Theoretical and experimental investigation on nonlinear dynamic of grain-beam system

We experimentally investigated the system of a simply supported beam immersed in a granular medium, which displays jump and new peaks in its amplitude-frequency curve under harmonic excitation. The relationship between the macroscopic nonlinear response and microscopic state of the granular medium was studied using the discrete element method. Using the dynamic modulus and vibrational density of states as indicators, we show that the granular medium changes from a solid-like to liquid-like state when the frequency increases to approach the jumping point. Considering the similarity between this system and acoustic metamaterial beams, an equivalent theoretical model was established for the former. Numerical results of the theoretical model were consistent with the experimental ones. It was revealed that the new peak and jump phenomena were caused by negative equivalent mass, negative equivalent stiffness of the granular medium and abrupt change in the additional stiffness cause by the jamming transition. This theoretical model is useful for studying the nonlinear dynamic characteristics of this coupled grain-beam system.