Dynamics of Time-Varying and Nonlinear Phononic Lattices

Citation

Kim, Brian Lee Kiwon (2023) Dynamics of Time-Varying and Nonlinear Phononic Lattices. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/n7mv-eg68. https://resolver.caltech.edu/CaltechTHESIS:05042023-201010843

Abstract

The control of waves and vibrations in materials and structures underpins both the most common and the most advanced technologies. Spatially structured and periodic media have been widely studied and applied to signal processing, vibration mitigation, focusing, and other applications beyond the capabilities of bulk materials. Recently, interest has grown in the effects of temporal variation of material and medium properties on wave propagation. Temporal variations serve as an additional dimension for the design and structure of materials, further expanding potential functionalities and performance. Many of the concepts of waves in time-varying media have been developed in photonics and other electromagnetic systems, but the same fundamental dynamics govern acoustic and elastic systems, which provide alternative opportunities for implementation and new applications of time-varying media. In this thesis, we employ a one-dimensional phononic lattice composed of repelling ring magnets with electromagnetic coils that act as time-dependent grounding stiffness. The lattice provides an excellent platform for studying waves in time-varying media, with implementation and modeling of time-variation of elastic properties made simple by its discreteness. In addition, the repelling force between the magnets allows not only for the study of the linear dynamics of time-varying systems for small displacements but also for the exploration of the interaction between time-variation and nonlinear effects. We first present novel demonstrations of two types of time-varying wave phenomena in acoustic or elastic systems. First, the measurement of the propagation of waves across a temporal discontinuity in elastic properties demonstrates the temporal analog to refraction across a spatial boundary. Second, the experimental reconstruction of the dispersion relation of a time-periodic periodic medium shows the opening of wavenumber band gaps. We then characterize the dynamic stability of the time-periodic lattice and consider the role of nonlinearity. Finally, we investigate the possible existence of wavenumber gap breathers, temporally localized solutions of the discrete, nonlinear system.

Thesis Files