Asymmetric scattering in elastic waveguides with applications to nondestructive evaluation and acoustic metamaterials



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Asymmetric scattering in waveguides is a behavior in which the field scattered from a discontinuity is dependent on the direction of incidence. The existence of multiple propagating modes in waveguide systems like plates and beams provides a platform to explore asymmetric scattering through direction-dependent mode coupling and asymmetric absorption. While asymmetric scattering is a well-known behavior, the physical conditions required to produce the behavior are not well-understood, hindering its use for design of engineered materials and for novel nondestructive evaluation techniques. This work investigates asymmetric scattering and its applications to nondestructive evaluation (NDE) techniques and design of acoustic and elastic metamaterials (AMM). First, a pump-probe technique called Dynamic Asymmetric Transmission Measurement (DATM) is developed for use with elastic beams to detect and classify damage that is has stress-dependent scattering behavior. When subjected to a time-harmonic background stress field, local nonlinearities like surface-breaking cracks display a scattering behavior that is asymmetric with respect to the oscillatory phase of the background stress field. The method utilizes mode conversion between the fundamental symmetric and antisymmetric Lamb modes to capture the variation in scattering response with the background stress field. The method is demonstrated on elastic beams with localized damage and provides an enhanced ability to classify damage compared to existing NDE techniques. Next, constraints on asymmetric scattering imposed by reciprocity and passivity were investigated theoretically to understand implications on scatterer properties with application to NDE techniques like DATM and ultrasonic inspection as well as to inform design considerations for AMM applications. In a multi-modal Lamb wave system, reciprocity was shown to relate various Lamb wave scattering parameters for reflection and transmission, respectively. Combined with symmetry arguments and consideration of passivity, necessary conditions to produce asymmetric scattering and asymmetric absorption were developed. These conditions were verified through numerical studies, with applications to novel NDE techniques and AMM design. Finally, a scatterer that is geometrically asymmetric and resonant was then investigated with applications to Willis materials, a class of homogenized materials that has constitutive relationships of stress and momentum that are a function both strain and velocity. Simulations showed that the scatterer displayed strongly asymmetric mode coupling when excited with the fundamental symmetric and antisymmetric Lamb modes. The scatterer is then modeled using reduced-order beam theories, incorporating necessary Willis coupling coefficients to derive constitutive relationships. An effective material property extraction technique is proposed and demonstrated numerically to determine the effective properties of the scatterer as defined in the constitutive relationships.


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