Session: 01-01-04: Elastic and Acoustic Metamaterial

Paper Number: 99108

99108 - Conditions and Mechanisms of Local Resonance Band Gap Merging in Dual-Periodic Acoustic Metamaterials 

Despite the promise of a size-independent, mechanically-tunable band gap that can extend to low frequency regimes, the potential of local resonance band gaps remains largely untapped due to their narrow frequency range, unlike wide Bragg scattering band gaps in periodic crystals. As a result, multiple efforts have surfaced with a common theme of exploring novel configurations of acoustic metamaterials (AMs) which exhibit wider gaps and broader dispersive characteristics. Notable among these are designs which involve interactions of neighboring resonators, either in spring-mass or continuum form, non-local resonators, electromechanically resonant systems, origami designs, as well as metamaterials with inertial amplification mechanisms. Of particular interest to this work is the notion of using two distinct mechanical resonators embedded within two identical outer masses, which are connected in series to form a dual-periodic AM unit cell. The early work of Gao and Wang (2020) has demonstrated the possibility of local resonance band gap coupling between two distinct tuning frequencies in such systems, and has since been followed by a number of efforts focused on exploiting these concept for practical applications ranging from double negativity to sound transmission and broadband noise control. However, to date, the underlying reasons behind a smooth, uninterrupted coalescence of two local resonance band gaps when certain conditions are met, or the lack thereof when such conditions are not satisfied, have not been thoroughly or analytically investigated. The primary aim of this work is to provide a comprehensive mathematical interpretation of a wide array of dispersion scenarios associated with an infinite space of dual-periodic AM configurations, which emerge from separately and independently tuning the two resonators. In the process, we explain the different scenarios and mechanisms by which single- and double-peak local resonance band gap merging takes place in the infinite realizations of such systems via the commonly used unit cell analysis. In addition, we discuss a number of intriguing band structure features which accompany the band gap merging, including the appearance, shifting, and vanishing of Bragg band gaps along the wavenumber axis. We end with a frequency-domain, closed-form transfer function approach which captures the free vibrational dynamics of finite dual-periodic lattices, and connects the aforementioned scenarios to their counterparts in the finite chain. The presented work provides a pathway for resonance-based acoustic metamaterials to play a more robust role in applications requiring broadband attenuation of vibroacoustic loads, particularly using recent advances in physics-based inverse design and multi-objective optimization algorithms.

Presenting Author: Adrian Stein University at Buffalo (SUNY)

Presenting Author Biography: PhD candidate<br/>Dept. of Mechanical and Aerospace Engineering<br/>University at Buffalo (SUNY)

Authors:

Adrian Stein University at Buffalo (SUNY)
Mostafa Nouh University at Buffalo (SUNY)
Tarunraj Singh University at Buffalo (SUNY)