Customized shaping of vibration modes by acoustic metamaterial synthesis

Abstract

Acoustic metamaterials have attractive potential in elastic wave guiding and attenuation over specific frequency ranges. The vast majority of related investigations are on transient waves. In this research we focus on stationary wave manipulation, i.e., shaping of vibration modes. Periodically arranged piezoelectric transducers shunted with inductive circuits are integrated to a beam structure to form a finite-length metamaterial beam. We demonstrate for the first time that, under a given operating frequency of interest, we can facilitate a metamaterial design such that this frequency becomes a natural frequency of the integrated system. Moreover, the vibration mode corresponding to this natural frequency can be customized and shaped to realize tailored/localized response distribution. This is fundamentally different from previous practices of utilizing geometry modification and/or feedback control to achieve mode tailoring. The metamaterial design is built upon the combinatorial effects of the bandgap feature and the effective resonant cavity feature, both attributed to the dynamic characteristics of the metamaterial beam. Analytical investigations based on unit-cell dynamics and modal analysis of the metamaterial beam are presented to reveal the underlying mechanism. Case illustrations are validated by finite element analyses. Owing to the online tunability of circuitry integrated, the proposed mode shaping technique can be online adjusted to fit specific requirements. The customized shaping of vibration modes by acoustic metamaterial synthesis has potential applications in vibration suppression, sensing enhancement and energy harvesting.

Broadening Bandgap Width of Piezoelectric Metamaterial by Introducing Cavity

“…The displacement distributions and the forced responses at the right free-end are computed. The dispersion relations are obtained through the displacement distributions of the metamaterial beam by using Fournier transform [25,39], ( ) Similarly, Figure 7 illustrates the frequency boundaries and the bandgap width of the unit-cell, where the cavity introduced has height of 2 mm. The results generally resemble those shown in Figure 6, i.e., the introduction of cavity underneath the substrate, can effectively increase the bandgap width.…”

“…The displacement distributions and the forced responses at the right free-end are computed. The dispersion relations are obtained through the displacement distributions of the metamaterial beam by using Fournier transform [25,39], ( ) Figure 6 shows the frequency boundaries and the width of the bandgap. All the cavities have constant height of 1 mm and constant length of 25.38 mm.…”

“…The displacement distributions and the forced responses at the right free-end are computed. The dispersion relations are obtained through the displacement distributions of the metamaterial beam by using Fournier transform [25,39],…”

“…Theoretical and experimental investigations on photonic rods and beams [23] with shunt circuits have been performed. Recently, piezoelectric metamaterials were applied in two-dimensional wave steering [24] and vibration mode customization [25]. Notably, piezoelectric metamaterial has advantages over the more conventional mechanical metamaterial in two aspects: Relatively simple configuration and adaptivity.…”

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 ].…”