Selective wave transmission in strongly nonlinear disordered granular chains

Chains of 1000 granules in mutual contact, without precompression, and with random radii that follow a normal distribution are studied numerically. The standard deviation σ controls the disorder level. The chains are subject to (i) a striker impact and (ii) an actuator that imposes band-limited white-noise motion at one boundary. For striker excitation, a critical σ_{c}≈0.1 separates weak and strong disorder, and the propagation of the median peak momentum exhibits two regimes: (i) for short distances, a σ-dependent decay, and (ii), at long distances, a universal power law ∝k^{-0.83}, where k denotes the granule position. For actuator excitation, the transfer function reveals a transition from a low-pass response, at σ<0.3, to broadband mechanical noise suppression for higher disorder levels. The narrow passbands at a few hundred hertz that we observe are consistent with the preferred transmission bands in soils reported experimentally in the literature. Thus, simple disordered granular chains provide a minimal model to investigate selective transmission or attenuation in random granular media. The findings are relevant to near-surface site characterization, shallow buried-object detection, and related geophysical applications.