Material property extraction procedure for electromomentum coupled metamaterials



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Electromomentum (Eμ) coupling is a material response that couples the macroscopically observable time-varying electric field to the momentum of the material. This unique behavior has been shown theoretically to result from dynamics at subwavelength length-scales due to asymmetries in heterogeneous piezoelectric materials. Electromomentum coupling is of interest to the engineering and scientific community for its ability to simultaneously sense both the acoustic pressure and particle velocity at a single point in space, thus enabling the creation of vector sensor devices using a single material. This thesis presents a study of the characterization of this novel transduction behavior through multiscale models and numerical experiments. The material models include analytical and finite element methods that extend the work of Pernas-Salomón et al. [Wave Motion, 106, 102797, (2021)]. The models simultaneously provide insight into the subwavelength behavior that leads to Eμ coupling on the macroscopic scale as well as metrics of the coupling strength. Additionally, these models are employed in a design strategy to maximize Eμ coupling demonstrated by a heterogeneous piezoelectric scatterer using readily available materials and easily manufactured geometries. To achieve this, a series of candidate designs are modeled and their Willis and/or Eμ coupling is quantified. The models are then employed to design an experimental method to characterize Eμ coupling of a sample using a water-filled impedance tube. The impedance tube measurement procedure presented in this work is a generalization of existing methods used to infer the frequency-dependent material properties of a sample from measurements of its scattering coefficients and associated property extraction algorithms. Namely, the works of Song and Bolton to measure the complex impedance and wavenumber or phase speed and attenuation [J. Acoust. Soc. Am., 107(3), pp. 1131-1152, (2000)], Fokin et al. to measure the complex-valued density and bulk modulus, including negative values, [Phys. Rev. B, 76(14), 114302, (2007)], and Muhlestein et al. who extended the work of Fokin et al. to measure Willis coupling in addition to density and bulk modulus [Nat. Commun., 8, 15625, (2017)]. This work also considers practical details such as dispersion, hydrophone calibration, and sample mounting, that are specific to measurements in a water-filled impedance tube and their influence on the accuracy of measurements of scattering coefficients using this apparatus, ending with recommendations for future measurements.


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