Seminar Series - Dr. Matthew Fronk
Wave Propagation in Nonlinear Periodic Media
Wave Propagation in Nonlinear Periodic Media: Recent Advancements and Future Directions
Abstract
Recent focus has increased on the interaction of elastic and acoustic waves in periodic media as it possesses remarkable features such as filtering, focusing, and wave-guiding. Periodicity within a mechanical structure may arise from repetitions of geometry, material properties, or boundary conditions. This talk will present opportunities enabled by nonlinearity in periodic media, citing recent advancements and proposing new directions for the design and analysis of materials and devices. Waveform invariance in weakly nonlinear lattices will be addressed, in which specific multi-harmonic content maintains its coherence over long spatio-temporal scales. At select frequencies, these invariant waveforms circumvent the production of higher harmonics and can also engage in a slow scale energy exchange with internally-resonant modes. The stability of plane waves in nonlinear periodic media will also be detailed, identifying amplitude and direction-dependence which may lead-to novel wave-based encryption strategies. Lastly, non-reciprocity as enabled by lattices with nonlinearity, internal hierarchy, and asymmetry will be discussed. Without any influence from an external bias or energy source, such lattices prevent a source and receiver from exchanging the same energy when their locations swap, paving the way for the shielding and rectification of elastic and acoustic waves.
BioMatthew Fronk is an assistant professor in the Department of Physics at the United States Naval Academy. His current research interests center around nonlinear wave propagation, periodic media, and acoustic metamaterials. In May 2020, he received a Doctor of Philosophy in mechanical engineering from the Georgia Institute of Technology under the advisement of Professor Michael Leamy. He also holds Bachelor of Science and Master of Science degrees in mechanical engineering from the Georgia Institute of Technology. In addition to his primary research, he has recently collaborated with Sandia National Laboratories in a project characterizing the nonlinear dynamics of bolted assemblies.