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

Abstract

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.

Towards Broadband High-Frequency Vibration Attenuation Using Notched Cross-Shaped Metamaterial

“…We can observe that the effective bandgap width increased firstly and then decreased with h 2 and b 1 increasing, but a significant effect was obtained for the case of b 1 . Thus, the coupling between parameters has no significant effect on the effective bandgap width [ 36 ]. Therefore, the parameters of the unit cell were optimized as follows: a = 6.5 mm, h 1 = 1 mm, h 2 = 4 mm, b 1 = 2.5 mm, L 1 = 2.6 mm, L 2 = 2 mm, b 2 = 0.6 mm.…”

“…In contrast, when embedded parallel oscillators are adopted, the resonant frequencies of each oscillator can be designed and adjusted by the desired frequency band without periodic limitations [ 35 ]. Stein et al found that the bandgap of metamaterials can be widened by introducing multiple parallel oscillators [ 36 ]. Tian et al theoretically and experimentally investigated the elastic metamaterials with two parallel local resonators and effectively created two bandgaps of the bending wave [ 37 ].…”

A brief review of metamaterials for opening low-frequency band gaps

“…That is, the resonators consisted by elastic materials are able to open multiple types of band gaps, such as the longitudinal wave band gap, the bending wave band gap, and the torsional wave band gap [57] . Hollowing out a continuum, such as beam or plate, to form some special geometries is another avenue to design a resonator with a low resonant frequency [53][54] , as presented in Figs. 4(f) and 4(g).…”

On band gaps of nonlocal acoustic lattice metamaterials: a robust strain gradient model

“…Thus, the developments of acoustic metamaterials have greatly expanded the application range of acoustic engineering. Intensive research efforts have been devoted to the analyses of the propagation and dispersion characteristics of elastic waves in acoustic metamaterials [5][6][7][8] with negative effective properties [9][10][11] .…”