A double root, commonly referred to as an exceptional point (EP), for modal frequencies in a 2D or 3D waveguide can exhibit almost perfect absorption over a relatively broad frequency range.   The key to the phenomenon is that the wall impedance is such that modes coalesce at a complex-valued frequency. The connection between double roots and acoustic wave attenuation goes back to the observation of Cremer (1953) that optimal attenuation in a duct occurs when the two lowest modes have equal complex-valued eigenvalues, although the physical basis for this effect remains unclear.  In an attempt to understand Cremer’s observation, we consider the model cases of a two and three-dimensional waveguide with the same impedance condition on all boundaries.  This allows us to determine possible passive impedance conditions that give rise to EPs, and from these select impedances appropriate for a particular frequency band. The theoretical findings are compared to realistic passive impedance values based on various models of common wave attenuation techniques such as perforated panels and porous foams. All comparisons are done via COMSOL Multiphysics and results validate the functionality of double root boundaries showing above average performance. However, the feasibility of boundaries with these characteristics is put into question as physical constraints are revealed when studying general acoustic networks of lumped elements. In summary, most passive impedances lack the appropriate frequency dependence crucial to broadband mode coalescence. Only near boundary resonances do we see that any intersection can occur. With this constraint in mind,  we introduce a novel approach to feasibly achieve the aforementioned wall impedance with only the use of simple resonators, which can be shown to exhibit mode coalescence at distinct frequencies when treated as a unit cell component of a larger metasurface. When using this approach, we see that the number of EP intersections is dependent on the number of resonators per unit cell and modes per resonator. In order to evaluate each unit cell design, an efficiency parameter, EP density, was created which quantifies the number of double root frequencies within a given range all while satisfying the following constraints: realizable resonator dimensions, scale separation, and target absorption/attenuation goals. Strategies capable of deriving the necessary resonator parameters for this effect are given. The impact of these strategies on feasibility and performance are discussed via simulated and numerical results. An experiment design consisting of additively manufactured Helmholtz resonators incorporated onto a custom-made impedance tube to simulate the resonant metasurface is discussed along with preliminary results. Work supported by NSF.


Passively Achieving Mode Coalescence in Acoustic Waveguides With Metasurfaces

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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