Nonlinear Dynamical Interactions in Multistable Metastructures

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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.