62 R. Romeo and R. Schultz The next step in this work will be to implement this ROM method on a three-dimensional model of a more geometrically complicated metamaterial. Lessons learned from this work, in terms of reduction methods and sensitivities, will be useful for developing the ROMs of the 3-D model. Likely, the main challenge with implementing this ROM method to a selfrepeating three-dimensional model will be in the bookkeeping—keeping track of the cell-level interface DOF and making proper connections between the reduced cell DOF during the system assembly process. References 1. Nonis, C., Thibault, L., Marinone, T., Avitabile, P.: Development of full space system model modes from expansion of reduced order component modal information. In: Topics in Modal Analysis, vol. 7. Springer, New York (2014) 2. Matlack, K.H., Bauhofer, A., Krödel, S., Palermo, A., Daraio, C.: Composite 3D-printed metastructures for low-frequency and broadband vibration absorption. Proc. Natl. Acad. Sci. U. S. A. 113(30), 8386–8390 (2016) 3. Guyan, R.J.: Reudction of stiffness and mass matrices. AIAA J. 3(2), 380 (1965) 4. Avitabile, P.: Model reduction and model expansion and their applications Part 1—Theory. Modal Analysis and Controls Laboratory, University of Massachusetts Lowell, Lowell, MA (2005) 5. Craig, R.R., Kurdila, A.J.: Fundamentals of Structural Dynamics. Wiley, Hoboken, NJ (2006) 6. Avitabile, P.: Test-Analysis Correlation-Updating Considerations. Modal Analysis and Controls Laboratory, University of Massachusetts Lowell, Lowell, MA (2001)
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