Flexural vibration bandgaps of the multiple local resonance elastic metamaterial plates with irregular resonators

Abstract

This paper presents the modeling technique, the design method, the local resonator with new modes of action, and influence factors for elastic metamaterial plates with broadband elastic flexural vibration suppression. Two new types of elastic metamaterial plates with two flexural vibration bandgaps (FVBGs) at low frequencies were designed, and the band structures, the transmission spectrum, and the dynamic effective mass density of the metamaterial plates were systematically investigated by the finite element method (FEM). The formation mechanisms of the two FVBGs were further analyzed by studying the displacement field of the eigenmodes at the bandgap edges. Finally, the effects on the FVBGs of the geometrical parameters including the asymmetry of the mass and rubber, the thickness of the rubber for the wedge-mass elastic metamaterial plate, the thickness of the mass for the wedge-rubber elastic metamaterial plate and the installation angles for the double-side metamaterial plates were studied in detail. The related results confirm well that the proposed elastic metamaterial plates with wedge mass or wedge rubber exhibit lower and wider FVBGs than those with the regular geometry mass or rubber due to the multiple local resonance behavior. The new working mechanism and the related calculation results of the designed structures would provide an effective approach for elastic metamaterial plates to broaden FVBGs at low frequencies, which has potential applications in low-frequency vibration and noise reduction.