This project aimed at exploiting the nonlinearity, damping, material/geometrical periodicity, and topological phenomena in mechanical lattice structures for simultaneous fluid-flow-induced vibration attenuation and energy harvesting purposes. The main focus was on metamaterials and phononic-like structures in their mechanical setup having periodic architecture such that they possess unique wave propagation and topological properties. A mathematical model based on cubic nonlinear stiffness and fractional-order damping were suggested to study wave propagation in a periodic lattice chain. The proposed approach enabled a study of the effects of nonlinearity and fractional damping on dispersion characteristics and band gaps capable of stopping the waves at certain frequency ranges.
Exotic topological phenomena can be also found in mechanical metamaterials inducing localized edge/interface states that are robust to defects and disorders in the lattice. In this project, we proposed one such phononic-like lattice based on elastically coupled beam elements having multiple existing interface modes. Properties of conventional lattices were extended through the application of inerter elements. The project develops computational analytical models to better understand the behavior and tunability of topological properties of such enhanced mechanical lattices. A step forward in this direction was the introduction of periodic and quasi-periodic inerter-based locally resonant lattices with emerging interface modes in the sub-wavelength range. The inerter elements were shown to be capable of tuning interface modes frequencies without changing their main topological properties. The effect of viscous damping was examined showing a significant effect on the amplitude of the localized interface mode. Moreover, uncertainty quantification of inerter-based locally resonant quasi-periodic lattices demonstrated the existence of multiple robust edge modes that can be utilized for energy harvesting.
Remarkable wave propagation properties were discovered in the suggested novel design of two-dimensional lattices with curved beam elements. The Bloch wave analysis based on equivalent unit cell architecture revealed the newly emerged band gaps for increasing curvature angle when compared to the conventional hexagonal- and auxetic-like lattices. Directional wave propagation was also identified showing the high potential for the appearance of the phenomena such as lensing and wave beaming.
