Dynamics of nonlinear and localized vibrational modes in 2D mechanical networks

Amorphous materials show surprising and potentially useful acoustic properties at low frequencies. A notable example are the low-temperature acoustic properties of dielectric glasses, where quasi-localized, resonant states absorb energy and form memories of past excitations. To probe these phenomena at low-frequencies and over long times, we study the vibrational modes of quasi-2D networks of coupled oscillators using parallelized, GPU computing. We vary the degree of pre-stretching (tension) in the network, disorder in site masses, and disorder in the network connectivity. Even with a crystalline network structure, disorder in the site masses gives rise to low-frequency, quasi-localized modes, similar to those studied in glasses and jammed systems. The anharmonic properties of these modes become exceedingly important over thousands of cycles of oscillations. In addition, in order to realize some of these properties in the laboratory, we have developed a mechanical metamaterial fabricated from a silicon nitride layer on a silicon wafer using standard photolithography. The degree and type of disorder can be tuned prior to fabrication, leading to a high-Q, constituent-level visualization of vibrational modes in disordered materials.