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 in 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 amplitude filtering effects of each nonlinear unit cell is first predicted using a series of numerical simulations, then supported using an analytical nonlinear harmonic balance analysis, and verified using a series of experimental tests using fabricated lattices and nonlinear unit cells. The proposed work focuses on experimentally verifying the friction-induced memory effect in quasistatic pre-loaded elastomeric rollers by utilizing digital image correlation (DIC). DIC allows for rapid generation of displacement and strain fields across large sections of the roller sidewall and interface. The proposed 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 during 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.