the band gaps are decided by the natural frequencies of each resonator, and the width of frequency band with negative effective mass can be broadened by enlarging the mass ratio of the local resonator. The EMs plate with the thickness of only 2.5 mm designed on the basis of theoretical research exhibits two flexural vibration band gaps (FVBGs) with the total width of 78.4 Hz below 200 Hz, which has been verified by the transmission testing experiments. For the formation mechanism of the FVBGs, the vibration is localized in the according resonator at the lower edge of each band gap, while at the upper edges the local resonance mass and the base plate vibrate in a reverse phase. Based on the theoretical and numerical analyses, the EMs with multiple parallel local resonators would be used in various fields, such as noise and vibration isolation, filters, and other renewed devices.