Redefining Geometric Periodicity to Enable New Wave Responses in Radial Phononic Materials

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This grant will support fundamental research to model and characterize new structures that can passively control radially-propagating vibrations. Vibrations plague machinery, turbine blades, gear trains, and reciprocating mechanisms. They are particularly problematic when propagating radially through these components, and can cause severe damage and rapid wear of structural components. This work aims to engineer the vibration mitigating properties directly into the geometry of such components. While existing materials can passively mitigate vibrations, these behaviors are unattainable for radially-propagating waves. Results of this research have applications in improving safety, efficiency, and longevity of structures in aircraft, automotive, and energy infrastructure, which remains as one of society's pressing needs. This research will positively impact education through K-12 outreach activities and new laboratory-based learning modules in both undergraduate and graduate courses.This grant will introduce new mathematical models, computational models, and experiments for radially-propagating waves. The specific objectives of this work are to introduce a modeling and experimental framework to characterize radial metastructures that passively mitigate damaging radial vibrations. Existing phononic materials are promising candidates for vibration mitigation, since they can forbid certain frequencies from propagating through the material. However, these beneficial phononic properties are unattainable for radially propagating waves. This is because analysis methods for phononic materials, e.g., Bloch theorem, are not applicable to radially propagating waves, since periodically varying material properties do not lead to periodic coefficients in the wave equation in radial coordinates. The work will address these challenges by introducing (1) new architected materials with radially dependent properties that will enable modifications of the equations of motion to enforce periodicity mathematically; and (2) a modeling framework for radial metastructures with effective periodicity. Specifically, this work will introduce a new modeling framework that redefines parameters in the wave equation to be radially dependent in order to achieve periodic coefficients, and thus enable Bloch analysis. The models of radial elastic wave propagation in anisotropic layered media will be validated by finite element simulations and verified by experiments. This work will result in new anisotropic structures that exhibit phononic behaviors in the absence of geometric periodicity, and lays the foundation to explore interactions between material dispersion and source geometry.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.