Investigation of 2D Rainbow Metamaterials for Broadband Vibration Attenuation

Abstract

Phononic crystals (PnCs) and metamaterials are widely investigated for vibration suppression owing to the bandgaps, within which, wave propagation is prohibited or the attenuation level is above requirements. The application of PnCs and metamaterials is, however, limited by the widths of bandgaps. The recently developed rainbow structures consisting of spatially varied profiles have been shown to generate wider bandgaps than periodic structures. Inspired by this design strategy, rainbow metamaterials composed of nonperiodic mass blocks in two-dimensional (2D) space were proposed in the present study. The blocks were connected by curved beams and tessellated with internal voids to adjust their masses. In order to demonstrate the effects of the rainbow design, two 2D metamaterials, with periodic and nonperiodic units, respectively, were investigated and manufactured using additive manufacturing technologies. Receptance functions, i.e., displacement frequency response functions, of the manufactured metamaterials were calculated with finite element models and measured with a testing system containing a mechanical shaker, an impedance head, and a laser Doppler vibrometer. The obtained numerical and experimental results showed that the metamaterial with rainbow blocks has extended bandgaps compared with the periodic metamaterial.

Broadband Vibration Attenuation Achieved by 2D Elasto-Acoustic Metamaterial Plates with Rainbow Stepped Resonators

“…However, in contrast, the dispersion curves do not possess an integrated bandgap consistent with the vibration attenuation band (i.e., the spectrum band of 155-228 Hz within which considerable attenuation could be achieved) as shown in Figure 7b. The 2D metamaterial plates were hence different from the 1D metamaterial beams that showed extended attenuation bands as well as bandgaps due to the existence of rainbow resonators [56]. The whole bandgap of the periodic metamaterial plate was replaced by narrower completed and directional bandgaps owing to the modes of the distributed nonperiodic resonators as shown in the subfigure of Figure 7b.…”

“…Beli et al [54] proved that the spatial correlated variability could lead to widened bandgaps for cantilever-in-mass metamaterials. Meng et al [55][56][57][58][59] investigated rainbow metamaterial beams with spatially varying oscillators and rainbow phononic crystal lattices with spatial varying mass blocks and found that the rainbow structures could generate broader bandgaps compared with periodic ones.…”

A Ternary Seismic Metamaterial for Low Frequency Vibration Attenuation

“…Based on the concept of phononic crystal, seismic metamaterials can block the propagation of elastic waves in a certain frequency range, which is called band gap [ 14 , 15 , 16 , 17 , 18 , 19 , 20 ]. Therefore, seismic metamaterial shows broad development prospects for the low-frequency vibration attenuation induced by elastic wave [ 21 , 22 , 23 , 24 ]. Local resonance phononic crystal proposed by Liu et al provided a new idea to design seismic metamaterial for low frequency vibration attenuation [ 25 ].…”

Mechanical Shunt Resonators-Based Piezoelectric Metamaterial for Elastic Wave Attenuation

“…Phononic crystals and metamaterials have attractive potential in elastic wave manipulation and attenuation [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 ]. They show promising advantages in the applications of negative refraction [ 2 , 3 ], acoustic cloaking [ 4 , 5 ], wave focusing [ 6 , 7 , 8 , 9 , 10 ], wave attenuation [ 11 , 12 , 13 , 14 , 15 , 16 , 17 ], and vibration-mode tailoring [ 18 ]. The features of phononic crystals and metamaterials stem from Bragg scattering and local resonance, respectively [ 19 , 20 , 21 , 22 , 23 ].…”

“…In addition, it was demonstrated that the width of the bandgap of metamaterials, i.e., the frequency range of wave attenuation, is expandable by structural parametric optimization [ 12 ]. It is worth mentioning that the frequency range of wave attenuation is expandable by adopting rainbow resonators [ 15 , 16 ]. In the past, the metamaterials were assembled by local mechanical resonators integrated into primary structures [ 12 , 25 , 30 , 31 ].…”