Dynamic Behavior Of Periodic Media And Elastic Metamaterials

Periodic media and resonant, acoustic/elastic metamaterials possess extraordinary frequency band gaps where no waves may propagate. In this dissertation, we leverage numerical simulations to gain insight into practical ways to effectively measure and characterize the behavior of these materials from experimental observables and also explore physical mechanisms to optimize their performance, particularly in the context of resonant metamaterials. With respect to the former, the finite nature of experiments prevents the usage of Bloch's theorem and unit cell analysis. To circumvent this, an FFT procedure combined with an exponential fitting method are used to extract the real and imaginary part of dispersion relations from real-time simulation data. Difficulties such as sample length and frequency domain resolution, associated with this type of analysis, are examined parametrically using synthetic data from numerical simulations. In addition to this study, an additively manufactured, resonant metamaterial made of a soft PDMS rubber is analyzed using both experimental data and finite element models. By isolating several physical features of the material, a new mechanism for band gap formation is discovered where band gaps associated with different vibrational modes are combined to produce an ultrabroad band gap through the use of a compliant frame.