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

这笔赠款将支持对能够被动控制径向传播振动的新结构进行建模和表征的基础研究。振动困扰着机械、涡轮叶片、轮系和往复机构。当它们通过这些部件径向传播时，问题尤其严重，并可能导致结构部件的严重损坏和快速磨损。这项工作的目的是将减振特性直接工程到此类部件的几何形状中。虽然现有的材料可以被动地缓解振动，但对于径向传播的波来说，这些行为是无法实现的。这项研究的结果在提高飞机、汽车和能源基础设施中的结构的安全性、效率和寿命方面具有应用价值，这仍然是社会的迫切需求之一。这项研究将在本科和研究生课程中通过K-12外展活动和新的基于实验室的学习模块对教育产生积极影响。这项拨款将引入新的数学模型、计算模型和辐射传播波的实验。这项工作的具体目标是介绍一个建模和实验框架，以表征被动地减轻破坏性径向振动的径向亚结构。现有的声子材料是很有希望的振动缓解候选材料，因为它们可以阻止某些频率通过材料传播。然而，对于径向传播的波来说，这些有益的声子特性是无法实现的。这是因为声子材料的分析方法，如Bloch定理，不适用于径向传播的波，因为周期性变化的材料性质不会导致在径向坐标下波动方程中的周期系数。这项工作将通过引入(1)具有径向相关性质的新的建筑材料来解决这些挑战，这些材料将使运动方程的修改能够在数学上强制周期性；以及(2)具有有效周期性的径向元结构的建模框架。具体地说，这项工作将引入一个新的建模框架，该框架将波动方程中的参数重新定义为径向相关的，以获得周期系数，从而实现Bloch分析。径向弹性波在各向异性层状介质中的传播模型将通过有限元模拟和实验进行验证。这项工作将产生在没有几何周期的情况下表现出声子行为的新的各向异性结构，并为探索材料弥散和源几何之间的相互作用奠定基础。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.