  The geometric of Berry phase concept, traditionally rooted in quantum
mechanics, has been found to be increasingly significant in classical
mechanics, particularly for understanding the dynamics of linear and nonlinear
systems. In this study, we demonstrate the controlled accumulation of the Berry
phase in a classical system using a two-level time-dependent elastic bit,
analogous to a quantum bit, within a nonlinear environment generated by a
two-granular network. The nonlinearity of the granular beads is modulated
through the frequency and amplitude of external harmonic excitation, along with
static preloading. By employing the orthonormal basis of the nonlinear
responses and mapping the displacement coefficients in Bloch states, we reveal
how time influences the manipulation of the elastic bit and its states. Our
analytical and experimental investigations uncover the Berry phase's role in
exposing the various topological characteristics of the classical granular
network. This research establishes a crucial link between classical and quantum
realms via the Berry phase of an elastic bit, with significant implications for
decoherence-free and robust data transfer and information processing.
