Session: 15-01-01: ASME International Undergraduate Research and Design Exposition

Paper Number: 151895

151895 - 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. Through 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 uni-directional wave propagation. Recently, locally resonant structures, often referred to 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 typically 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. Locally resonant bandgaps in acoustic metamaterials occur near the natural frequencies of the local resonators and are often attributed to their negative effective mass. 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 understand the behavior of truncation resonances that occur within the locally resonant bandgap of acoustic metamaterials, particularly their emergence due to structural asymmetry, which remain 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 numerical investigation of such parameters. Additionally, the effect of boundary conditions—such as free-free, fixed-free, free-fixed, and fixed-fixed—will be investigated. The characteristics of these truncation resonances will be analyzed using the transfer matrix method in conjunction with MATLAB. The occurrences of truncation resonances obtained through the transfer matrix method will also be numerically validated. In this study, numerical simulations will be conducted on a discrete model of the acoustic metamaterials, which will later be extended to a continuously solid model.

 

Future directions of this work may include testing a physical model of an acoustic metamaterial structure with varying asymmetries to verify the existence of truncation resonances. Such work could be valuable in applications that rely on truncation resonances, including flow control via subsurface acoustic metamaterials and topologically protected mechanical structures.

Presenting Author: Peter Schroder Union College

Presenting Author Biography: Peter Schroder is an undergraduate mechanical engineering senior at Union College in Schenectady, NY and is expected to graduate in 2025. Peter is also a member of Pi Tau Sigma honor society and has previously conducted research at the Union College Aerogel Lab.

Authors:

Peter Schroder Union College
Hasan Al Ba'ba'a Union College