Vibration Characteristics of Metamaterial Beams With Periodic Local Resonances

Abstract

Vibration characteristics of metamaterial beams manufactured of assemblies of periodic cells with built-in local resonances are presented. Each cell consists of a base structure provided with cavities filled by a viscoelastic membrane that supports a small mass to form a source of local resonance. This class of metamaterial structures exhibits unique band gap behavior extending to very low-frequency ranges. A finite element model (FEM) is developed to predict the modal, frequency response, and band gap characteristics of different configurations of the metamaterial beams. The model is exercised to demonstrate the band gap and mechanical filtering capabilities of this class of metamaterial beams. The predictions of the FEM are validated experimentally when the beams are subjected to excitations ranging between 10 and 5000 Hz. It is observed that there is excellent agreement between the theoretical predictions and the experimental results for plain beams, beams with cavities, and beams with cavities provided with local resonant sources. The obtained results emphasize the potential of the metamaterial beams for providing significant vibration attenuation and exhibiting band gaps extending to low frequencies. Such characteristics indicate that metamaterial beams are more effective in attenuating and filtering low-frequency structural vibrations than plain periodic beams of similar size and weight.

Dispersion characteristics of a nonlinear elastic metamaterial

“…[26], an analysis of these two structure yields the band-gap edge frequencies of the original infinite 1D MM, i.e., the same frequencies obtained from Eqs. (25) and (26), respectively. We consider a harmonic wave solution for the rod structures of Fig.…”

“…In one-dimensional (1D) structures, among the metamaterial configurations investigated are three-phase rods, 18 beams with resonating rings, 19,20 sandwich beams with internal mass-spring resonators, 21 beams with side stubs, 22,23 chains of beads with cylindrical resonators, 24 and beams with small masses suspended on membranes. 25 The band-gap formation mechanism in this class of 1D systems was studied analytically by Xiao et al in the context of mass resonators attached to strings, 26 rods 27 and beams. 28 In the case of rods, multi-degree-of-freedom resonators were considered to achieve a cluster of multiple subwavelength band gaps.…”

“…Now that the physical interpretation of Eqs. (25) and (26) is elucidated, it is worth pointing out, as done for the analogous string-based problem in Ref. [26], that Eqs.…”

Locally Resonant Metasurfaces for Shear Waves in Granular Media

“…Despite the differences in terms of the size and targeted frequency, the majority of the proposed designs rely on the coupling between a structural component (beam [13,14] or plate [15,16,17]) and an array of mechanical resonators. The coupling occurring between the resonators and the waves propagating inside the component induces a bandgap in the subwavelength regime [18].…”

Vibrational behavior of sandwich structures overloaded by fractal distribution of masses

“…Studies 11 comparing classically ordered networks with quasi-ordered fractal networks demonstrated that by removing some scatterers, the attenua-tion band gaps can be broadened and dropped to lower frequencies. Nouh et al proposed meta-structures, as beams 12 and plates. 13 They were made of aluminum which were drilled to create multiple holes, filled with a viscoelastic membrane, surmounted by small masses.…”