SUMMARY

Nonlinear mechanics continue to intrigue researchers in a wide range of applications, including wave propagation and friction contact problems. Nonlinearities in periodic structures enforce unique dynamic behavior such as non-reciprocity, negative refractive indexes, and amplitude dependent characteristics (e.g. group velocity, bandgap tunability). Similarly, nonlinear friction forces developed during contact are predicted to enforce a memory effect, where the material displacement and strain depend on the loading history. This work investigates a novel filtering approach for acoustic signals in periodic media that is dependent on the signal amplitude. Two unique hierarchical unit cells are presented resulting in high-pass as well as low-pass amplitude dependent filtering of acoustics signals. The second part of this work transitions focus to experimentally verifying the friction-induced memory effect in quasistatic elastomeric rollers under normal and tangential loading by utilizing digital image correlation (DIC). DIC allows for experimental generation of displacement and strain fields across large sections of the roller sidewall and contact interface by monitoring the contact of a roller along two planes. This work also includes improving the current DIC software, Ncorr, enabling its use for full dynamic rolling tests to investigate the memory effect and strain field evolution in the contact region during multiple cycles of rolling. Amplitude-dependent filtering may prove useful for sensors to filter out low-amplitude background noise or protect delicate circuitry from potentially harmful signals. Understanding frictional contact may also prove valuable in roller design and shed light onto rolling instabilities and their effects on global roller mechanics.