Nonlinear Dynamical Interactions in Multistable Metastructures

该项目将支持揭示结构中新的动力行为的基础研究，这将促进材料和结构领域的科学进步和技术进步。超材料是一种工程系统，具有传统材料所不具备的特性，可以增强对声音、振动和机械波的控制，超出目前技术所能产生的范围。尽管超材料研究最近取得了进展，但基本的性能极限仍然存在；有效工作频率太高太窄，不适合许多有用的结构应用。该项目支持对解决这些操作限制的新的动力学相互作用的基础研究，从而加速将超材料应用到结构应用中。具体地说，派生的理论将产生一种新的动力相互作用，允许操纵低频振动，与民用、航空航天、汽车和医疗行业的应用相关，如构建弹性基础设施、振动衰减和为物联网提供本地电源。发现的新物理和潜在的应用将对美国的技术和科学优势产生积极影响，最终造福于美国的经济和社会。这项研究涉及多个学科，包括工程、物理和应用数学，这将允许利用所取得的成果来促进科学、技术、工程和数学教育。此外，教育活动将支持未被充分代表的群体参与研究，有助于扩大工程教育的多样性。超材料通过微米或毫米尺度的工程单元单元显示出有效的、非常规的特性。然而，这些性质强烈地依赖于单胞的大小，将有效行为限制在较窄的高频带或导致较大的排列。因此，需要发现允许获得与单元大小无关的宽带超材料的机制。这项研究利用多稳态元结构中涉及跃迁波的新型非线性相互作用，研究了一种能够实现低频、宽带行为的机制。具体地说，这项工作将建立基于物理的模型，捕捉过渡波激发亚结构振动模式，反之亦然。理论和数值分析将揭示发生这种相互作用的动力学机制和亚结构参数。实验计划使用3D打印的多稳定元结构来验证这种非线性相互作用的关键物理。这些活动将检验这一假设，即过渡波允许低频率、宽带的动力学行为，使得在结构应用中能够非传统地操纵振动。总体成果是一个设计和分析超结构非线性相互作用的数学框架，从而使超材料在结构应用中的实施成为可能。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 project will support fundamental research uncovering new dynamic behaviors in structures, which will promote both the progress of science and technological advance in the field of materials and structures. Metamaterials are engineered systems that exhibit properties not commonly found in conventional materials, which can enhance the control of sound, vibrations and mechanical waves beyond what current technology can produce. Despite recent progress in metamaterial research, fundamental performance limits exist; the effective working frequencies are too high and narrow for many useful structural applications. This project supports fundamental investigations into new dynamical interactions addressing these operational limitations, thereby accelerating the implementation of metamaterials into structural applications. Specifically, the derived theory will yield a new class of dynamical interactions allowing the manipulation of low frequency vibrations, relevant for applications in civil, aerospace, automotive and medical industries, such as constructing resilient infrastructure, vibration attenuation and providing local power to the internet of things. The uncovered new physics and potential applications will positively impact the U.S. technological and scientific edge, ultimately benefiting its economy and society. This research involves multiple disciplines including engineering, physics and applied mathematics, which will allow for leveraging the obtained results to promote Science, Technology, Engineering, and Mathematics education. Furthermore, the educational activities will support the participation of underrepresented groups in research, contributing to broadening diversity in engineering education.Metamaterials exhibit effective, unconventional properties by engineering unit cells at the micrometer or millimeter scales. However, these properties are strongly dependent on the size of the unit cells, restricting the effective behavior to narrow, high frequency bands or resulting in large arrangements. Thus, there is a need to discover mechanisms allowing to obtain unit-cell size independent, broadband metamaterials. This research investigates a mechanism enabling low frequency, broadband behavior exploiting new types of nonlinear interactions involving transition waves in multistable metastructures. Concretely, this effort will establish physics-based models capturing the excitation of metastructural vibration modes by transition waves, and vice versa. Theoretical and numerical analyses will reveal the dynamical regimes and metastructures' parameters for which such interactions occur. Experiments are planned using 3D-printed multistable metastructures to validate the key physics of such nonlinear interactions. These activities will test the hypothesis stating that transition waves allow for low frequency, broadband dynamical behavior enabling unconventional manipulation of vibrations in structural applications. The overall outcome is a mathematical framework for designing and analyzing metastructural nonlinear interactions, thereby enabling the implementation of metamaterials in structural applications.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.