Asymmetry Effects on Truncation Resonances in Acoustic Metamaterials

Periodic structures have repetitive physical characteristics and may take the form of discrete spring-mass lattices or continuum structures. With the emergence of bandgaps, i.e., frequency ranges of wave attenuation, periodic structures have paved the way for novel engineering applications, ranging from noise control to unidirectional wave propagation. Recently, locally resonant structures, also known as acoustic metamaterials, have gained significant research interest due to their ability to block waves at considerably lower frequencies through locally resonant bandgaps. Unlike regular periodic structures, acoustic metamaterials uniquely utilize local resonators, which are usually small relative to the host structure. These local resonators serve as mechanical absorbers and can be placed in the host structure periodically, inducing low-frequency, locally resonant bandgaps with strong attenuation capacity, thanks to anti-resonance effects. Consequently, these bandgaps are largely dependent on the mechanical properties of the local resonator and can emerge in the sub-wavelength regime. This research aims to explore the behavior of truncation resonances that occur within the locally resonant bandgap of acoustic metamaterials, particularly their emergence due to structural asymmetry, which remains largely unexplored. By definition, truncation resonances are natural frequencies emerging within a bandgap and result in mode shapes of high localization of structural vibrations. Existing research indicates that factors such as the mass ratio and stiffness ratio between the local resonator and the host structure in acoustic metamaterials affect the frequency range of locally resonant bandgaps. As such, these critical parameters may influence the location of truncation resonances within the bandgap, warranting a comprehensive investigation of such parameters. The characteristics of these truncation resonances will be analyzed using the transfer matrix method for discrete and continuum models of the acoustic metamaterials in conjunction with MATLAB. Finally, numerical simulations are conducted to verify the analytical models established via the transfer matrix method.