Modeling and simulations of a nonlinear granular metamaterial: application to geometric phase-based mass sensing

Dynamical simulations of an externally harmonically driven model granular metamaterial composed of four linearly and nonlinearly coupled granules show that the nonlinear normal mode can be expressed in a linear normal mode orthonormal basis with time dependent complex coefficients. These coefficients form the components of a state vector that spans a 2(2) dimensional Hilbert space parametrically with time. Local pi jumps in the phase of these components occurring periodically are indicative of topological features in the manifold spanned by the geometric phase of the vibrational state of the metamaterial. We demonstrate that these topological features can be exploited to realize high sensitivity mass sensor. The effect of dissipation on sensitivity is also reported. Nonlinear granular metamaterials with very low dissipation could serve as mass sensors with considerable sensitivity to small mass changes via large changes in geometric phase.