<p>Phononic crystals (PnC) are of significant interest for passive elimination of troublesome frequency bands. Recently, a tuned phononic crystal was embedded in an incompressible channel flow configuration and it was computationally demonstrated to passively quiet Tollmien-Schlichting (T-S) waves. This strategy works by designing a truncation resonance (i.e. a resonance existing in the band gap of the PnC) to coincide with the T–S wave frequency. The exposed end of the PnC then oscillates out of phase with the pressure disturbances, which cause a local acoustic field to be emitted by the vibration of the PnC surface, causing diminishing growth of the boundary layer instability.&nbsp; Due to Bragg’s law, the size of a PnC unit cell, composed of layered bulk materials, is dictated by its constituitive material properties, and for standard materials, this can lead to relatively large unit cells. When low frequencies are targeted, the size of the required PnC can be prohibitive due to the limited space available for their installation. However, it can be desirable to use PnC-based bandgaps over resonant metamaterial-bandgaps due to their larger widths.&nbsp; Recent work in acoustic control has used coiled cavities to compress the effective dimension of wave propagation, enabling a metamaterial effect from a thin platform, relative to the acoustic wavelength.&nbsp; In this work, a coiled structure is explored as a space saving PnC whose unit cell is composed of beams and masses. This study is concerned with a PnC’s ability to act as a multi-degree-of-freedom resonator capable of producing passive control efforts in response to excitation. &nbsp;In addition to the space savings, another advantage of this type of PnC is the large range of unit cell constitutive properties that can be achieved.&nbsp; Analysis techniques based on the spectral element and transfer matrix methods are employed to study the bandgap generation mechanics. Comparisons are made to traditional PnCs in order to highlight the origins of the band gaps in terms of the unit cell parameters.&nbsp; Additionally, a tuning method for adjusting the resonances of the finite PnC by the addition of termination structures is discussed.&nbsp; The predictions by the analysis techniques are then compared to an experimentally measured frequency response function of a fabricated coiled beam PnC. This talk will focus on the design of the coiled-beam PnC, and how the dispersion diagram shifts in response to changes of material or geometry.&nbsp; The application of a coiled beam-based phononic crystal to quieting T-S waves will not be covered in detail. &nbsp;</p>

Analysis of a Coiled Beam-Based Phononic Crystal

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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